American Institute of Physics: Journal of Mathematical Physics: Table of Contents
Table of Contents for Journal of Mathematical Physics. List of articles from both the latest and ahead of print issues.
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American Institute of Physics: Journal of Mathematical Physics: Table of Contents
American Institute of Physics
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Journal of Mathematical Physics
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On quantitative hypocoercivity estimates based on Harristype theorems
https://aip.scitation.org/doi/10.1063/5.0089698?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/64/3">Volume 64, Issue 3</a>, March 2023. <br/>This Review concerns recent results on the quantitative study of convergence toward the stationary state for spatially inhomogeneous kinetic equations. We focus on analytical results obtained by means of certain probabilistic techniques from the ergodic theory of Markov processes. These techniques are sometimes referred to as Harristype theorems. They provide constructive proofs for convergence results in the L1 (or total variation) setting for a large class of initial data. The convergence rates can be made explicit (for both geometric and subgeometric rates) by tracking the constants appearing in the hypotheses. Harristype theorems are particularly welladapted for equations exhibiting nonexplicit and nonequilibrium steady states since they do not require prior information on the existence of stationary states. This allows for significant improvements of some alreadyexisting results by relaxing assumptions and providing explicit convergence rates. We aim to present Harristype theorems, providing a guideline on how to apply these techniques to kinetic equations at hand. We discuss recent quantitative results obtained for kinetic equations in gas theory and mathematical biology, giving some perspectives on potential extensions to nonlinear equations.
Journal of Mathematical Physics, Volume 64, Issue 3, March 2023. <br/>This Review concerns recent results on the quantitative study of convergence toward the stationary state for spatially inhomogeneous kinetic equations. We focus on analytical results obtained by means of certain probabilistic techniques from the ergodic theory of Markov processes. These techniques are sometimes referred to as Harristype theorems. They provide constructive proofs for convergence results in the L1 (or total variation) setting for a large class of initial data. The convergence rates can be made explicit (for both geometric and subgeometric rates) by tracking the constants appearing in the hypotheses. Harristype theorems are particularly welladapted for equations exhibiting nonexplicit and nonequilibrium steady states since they do not require prior information on the existence of stationary states. This allows for significant improvements of some alreadyexisting results by relaxing assumptions and providing explicit convergence rates. We aim to present Harristype theorems, providing a guideline on how to apply these techniques to kinetic equations at hand. We discuss recent quantitative results obtained for kinetic equations in gas theory and mathematical biology, giving some perspectives on potential extensions to nonlinear equations.
On quantitative hypocoercivity estimates based on Harristype theorems
10.1063/5.0089698
Journal of Mathematical Physics
20230320T11:14:13Z
© 2023 Author(s).
Havva Yoldaş

Incompressible limit of isentropic magnetohydrodynamic equations with illprepared data in bounded domains
https://aip.scitation.org/doi/10.1063/5.0140349?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/64/3">Volume 64, Issue 3</a>, March 2023. <br/>This paper rigorously justifies the incompressible limit of strong solutions to isentropic compressible magnetohydrodynamic equations with illprepared initial data in a threedimensional bounded domain as the Mach number goes to zero. In both cases of viscous and inviscid magnetic fields, we establish a new energy functional with weight to obtain uniform estimates for strong solutions with respect to the Mach number. Then, we prove the weak convergence of a velocity and the strong convergence of a magnetic field and the divergencefree component of a velocity field, which yields the corresponding incompressible limit.
Journal of Mathematical Physics, Volume 64, Issue 3, March 2023. <br/>This paper rigorously justifies the incompressible limit of strong solutions to isentropic compressible magnetohydrodynamic equations with illprepared initial data in a threedimensional bounded domain as the Mach number goes to zero. In both cases of viscous and inviscid magnetic fields, we establish a new energy functional with weight to obtain uniform estimates for strong solutions with respect to the Mach number. Then, we prove the weak convergence of a velocity and the strong convergence of a magnetic field and the divergencefree component of a velocity field, which yields the corresponding incompressible limit.
Incompressible limit of isentropic magnetohydrodynamic equations with illprepared data in bounded domains
10.1063/5.0140349
Journal of Mathematical Physics
20230307T11:10:05Z
© 2023 Author(s).
Xiaoyu Gu
Yaobin Ou
Lu Yang

Bistritzer–MacDonald dynamics in twisted bilayer graphene
https://aip.scitation.org/doi/10.1063/5.0115771?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/64/3">Volume 64, Issue 3</a>, March 2023. <br/>The Bistritzer–MacDonald (BM) model, introduced by Bistritzer and MacDonald [Proc. Natl. Acad. Sci. U. S. A. 108, 12233–12237 (2011); arXiv:1009.4203], attempts to capture electronic properties of twisted bilayer graphene (TBG), even at incommensurate twist angles, by using an effective periodic model over the bilayer moiré pattern. Starting from a tightbinding model, we identify a regime where the BM model emerges as the effective dynamics for electrons modeled as wavepackets spectrally concentrated at monolayer Dirac points up to error that can be rigorously estimated. Using measured values of relevant physical constants, we argue that this regime is realized in TBG at the first “magic” angle.
Journal of Mathematical Physics, Volume 64, Issue 3, March 2023. <br/>The Bistritzer–MacDonald (BM) model, introduced by Bistritzer and MacDonald [Proc. Natl. Acad. Sci. U. S. A. 108, 12233–12237 (2011); arXiv:1009.4203], attempts to capture electronic properties of twisted bilayer graphene (TBG), even at incommensurate twist angles, by using an effective periodic model over the bilayer moiré pattern. Starting from a tightbinding model, we identify a regime where the BM model emerges as the effective dynamics for electrons modeled as wavepackets spectrally concentrated at monolayer Dirac points up to error that can be rigorously estimated. Using measured values of relevant physical constants, we argue that this regime is realized in TBG at the first “magic” angle.
Bistritzer–MacDonald dynamics in twisted bilayer graphene
10.1063/5.0115771
Journal of Mathematical Physics
20230313T11:20:37Z
© 2023 Author(s).
Alexander B. Watson
Tianyu Kong
Allan H. MacDonald
Mitchell Luskin

Existence results for fractional Kirchhoff problems with magnetic field and supercritical growth
https://aip.scitation.org/doi/10.1063/5.0127185?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/64/3">Volume 64, Issue 3</a>, March 2023. <br/>In this paper, we investigate a class of fractional Kirchhoff problems with a magnetic field and supercritical growth. By employing a truncation argument and Moser iterative method, we obtain the existence of nontrivial solutions. Our results are new and supplement the previous ones in the literature.
Journal of Mathematical Physics, Volume 64, Issue 3, March 2023. <br/>In this paper, we investigate a class of fractional Kirchhoff problems with a magnetic field and supercritical growth. By employing a truncation argument and Moser iterative method, we obtain the existence of nontrivial solutions. Our results are new and supplement the previous ones in the literature.
Existence results for fractional Kirchhoff problems with magnetic field and supercritical growth
10.1063/5.0127185
Journal of Mathematical Physics
20230313T11:20:38Z
© 2023 Author(s).
Liu Gao
Zhong Tan

Global solutions and exponential time decay rates to the Navier–Stokes–Vlasov–Fokker–Planck system in low regularity space
https://aip.scitation.org/doi/10.1063/5.0132586?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/64/3">Volume 64, Issue 3</a>, March 2023. <br/>In this paper, we show that the mild solutions to the Navier–Stokes–Vlasov–Fokker–Planck system exist globally in time near a global Maxwellian, provided that we take smallamplitude initial data in the function space [math]. As a product, we also get the exponential time decay rates for the solutions. Our analysis relies on the refined energy estimates and the low regularity function space [math] introduced by the work in Duan et al. [Commun. Pure Appl. Math. 74(5), 932–1020 (2021)].
Journal of Mathematical Physics, Volume 64, Issue 3, March 2023. <br/>In this paper, we show that the mild solutions to the Navier–Stokes–Vlasov–Fokker–Planck system exist globally in time near a global Maxwellian, provided that we take smallamplitude initial data in the function space [math]. As a product, we also get the exponential time decay rates for the solutions. Our analysis relies on the refined energy estimates and the low regularity function space [math] introduced by the work in Duan et al. [Commun. Pure Appl. Math. 74(5), 932–1020 (2021)].
Global solutions and exponential time decay rates to the Navier–Stokes–Vlasov–Fokker–Planck system in low regularity space
10.1063/5.0132586
Journal of Mathematical Physics
20230316T10:22:50Z
© 2023 Author(s).
Lihua Tan
Yingzhe Fan

Gradient estimates for the insulated conductivity problem: The case of mconvex inclusions
https://aip.scitation.org/doi/10.1063/5.0100907?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/64/3">Volume 64, Issue 3</a>, March 2023. <br/>We consider an insulated conductivity model with two neighboring inclusions of mconvex shapes in [math] when m ≥ 2 and d ≥ 3. We establish pointwise gradient estimates for the insulated conductivity problem and capture the gradient blowup rate of order ɛ−1/m+β with [math] as the distance ɛ between these two insulators tends to zero. In particular, the optimality of the blowup rate is also demonstrated for a class of axisymmetric mconvex inclusions.
Journal of Mathematical Physics, Volume 64, Issue 3, March 2023. <br/>We consider an insulated conductivity model with two neighboring inclusions of mconvex shapes in [math] when m ≥ 2 and d ≥ 3. We establish pointwise gradient estimates for the insulated conductivity problem and capture the gradient blowup rate of order ɛ−1/m+β with [math] as the distance ɛ between these two insulators tends to zero. In particular, the optimality of the blowup rate is also demonstrated for a class of axisymmetric mconvex inclusions.
Gradient estimates for the insulated conductivity problem: The case of mconvex inclusions
10.1063/5.0100907
Journal of Mathematical Physics
20230317T10:30:40Z
© 2023 Author(s).
Zhiwen Zhao

On the strong solution of 3D nonisothermal Navier–Stokes–Cahn–Hilliard equations
https://aip.scitation.org/doi/10.1063/5.0099260?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/64/3">Volume 64, Issue 3</a>, March 2023. <br/>In this paper, we consider the global existence of strong solutions of a thermodynamically consistent diffuse interface model describing twophase flows of incompressible fluids in a nonisothermal setting. In the diffuse interface model, the evolution of the velocity u is ruled by the Navier–Stokes system, while the order parameter φ representing the difference of the fluid concentration of the two fluids is assumed to satisfy a convective Cahn–Hilliard equation. The effects of the temperature are prescribed by a suitable form of heat equation. By using a refined pure energy method, we prove the existence of the global strong solution by assuming that [math] is sufficiently small, and higher order derivatives can be arbitrarily large.
Journal of Mathematical Physics, Volume 64, Issue 3, March 2023. <br/>In this paper, we consider the global existence of strong solutions of a thermodynamically consistent diffuse interface model describing twophase flows of incompressible fluids in a nonisothermal setting. In the diffuse interface model, the evolution of the velocity u is ruled by the Navier–Stokes system, while the order parameter φ representing the difference of the fluid concentration of the two fluids is assumed to satisfy a convective Cahn–Hilliard equation. The effects of the temperature are prescribed by a suitable form of heat equation. By using a refined pure energy method, we prove the existence of the global strong solution by assuming that [math] is sufficiently small, and higher order derivatives can be arbitrarily large.
On the strong solution of 3D nonisothermal Navier–Stokes–Cahn–Hilliard equations
10.1063/5.0099260
Journal of Mathematical Physics
20230320T11:14:13Z
© 2023 Author(s).
Xiaopeng Zhao

Orbital stability of periodic peakons for a new higherorder μCamassa–Holm equation
https://aip.scitation.org/doi/10.1063/5.0132297?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/64/3">Volume 64, Issue 3</a>, March 2023. <br/>The consideration here is a higherorder μCamassa–Holm equation, which is a higherorder extension of the μCamassa–Holm equation and retains some properties of the μCamassa–Holm equation and the modified μCamassa–Holm equation. By utilizing the inequalities with the maximum and minimum of solutions related to the first three conservation laws, we establish that the periodic peakons of this equation are orbitally stable under small perturbations in the energy space.
Journal of Mathematical Physics, Volume 64, Issue 3, March 2023. <br/>The consideration here is a higherorder μCamassa–Holm equation, which is a higherorder extension of the μCamassa–Holm equation and retains some properties of the μCamassa–Holm equation and the modified μCamassa–Holm equation. By utilizing the inequalities with the maximum and minimum of solutions related to the first three conservation laws, we establish that the periodic peakons of this equation are orbitally stable under small perturbations in the energy space.
Orbital stability of periodic peakons for a new higherorder μCamassa–Holm equation
10.1063/5.0132297
Journal of Mathematical Physics
20230324T10:09:40Z
© 2023 Author(s).
Gezi Chong
Ying Fu

Topological charge conservation for continuous insulators
https://aip.scitation.org/doi/10.1063/5.0102607?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/64/3">Volume 64, Issue 3</a>, March 2023. <br/>This paper proposes a classification of elliptic (pseudo)differential Hamiltonians describing topological insulators and superconductors in Euclidean space by means of domain walls. Augmenting a given Hamiltonian by one or several domain walls results in confinement that naturally yields a Fredholm operator, whose index is taken as the topological charge of the system. The index is computed explicitly in terms of the symbol of the Hamiltonian by a Fedosov–Hörmander formula, which implements in Euclidean spaces an Atiyah–Singer index theorem. For Hamiltonians admitting an appropriate decomposition in a Clifford algebra, the index is given by the easily computable topological degree of a naturally associated map. A practically important property of topological insulators is the asymmetric transport observed along onedimensional lines generated by the domain walls. This asymmetry is captured by the edge conductivity, a physical observable of the system. We prove that the edge conductivity is quantized and given by the index of a second Fredholm operator of the Toeplitz type. We also prove topological charge conservation by stating that the two aforementioned indices agree. This result generalizes to higher dimensions and higherorder topological insulators, the bulkedge correspondence of twodimensional materials. We apply this procedure to evaluate the topological charge of several classical examples of (standard and higherorder) topological insulators and superconductors in one, two, and three spatial dimensions.
Journal of Mathematical Physics, Volume 64, Issue 3, March 2023. <br/>This paper proposes a classification of elliptic (pseudo)differential Hamiltonians describing topological insulators and superconductors in Euclidean space by means of domain walls. Augmenting a given Hamiltonian by one or several domain walls results in confinement that naturally yields a Fredholm operator, whose index is taken as the topological charge of the system. The index is computed explicitly in terms of the symbol of the Hamiltonian by a Fedosov–Hörmander formula, which implements in Euclidean spaces an Atiyah–Singer index theorem. For Hamiltonians admitting an appropriate decomposition in a Clifford algebra, the index is given by the easily computable topological degree of a naturally associated map. A practically important property of topological insulators is the asymmetric transport observed along onedimensional lines generated by the domain walls. This asymmetry is captured by the edge conductivity, a physical observable of the system. We prove that the edge conductivity is quantized and given by the index of a second Fredholm operator of the Toeplitz type. We also prove topological charge conservation by stating that the two aforementioned indices agree. This result generalizes to higher dimensions and higherorder topological insulators, the bulkedge correspondence of twodimensional materials. We apply this procedure to evaluate the topological charge of several classical examples of (standard and higherorder) topological insulators and superconductors in one, two, and three spatial dimensions.
Topological charge conservation for continuous insulators
10.1063/5.0102607
Journal of Mathematical Physics
20230324T10:09:42Z
© 2023 Author(s).
Guillaume Bal

Local uniqueness of multipeak solutions to a class of Schrödinger equations with competing potential
https://aip.scitation.org/doi/10.1063/5.0134220?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/64/3">Volume 64, Issue 3</a>, March 2023. <br/>In this paper, we consider the nonlinear Schrödinger equations. Let [math]. Under some conditions on [math], we show the local uniqueness of positive multipeak solutions concentrating near k(k ≥ 2) distinct nondegenerate critical points of [math] by using the local Pohozaev identity. We generalize Cao–Li–Luo’s results to the competing potential cases and show how these two potentials impact the uniqueness of concentrated solutions.
Journal of Mathematical Physics, Volume 64, Issue 3, March 2023. <br/>In this paper, we consider the nonlinear Schrödinger equations. Let [math]. Under some conditions on [math], we show the local uniqueness of positive multipeak solutions concentrating near k(k ≥ 2) distinct nondegenerate critical points of [math] by using the local Pohozaev identity. We generalize Cao–Li–Luo’s results to the competing potential cases and show how these two potentials impact the uniqueness of concentrated solutions.
Local uniqueness of multipeak solutions to a class of Schrödinger equations with competing potential
10.1063/5.0134220
Journal of Mathematical Physics
20230327T10:06:08Z
© 2023 Author(s).
Yahui Niu
Shuying Tian
Pingping Yang

Regularity of weak solutions for the stationary Ericksen–Leslie and MHD systems
https://aip.scitation.org/doi/10.1063/5.0133975?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/64/3">Volume 64, Issue 3</a>, March 2023. <br/>We consider two elliptic coupled systems of relevance in the fluid dynamics. These systems are posed on the whole space [math], and they consider the action of external forces. The first system deals with the simplified Ericksen–Leslie (SEL) system, which describes the dynamics of liquid crystal flows. The second system is the timeindependent magnetohydrodynamic (MHD) equations. For the SEL system, we obtain a new criterion to improve the regularity of weak solutions, provided that they belong to some homogeneous Morrey space. As a biproduct, we also obtain some new regularity criterion for the stationary Navier–Stokes equations and for a nonlinear harmonic map flow. This new regularity criterion also holds true for the MHD equations. Furthermore, for this last system, we are able to use the Gevrey class to prove that all finite energy weak solutions are analytic functions, provided that the external forces belong to some Gevrey class.
Journal of Mathematical Physics, Volume 64, Issue 3, March 2023. <br/>We consider two elliptic coupled systems of relevance in the fluid dynamics. These systems are posed on the whole space [math], and they consider the action of external forces. The first system deals with the simplified Ericksen–Leslie (SEL) system, which describes the dynamics of liquid crystal flows. The second system is the timeindependent magnetohydrodynamic (MHD) equations. For the SEL system, we obtain a new criterion to improve the regularity of weak solutions, provided that they belong to some homogeneous Morrey space. As a biproduct, we also obtain some new regularity criterion for the stationary Navier–Stokes equations and for a nonlinear harmonic map flow. This new regularity criterion also holds true for the MHD equations. Furthermore, for this last system, we are able to use the Gevrey class to prove that all finite energy weak solutions are analytic functions, provided that the external forces belong to some Gevrey class.
Regularity of weak solutions for the stationary Ericksen–Leslie and MHD systems
10.1063/5.0133975
Journal of Mathematical Physics
20230327T10:06:09Z
© 2023 Author(s).
Oscar Jarrín

kth singular locus moduli algebras of singularities and their derivation Lie algebras
https://aip.scitation.org/doi/10.1063/5.0121485?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/64/3">Volume 64, Issue 3</a>, March 2023. <br/>In this paper, we introduce a series of new invariants for singularities. A new conjecture about the nonexistence of negative weight derivations of the new kth singular locus moduli algebras for weighted homogeneous isolated hypersurface singularities is proposed. We verify this conjecture in some cases.
Journal of Mathematical Physics, Volume 64, Issue 3, March 2023. <br/>In this paper, we introduce a series of new invariants for singularities. A new conjecture about the nonexistence of negative weight derivations of the new kth singular locus moduli algebras for weighted homogeneous isolated hypersurface singularities is proposed. We verify this conjecture in some cases.
kth singular locus moduli algebras of singularities and their derivation Lie algebras
10.1063/5.0121485
Journal of Mathematical Physics
20230317T10:30:40Z
© 2023 Author(s).
Guorui Ma
Stephen S.T. Yau
Huaiqing Zuo

RNA foldings, oriented stuck knots, and state sum invariants
https://aip.scitation.org/doi/10.1063/5.0140652?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/64/3">Volume 64, Issue 3</a>, March 2023. <br/>We extend the quandle cocycle invariant to the context of stuck links. More precisely, we define an invariant of stuck links by assigning Boltzmann weights at both classical and stuck crossings. As an application, we define a singlevariable and a twovariable polynomial invariant of stuck links. Furthermore, we define a singlevariable and twovariable polynomial invariant of arc diagrams of RNA foldings. We provide explicit computations of the new invariants.
Journal of Mathematical Physics, Volume 64, Issue 3, March 2023. <br/>We extend the quandle cocycle invariant to the context of stuck links. More precisely, we define an invariant of stuck links by assigning Boltzmann weights at both classical and stuck crossings. As an application, we define a singlevariable and a twovariable polynomial invariant of stuck links. Furthermore, we define a singlevariable and twovariable polynomial invariant of arc diagrams of RNA foldings. We provide explicit computations of the new invariants.
RNA foldings, oriented stuck knots, and state sum invariants
10.1063/5.0140652
Journal of Mathematical Physics
20230317T10:30:39Z
© 2023 Author(s).
Jose Ceniceros
Mohamed Elhamdadi
Brendan Magill
Gabriana Rosario

About integervalued variants of the theta and 6j symbols
https://aip.scitation.org/doi/10.1063/5.0131150?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/64/3">Volume 64, Issue 3</a>, March 2023. <br/>This article contains essentially a rewriting of several properties of two wellknown quantities, the socalled theta symbol (or triangular symbol), which is rational, and the 6j symbol, which is usually irrational, in terms of two related integervalued functions called gon and tet. Existence of these related integervalued avatars, sharing most essential properties with their more popular partners, although a known fact, is often overlooked. The properties of gon and tet are easier to obtain, or to formulate, than those of the corresponding theta and 6j symbols in both classical and quantum situations. Their evaluation is also simpler (this paper displays a number of explicit formulas and evaluation procedures that may speed up some computer programs). These two integervalued functions are unusual in that their properties do not appear to be often discussed in the literature, but their features reflect those of related realvalued functions discussed in many places. Some of the properties that we shall discuss seem, however, to be new, in particular several relations between the function gon and inverse Hilbert matrices.
Journal of Mathematical Physics, Volume 64, Issue 3, March 2023. <br/>This article contains essentially a rewriting of several properties of two wellknown quantities, the socalled theta symbol (or triangular symbol), which is rational, and the 6j symbol, which is usually irrational, in terms of two related integervalued functions called gon and tet. Existence of these related integervalued avatars, sharing most essential properties with their more popular partners, although a known fact, is often overlooked. The properties of gon and tet are easier to obtain, or to formulate, than those of the corresponding theta and 6j symbols in both classical and quantum situations. Their evaluation is also simpler (this paper displays a number of explicit formulas and evaluation procedures that may speed up some computer programs). These two integervalued functions are unusual in that their properties do not appear to be often discussed in the literature, but their features reflect those of related realvalued functions discussed in many places. Some of the properties that we shall discuss seem, however, to be new, in particular several relations between the function gon and inverse Hilbert matrices.
About integervalued variants of the theta and 6j symbols
10.1063/5.0131150
Journal of Mathematical Physics
20230321T11:49:50Z
© 2023 Author(s).
Robert Coquereaux

The asymmetric valencebondsolid states in quantum spin chains: The difference between odd and even spins
https://aip.scitation.org/doi/10.1063/5.0123743?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/64/3">Volume 64, Issue 3</a>, March 2023. <br/>The qualitative difference in lowenergy properties of spin S quantum antiferromagnetic chains with integer S and halfoddinteger S discovered by Haldane [F. D. M. Haldane, arXiv:1612.00076 (1981); Phys. Lett. A 93, 464–468 (1983); Phys. Rev. Lett. 50, 1153–1156 (1983)] and Tasaki [Tasaki, Graduate Texts in Physics (Springer, 2020)] can be intuitively understood in terms of the valencebond picture proposed by Affleck et al. [I. Affleck, Phys. Rev. Lett. 59, 799 (1987); Commun. Math. Phys. 115, 477–528 (1988)]. Here, we develop a similarly intuitive diagrammatic explanation of the qualitative difference between chains with odd S and even S, which is at the heart of the theory of symmetryprotected topological (SPT) phases. (There is a 24 min video in which the essence of the present work is discussed: https://youtu.be/URsf9e_PLlc.) More precisely, we define oneparameter families of states, which we call the asymmetric valencebond solid (VBS) states, that continuously interpolate between the Affleck–Kennedy–Lieb–Tasaki (AKLT) state and the trivial zero state in quantum spin chains with S = 1 and 2. The asymmetric VBS state is obtained by systematically modifying the AKLT state. It always has exponentially decaying truncated correlation functions and is a unique gapped ground state of a shortranged Hamiltonian. We also observe that the asymmetric VBS state possesses the timereversal, the [math], and the bondcentered inversion symmetries for S = 2 but not for S = 1. This is consistent with the known fact that the AKLT model belongs to the trivial SPT phase if S = 2 and to a nontrivial SPT phase if S = 1. Although such interpolating families of disordered states were already known, our construction is unified and is based on a simple physical picture. It also extends to spin chains with general integer S and provides us with an intuitive explanation of the essential difference between models with odd and even spins.
Journal of Mathematical Physics, Volume 64, Issue 3, March 2023. <br/>The qualitative difference in lowenergy properties of spin S quantum antiferromagnetic chains with integer S and halfoddinteger S discovered by Haldane [F. D. M. Haldane, arXiv:1612.00076 (1981); Phys. Lett. A 93, 464–468 (1983); Phys. Rev. Lett. 50, 1153–1156 (1983)] and Tasaki [Tasaki, Graduate Texts in Physics (Springer, 2020)] can be intuitively understood in terms of the valencebond picture proposed by Affleck et al. [I. Affleck, Phys. Rev. Lett. 59, 799 (1987); Commun. Math. Phys. 115, 477–528 (1988)]. Here, we develop a similarly intuitive diagrammatic explanation of the qualitative difference between chains with odd S and even S, which is at the heart of the theory of symmetryprotected topological (SPT) phases. (There is a 24 min video in which the essence of the present work is discussed: https://youtu.be/URsf9e_PLlc.) More precisely, we define oneparameter families of states, which we call the asymmetric valencebond solid (VBS) states, that continuously interpolate between the Affleck–Kennedy–Lieb–Tasaki (AKLT) state and the trivial zero state in quantum spin chains with S = 1 and 2. The asymmetric VBS state is obtained by systematically modifying the AKLT state. It always has exponentially decaying truncated correlation functions and is a unique gapped ground state of a shortranged Hamiltonian. We also observe that the asymmetric VBS state possesses the timereversal, the [math], and the bondcentered inversion symmetries for S = 2 but not for S = 1. This is consistent with the known fact that the AKLT model belongs to the trivial SPT phase if S = 2 and to a nontrivial SPT phase if S = 1. Although such interpolating families of disordered states were already known, our construction is unified and is based on a simple physical picture. It also extends to spin chains with general integer S and provides us with an intuitive explanation of the essential difference between models with odd and even spins.
The asymmetric valencebondsolid states in quantum spin chains: The difference between odd and even spins
10.1063/5.0123743
Journal of Mathematical Physics
20230320T11:14:14Z
© 2023 Author(s).
Daisuke Maekawa
Hal Tasaki

Bragg spectrum, Ktheory, and gap labeling of aperiodic solids
https://aip.scitation.org/doi/10.1063/5.0132332?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/64/3">Volume 64, Issue 3</a>, March 2023. <br/>The diffraction spectrum of an aperiodic solid is related to the group of eigenvalues of the dynamical system associated with the solid. Those eigenvalues with continuous eigenfunctions constitute the topological Bragg spectrum. We relate the topological Bragg spectrum to topological invariants (Chern numbers) of the solid and to the gaplabeling group, which is the group of possible gap labels for the spectrum of a Schrödinger operator describing the electronic motion in the solid.
Journal of Mathematical Physics, Volume 64, Issue 3, March 2023. <br/>The diffraction spectrum of an aperiodic solid is related to the group of eigenvalues of the dynamical system associated with the solid. Those eigenvalues with continuous eigenfunctions constitute the topological Bragg spectrum. We relate the topological Bragg spectrum to topological invariants (Chern numbers) of the solid and to the gaplabeling group, which is the group of possible gap labels for the spectrum of a Schrödinger operator describing the electronic motion in the solid.
Bragg spectrum, Ktheory, and gap labeling of aperiodic solids
10.1063/5.0132332
Journal of Mathematical Physics
20230322T11:23:40Z
© 2023 Author(s).
Johannes Kellendonk

Gauge invariance and anomalies in condensed matter physics
https://aip.scitation.org/doi/10.1063/5.0135142?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/64/3">Volume 64, Issue 3</a>, March 2023. <br/>This paper begins with a summary of a powerful formalism for the study of electronic states in condensed matter physics called “gauge theory of states/phases of matter.” The chiral anomaly, which plays quite a prominent role in that formalism, is recalled. I then sketch an application of the chiral anomaly in 1 + 1 dimensions to quantum wires. Subsequently, some elements of the quantum Hall effect in twodimensional (2D) gapped (“incompressible”) electron liquids are reviewed. In particular, I discuss the role of anomalous chiral edge currents and of the anomaly inflow in 2D gapped electron liquids with explicitly or spontaneously broken time reversal, i.e., in Hall and Chern insulators. The topological Chern–Simons action yielding transport equations valid in the bulk of such systems and the associated anomalous edge action are derived. The results of a general classification of “Abelian” Hall insulators are outlined. After some remarks on induced Chern–Simons actions, I sketch results on certain 2D chiral photonic wave guides. I then continue with an analysis of chiral edge spincurrents and bulk response equations in timereversal invariant 2D topological insulators of electron gases with spin–orbit interactions. The “chiral magnetic effect” in 3D systems and axionelectrodynamics are reviewed next. This prepares the ground for an outline of a general theory of 3D topological insulators, including “axionic insulators.” Some remarks on Weyl semimetals, which exhibit the chiral magnetic effect, and on Mott transitions in 3D systems with dynamical axionlike degrees of freedom conclude this review.
Journal of Mathematical Physics, Volume 64, Issue 3, March 2023. <br/>This paper begins with a summary of a powerful formalism for the study of electronic states in condensed matter physics called “gauge theory of states/phases of matter.” The chiral anomaly, which plays quite a prominent role in that formalism, is recalled. I then sketch an application of the chiral anomaly in 1 + 1 dimensions to quantum wires. Subsequently, some elements of the quantum Hall effect in twodimensional (2D) gapped (“incompressible”) electron liquids are reviewed. In particular, I discuss the role of anomalous chiral edge currents and of the anomaly inflow in 2D gapped electron liquids with explicitly or spontaneously broken time reversal, i.e., in Hall and Chern insulators. The topological Chern–Simons action yielding transport equations valid in the bulk of such systems and the associated anomalous edge action are derived. The results of a general classification of “Abelian” Hall insulators are outlined. After some remarks on induced Chern–Simons actions, I sketch results on certain 2D chiral photonic wave guides. I then continue with an analysis of chiral edge spincurrents and bulk response equations in timereversal invariant 2D topological insulators of electron gases with spin–orbit interactions. The “chiral magnetic effect” in 3D systems and axionelectrodynamics are reviewed next. This prepares the ground for an outline of a general theory of 3D topological insulators, including “axionic insulators.” Some remarks on Weyl semimetals, which exhibit the chiral magnetic effect, and on Mott transitions in 3D systems with dynamical axionlike degrees of freedom conclude this review.
Gauge invariance and anomalies in condensed matter physics
10.1063/5.0135142
Journal of Mathematical Physics
20230331T10:03:41Z
© 2023 Author(s).
Jürg Fröhlich

Tunneling from general Smith–Volterra–Cantor potential
https://aip.scitation.org/doi/10.1063/5.0109426?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/64/3">Volume 64, Issue 3</a>, March 2023. <br/>We study the tunneling problem from the general Smith–Volterra–Cantor (SVC) potential of finite length L characterized by the scaling parameter ρ and stage G. We show that the SVC(ρ) potential of stage G is a special case of the super periodic potential (SPP) of order G. By using the SPP formalism developed by us earlier, we provide the closed form expression of the tunneling probability TG(k) with the help of the qPochhammer symbol. The profile of TG(k) with wave vector k is found to saturate with increasing stage G. Very sharp transmission resonances are found to occur in this system, which may find applications in the design of sharp transmission filters.
Journal of Mathematical Physics, Volume 64, Issue 3, March 2023. <br/>We study the tunneling problem from the general Smith–Volterra–Cantor (SVC) potential of finite length L characterized by the scaling parameter ρ and stage G. We show that the SVC(ρ) potential of stage G is a special case of the super periodic potential (SPP) of order G. By using the SPP formalism developed by us earlier, we provide the closed form expression of the tunneling probability TG(k) with the help of the qPochhammer symbol. The profile of TG(k) with wave vector k is found to saturate with increasing stage G. Very sharp transmission resonances are found to occur in this system, which may find applications in the design of sharp transmission filters.
Tunneling from general Smith–Volterra–Cantor potential
10.1063/5.0109426
Journal of Mathematical Physics
20230301T11:04:45Z
© 2023 Author(s).
Vibhav Narayan Singh
Mohammad Umar
Mohammad Hasan
Bhabani Prasad Mandal

A study of random variables in terms of the number operator
https://aip.scitation.org/doi/10.1063/5.0124172?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/64/3">Volume 64, Issue 3</a>, March 2023. <br/>We show first how the joint semiquantum and quantum operators of a finite family of random variables having finite moments of all orders can be recovered from their joint number operator. We then characterize the polynomially symmetric and polynomially factorizable random variables in terms of their joint number operator. Finally, we present the quantum decomposition of the number and quantum operators of the random variables whose orthogonal polynomials are the Gegenbauer polynomials.
Journal of Mathematical Physics, Volume 64, Issue 3, March 2023. <br/>We show first how the joint semiquantum and quantum operators of a finite family of random variables having finite moments of all orders can be recovered from their joint number operator. We then characterize the polynomially symmetric and polynomially factorizable random variables in terms of their joint number operator. Finally, we present the quantum decomposition of the number and quantum operators of the random variables whose orthogonal polynomials are the Gegenbauer polynomials.
A study of random variables in terms of the number operator
10.1063/5.0124172
Journal of Mathematical Physics
20230301T11:04:50Z
© 2023 Author(s).
A. I. Stan
G. Popa
R. Dutta

The “most classical” states of Euclidean invariant elementary quantum mechanical systems
https://aip.scitation.org/doi/10.1063/5.0109613?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/64/3">Volume 64, Issue 3</a>, March 2023. <br/>Complex techniques of general relativity are used to determine all the states in two and threedimensional momentum spaces in which the equality holds in uncertainty relations for noncommuting basic observables of Euclidean invariant elementary quantum mechanical systems, even with nonzero intrinsic spin. It is shown that while there is a 1parameter family of such states for any two components of the angular momentum vector operator with any angle between them, such states exist for a component of the linear and angular momenta only if these components are orthogonal to each other, and hence, the problem is reduced to the twodimensional Euclidean invariant case. We also show that analogous states exist for a component of the linear momentum and of the centerofmass vector only if the angle between them is zero or an acute angle. No such state (represented by a square integrable and differentiable wave function) can exist for any pair of components of the centerofmass vector operator. Therefore, the existence of such states depends not only on the Lie algebra but on the choice of its generators as well.
Journal of Mathematical Physics, Volume 64, Issue 3, March 2023. <br/>Complex techniques of general relativity are used to determine all the states in two and threedimensional momentum spaces in which the equality holds in uncertainty relations for noncommuting basic observables of Euclidean invariant elementary quantum mechanical systems, even with nonzero intrinsic spin. It is shown that while there is a 1parameter family of such states for any two components of the angular momentum vector operator with any angle between them, such states exist for a component of the linear and angular momenta only if these components are orthogonal to each other, and hence, the problem is reduced to the twodimensional Euclidean invariant case. We also show that analogous states exist for a component of the linear momentum and of the centerofmass vector only if the angle between them is zero or an acute angle. No such state (represented by a square integrable and differentiable wave function) can exist for any pair of components of the centerofmass vector operator. Therefore, the existence of such states depends not only on the Lie algebra but on the choice of its generators as well.
The “most classical” states of Euclidean invariant elementary quantum mechanical systems
10.1063/5.0109613
Journal of Mathematical Physics
20230308T11:04:49Z
© 2023 Author(s).
László B. Szabados

An odd feature of the “most classical” states of SU(2) invariant quantum mechanical systems
https://aip.scitation.org/doi/10.1063/5.0109611?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/64/3">Volume 64, Issue 3</a>, March 2023. <br/>Complex and spinorial techniques of general relativity are used to determine all the states of SU(2) invariant quantum mechanical systems in which the equality holds in uncertainty relations for the components of the angular momentum vector operator in two given directions. The expectation values depend on a discrete quantum number and two parameters, one of them is the angle between two angular momentum components and the other is the quotient of two standard deviations. Allowing the angle between two angular momentum components to be arbitrary, a new genuine quantum mechanical phenomenon emerges: it is shown that although standard deviations change continuously, one of the expectation values changes discontinuously on this parameter space. Since physically neither of the angular momentum components is distinguished over the other, this discontinuity suggests that the genuine parameter space must be a double cover of this classical one: it must be diffeomorphic to a Riemann surface known in connection with the complex function [math]. Moreover, the angle between angular momentum components plays the role of the parameter of an interpolation between the continuous range of expectation values in the special case of orthogonal angular momentum components and the discrete point spectrum of one angular momentum component. The consequences in the simultaneous measurements of these angular momentum components are also discussed briefly.
Journal of Mathematical Physics, Volume 64, Issue 3, March 2023. <br/>Complex and spinorial techniques of general relativity are used to determine all the states of SU(2) invariant quantum mechanical systems in which the equality holds in uncertainty relations for the components of the angular momentum vector operator in two given directions. The expectation values depend on a discrete quantum number and two parameters, one of them is the angle between two angular momentum components and the other is the quotient of two standard deviations. Allowing the angle between two angular momentum components to be arbitrary, a new genuine quantum mechanical phenomenon emerges: it is shown that although standard deviations change continuously, one of the expectation values changes discontinuously on this parameter space. Since physically neither of the angular momentum components is distinguished over the other, this discontinuity suggests that the genuine parameter space must be a double cover of this classical one: it must be diffeomorphic to a Riemann surface known in connection with the complex function [math]. Moreover, the angle between angular momentum components plays the role of the parameter of an interpolation between the continuous range of expectation values in the special case of orthogonal angular momentum components and the discrete point spectrum of one angular momentum component. The consequences in the simultaneous measurements of these angular momentum components are also discussed briefly.
An odd feature of the “most classical” states of SU(2) invariant quantum mechanical systems
10.1063/5.0109611
Journal of Mathematical Physics
20230308T11:04:52Z
© 2023 Author(s).
László B. Szabados

Truncated generalized coherent states
https://aip.scitation.org/doi/10.1063/5.0127702?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/64/3">Volume 64, Issue 3</a>, March 2023. <br/>A generalization of the canonical coherent states of a quantum harmonic oscillator has been performed by requiring the conditions of normalizability, continuity in the label, and resolution of the identity operator with a positive weight function. Relying on this approach, in the present scenario, coherent states are generalized over the canonical or finite dimensional Fock space of the harmonic oscillator. A class of generalized coherent states is determined such that the corresponding distributions of the number of excitations depart from the Poisson statistics according to combinations of stretched exponential decays, power laws, and logarithmic forms. The analysis of the Mandel parameter shows that the generalized coherent states exhibit (nonclassical) subPoissonian or superPoissonian statistics of the number of excitations, based on the realization of determined constraints. MittagLeffler and Wright generalized coherent states are analyzed as particular cases.
Journal of Mathematical Physics, Volume 64, Issue 3, March 2023. <br/>A generalization of the canonical coherent states of a quantum harmonic oscillator has been performed by requiring the conditions of normalizability, continuity in the label, and resolution of the identity operator with a positive weight function. Relying on this approach, in the present scenario, coherent states are generalized over the canonical or finite dimensional Fock space of the harmonic oscillator. A class of generalized coherent states is determined such that the corresponding distributions of the number of excitations depart from the Poisson statistics according to combinations of stretched exponential decays, power laws, and logarithmic forms. The analysis of the Mandel parameter shows that the generalized coherent states exhibit (nonclassical) subPoissonian or superPoissonian statistics of the number of excitations, based on the realization of determined constraints. MittagLeffler and Wright generalized coherent states are analyzed as particular cases.
Truncated generalized coherent states
10.1063/5.0127702
Journal of Mathematical Physics
20230324T10:09:41Z
© 2023 Author(s).
Filippo Giraldi
Francesco Mainardi

Local additivity revisited
https://aip.scitation.org/doi/10.1063/5.0079780?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/64/3">Volume 64, Issue 3</a>, March 2023. <br/>We make a number of simplifications in Gour and Friedland’s proof of local additivity of the minimum output entropy of a quantum channel. We follow them in reframing the question as one about the entanglement entropy of bipartite states associated with a dB × dE matrix. We use a different approach to reduce the general case to that of a square positive definite matrix. We use the integral representation of the log to obtain expressions for the first and second derivatives of the entropy, and then exploit the modular operator and functional calculus to streamline the proof following their underlying strategy. We also extend this result to the maximum relative entropy with respect to a fixed reference state, which has important implications for studying the superadditivity of the capacity of a quantum channel to transmit classical information.
Journal of Mathematical Physics, Volume 64, Issue 3, March 2023. <br/>We make a number of simplifications in Gour and Friedland’s proof of local additivity of the minimum output entropy of a quantum channel. We follow them in reframing the question as one about the entanglement entropy of bipartite states associated with a dB × dE matrix. We use a different approach to reduce the general case to that of a square positive definite matrix. We use the integral representation of the log to obtain expressions for the first and second derivatives of the entropy, and then exploit the modular operator and functional calculus to streamline the proof following their underlying strategy. We also extend this result to the maximum relative entropy with respect to a fixed reference state, which has important implications for studying the superadditivity of the capacity of a quantum channel to transmit classical information.
Local additivity revisited
10.1063/5.0079780
Journal of Mathematical Physics
20230321T11:17:55Z
© 2023 Author(s).
Mary Beth Ruskai
Jon Yard

Dirac field in AdS2 and representations of [math]
https://aip.scitation.org/doi/10.1063/5.0135971?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/64/3">Volume 64, Issue 3</a>, March 2023. <br/>We analyze a massive spinor field satisfying the Dirac equation in the universal covering space of twodimensional antide Sitter space. In order to obtain welldefined dynamics for the classical field despite the lack of globalhyperbolicity of the spacetime, we impose a suitable set of boundary conditions that render the spatial component of the Dirac operator selfadjoint. Then, we find which of the solution spaces obtained by imposing the selfadjoint boundary conditions are invariant under the action of the isometry group of the spacetime manifold, namely, the universal covering group of [math]. The invariant solution spaces are then identified with unitary irreducible representations of this group using the classification given by Pukánszky [Math. Ann. 156, 96–143 (1964)]. We determine which of these correspond to invariant positive or negativefrequency subspaces and, thus, result in a vacuum state invariant under the isometry group after canonical quantization. Additionally, we examine the invariant theories obtained from the selfadjoint boundary conditions, which result in a noninvariant vacuum state, identifying the unitary representation this state belongs to.
Journal of Mathematical Physics, Volume 64, Issue 3, March 2023. <br/>We analyze a massive spinor field satisfying the Dirac equation in the universal covering space of twodimensional antide Sitter space. In order to obtain welldefined dynamics for the classical field despite the lack of globalhyperbolicity of the spacetime, we impose a suitable set of boundary conditions that render the spatial component of the Dirac operator selfadjoint. Then, we find which of the solution spaces obtained by imposing the selfadjoint boundary conditions are invariant under the action of the isometry group of the spacetime manifold, namely, the universal covering group of [math]. The invariant solution spaces are then identified with unitary irreducible representations of this group using the classification given by Pukánszky [Math. Ann. 156, 96–143 (1964)]. We determine which of these correspond to invariant positive or negativefrequency subspaces and, thus, result in a vacuum state invariant under the isometry group after canonical quantization. Additionally, we examine the invariant theories obtained from the selfadjoint boundary conditions, which result in a noninvariant vacuum state, identifying the unitary representation this state belongs to.
Dirac field in AdS2 and representations of [math]
10.1063/5.0135971
Journal of Mathematical Physics
20230301T11:04:48Z
© 2023 Author(s).
David Serrano Blanco

Mass gap in U(1) Higgs–Yukawa model on a unit lattice
https://aip.scitation.org/doi/10.1063/5.0107644?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/64/3">Volume 64, Issue 3</a>, March 2023. <br/>A nonperturbative proof of the mass generation of fermions via the Higgs mechanism is given. This is done by showing an exponential decay of the two point fermionic correlation function in a weakly coupled U(1) Higgs–Yukawa theory on a unit lattice in d = 4. This decay implies that the Higgs boson, the photon, and the fermion all have a nonzero physical mass, and the theory is said to have a mass gap.
Journal of Mathematical Physics, Volume 64, Issue 3, March 2023. <br/>A nonperturbative proof of the mass generation of fermions via the Higgs mechanism is given. This is done by showing an exponential decay of the two point fermionic correlation function in a weakly coupled U(1) Higgs–Yukawa theory on a unit lattice in d = 4. This decay implies that the Higgs boson, the photon, and the fermion all have a nonzero physical mass, and the theory is said to have a mass gap.
Mass gap in U(1) Higgs–Yukawa model on a unit lattice
10.1063/5.0107644
Journal of Mathematical Physics
20230303T11:18:04Z
© 2023 Author(s).
Abhishek Goswami

Anomaly cancellation in the lattice effective electroweak theory
https://aip.scitation.org/doi/10.1063/5.0093162?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/64/3">Volume 64, Issue 3</a>, March 2023. <br/>The anomaly cancellation is at the basis of the perturbative consistence of the Standard Model, and it provides a partial explanation of charge quantization. We consider an effective electroweak theory on a lattice, with a quartic interaction describing the weak forces and an interaction with the e.m. field. We prove the validity of the anomaly cancellation at a nonperturbative level and with a finite lattice cutoff, even if the lattice breaks some important symmetries, on which perturbative arguments for the cancellation are based. The method of the proof has analogies with the one adopted for establishing the universality in transport of quantum materials.
Journal of Mathematical Physics, Volume 64, Issue 3, March 2023. <br/>The anomaly cancellation is at the basis of the perturbative consistence of the Standard Model, and it provides a partial explanation of charge quantization. We consider an effective electroweak theory on a lattice, with a quartic interaction describing the weak forces and an interaction with the e.m. field. We prove the validity of the anomaly cancellation at a nonperturbative level and with a finite lattice cutoff, even if the lattice breaks some important symmetries, on which perturbative arguments for the cancellation are based. The method of the proof has analogies with the one adopted for establishing the universality in transport of quantum materials.
Anomaly cancellation in the lattice effective electroweak theory
10.1063/5.0093162
Journal of Mathematical Physics
20230308T11:04:47Z
© 2023 Author(s).
Vieri Mastropietro

Homotopy double copy and the Kawai–Lewellen–Tye relations for the nonabelian and tensor Navier–Stokes equations
https://aip.scitation.org/doi/10.1063/5.0119508?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/64/3">Volume 64, Issue 3</a>, March 2023. <br/>Recently, a nonabelian generalization of the Navier–Stokes equation that exhibits a manifest duality between color and kinematics has been proposed by Cheung and Mangan. In this paper, we offer a new perspective on the double copy formulation of this equation based on the homotopy algebraic picture suggested by Borsten, Kim, Jurčo, Macrelli, Saemann, and Wolf. In the process, we describe precisely how the double copy can be realized at the level of perturbiner expansions. Specifically, we will show that the colordressed Berends–Giele currents for the nonabelian version of the Navier–Stokes equation can be used to construct the Berends–Giele currents for the double copied equation by replacing the color factors with a second copy of kinematic numerators. We will also show a Kawai–Lewellen–Tye relation stating that the full treelevel scattering amplitudes in the latter can be written as a product of treelevel color ordered partial amplitudes in the former.
Journal of Mathematical Physics, Volume 64, Issue 3, March 2023. <br/>Recently, a nonabelian generalization of the Navier–Stokes equation that exhibits a manifest duality between color and kinematics has been proposed by Cheung and Mangan. In this paper, we offer a new perspective on the double copy formulation of this equation based on the homotopy algebraic picture suggested by Borsten, Kim, Jurčo, Macrelli, Saemann, and Wolf. In the process, we describe precisely how the double copy can be realized at the level of perturbiner expansions. Specifically, we will show that the colordressed Berends–Giele currents for the nonabelian version of the Navier–Stokes equation can be used to construct the Berends–Giele currents for the double copied equation by replacing the color factors with a second copy of kinematic numerators. We will also show a Kawai–Lewellen–Tye relation stating that the full treelevel scattering amplitudes in the latter can be written as a product of treelevel color ordered partial amplitudes in the former.
Homotopy double copy and the Kawai–Lewellen–Tye relations for the nonabelian and tensor Navier–Stokes equations
10.1063/5.0119508
Journal of Mathematical Physics
20230322T11:23:44Z
© 2023 Author(s).
Valentina Guarín Escudero
Cristhiam LopezArcos
Alexander Quintero Vélez

Study of stationary rigidly rotating anisotropic cylindrical fluids with new exact interior solutions of GR. II. More about axial pressure
https://aip.scitation.org/doi/10.1063/5.0121152?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/64/3">Volume 64, Issue 3</a>, March 2023. <br/>This paper is the second in a series devoted to the study of spacetimes sourced by a stationary cylinder of fluid rigidly rotating around its symmetry axis and exhibiting an anisotropic pressure by using new exact interior solutions of general relativity. The configurations have been specialized to three different cases where the pressure is, in turn, directed alongside each principal stress. The two first articles in the series display the analysis of the axial pressure case. Indeed, the first axial class published in Paper I is merely a special case. It is recalled here and its properties are revised and supplemented. Moreover, a fully general method aiming at constructing different classes of such solutions is displayed. This method described in Paper II represents a key result of this work. It is exemplified and applied to two new classes of solutions depending on a single constant parameter. One of them, denoted Class A, is shown to verify every condition needing to be satisfied by a fully achieved set of exact solutions: axisymmetry and, when appropriate, regularity conditions; matching to an exterior vacuum; proper metric signature; and weak and strong energy conditions. Other properties and general rules are exhibited, some shedding light on rather longstanding issues. Astrophysical and physical applications are suggested.
Journal of Mathematical Physics, Volume 64, Issue 3, March 2023. <br/>This paper is the second in a series devoted to the study of spacetimes sourced by a stationary cylinder of fluid rigidly rotating around its symmetry axis and exhibiting an anisotropic pressure by using new exact interior solutions of general relativity. The configurations have been specialized to three different cases where the pressure is, in turn, directed alongside each principal stress. The two first articles in the series display the analysis of the axial pressure case. Indeed, the first axial class published in Paper I is merely a special case. It is recalled here and its properties are revised and supplemented. Moreover, a fully general method aiming at constructing different classes of such solutions is displayed. This method described in Paper II represents a key result of this work. It is exemplified and applied to two new classes of solutions depending on a single constant parameter. One of them, denoted Class A, is shown to verify every condition needing to be satisfied by a fully achieved set of exact solutions: axisymmetry and, when appropriate, regularity conditions; matching to an exterior vacuum; proper metric signature; and weak and strong energy conditions. Other properties and general rules are exhibited, some shedding light on rather longstanding issues. Astrophysical and physical applications are suggested.
Study of stationary rigidly rotating anisotropic cylindrical fluids with new exact interior solutions of GR. II. More about axial pressure
10.1063/5.0121152
Journal of Mathematical Physics
20230310T11:02:44Z
© 2023 Author(s).
M.N. Célérier

Multiplane gravitational lenses with an abundance of images
https://aip.scitation.org/doi/10.1063/5.0124892?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/64/3">Volume 64, Issue 3</a>, March 2023. <br/>We consider gravitational lensing of a background source by a finite system of pointmasses. The problem of determining the maximum possible number of lensed images has been completely resolved in the singleplane setting (where the point masses all reside in a single lens plane), but this problem remains open in the multiplane setting. We construct examples of Kplane pointmass gravitational lens ensembles that produce [math] images of a single background source, where gi is the number of point masses in the ith plane. This gives asymptotically (for large gi with K fixed) 5K times the minimal number of lensed images. Our construction uses Rhie’s singleplane examples and a structured parameterrescaling algorithm to produce preliminary systems of equations with the desired number of solutions. Utilizing the stability principle from the differential topology, we then show that preliminary (nonphysical) examples can be perturbed to produce physically meaningful examples while preserving the number of solutions. We provide numerical simulations illustrating the result of our construction, including positions of lensed images and the structure of critical curves and caustics. We observe an interesting “caustic of multiplicity” phenomenon that occurs in the nonphysical case and has a noticeable effect on the caustic structure in the physically meaningful perturbative case.
Journal of Mathematical Physics, Volume 64, Issue 3, March 2023. <br/>We consider gravitational lensing of a background source by a finite system of pointmasses. The problem of determining the maximum possible number of lensed images has been completely resolved in the singleplane setting (where the point masses all reside in a single lens plane), but this problem remains open in the multiplane setting. We construct examples of Kplane pointmass gravitational lens ensembles that produce [math] images of a single background source, where gi is the number of point masses in the ith plane. This gives asymptotically (for large gi with K fixed) 5K times the minimal number of lensed images. Our construction uses Rhie’s singleplane examples and a structured parameterrescaling algorithm to produce preliminary systems of equations with the desired number of solutions. Utilizing the stability principle from the differential topology, we then show that preliminary (nonphysical) examples can be perturbed to produce physically meaningful examples while preserving the number of solutions. We provide numerical simulations illustrating the result of our construction, including positions of lensed images and the structure of critical curves and caustics. We observe an interesting “caustic of multiplicity” phenomenon that occurs in the nonphysical case and has a noticeable effect on the caustic structure in the physically meaningful perturbative case.
Multiplane gravitational lenses with an abundance of images
10.1063/5.0124892
Journal of Mathematical Physics
20230316T10:22:45Z
© 2023 Author(s).
Charles R. Keeton
Erik Lundberg
Sean Perry

A frame based approach to computing symmetries with nontrivial isotropy groups
https://aip.scitation.org/doi/10.1063/5.0134596?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/64/3">Volume 64, Issue 3</a>, March 2023. <br/>A frame approach to determining the most general solution admitting a desired symmetry group has previously been examined in Riemannian and teleparallel geometries with some success. In teleparallel geometries, one must determine the general form of the frame and spin connection to generate a general solution admitting the desired symmetry group. Current approaches often rely on the use of the proper frame, where the spin connection is zero. However, this leads to particular theoretical and practical problems. In this paper, we introduce an entirely general approach to determining the most general Riemann–Cartan geometries that admit a given symmetry group and apply these results to teleparallel geometries. To illustrate the approach, we determine the most general geometries, with the minimal number of arbitrary functions, for particular choices of symmetry groups with dimension one, three, six, and seven. In addition, we rigorously show how the teleparallel analog of the Robertson–Walker, de Sitter, and Einstein static spacetimes can be determined.
Journal of Mathematical Physics, Volume 64, Issue 3, March 2023. <br/>A frame approach to determining the most general solution admitting a desired symmetry group has previously been examined in Riemannian and teleparallel geometries with some success. In teleparallel geometries, one must determine the general form of the frame and spin connection to generate a general solution admitting the desired symmetry group. Current approaches often rely on the use of the proper frame, where the spin connection is zero. However, this leads to particular theoretical and practical problems. In this paper, we introduce an entirely general approach to determining the most general Riemann–Cartan geometries that admit a given symmetry group and apply these results to teleparallel geometries. To illustrate the approach, we determine the most general geometries, with the minimal number of arbitrary functions, for particular choices of symmetry groups with dimension one, three, six, and seven. In addition, we rigorously show how the teleparallel analog of the Robertson–Walker, de Sitter, and Einstein static spacetimes can be determined.
A frame based approach to computing symmetries with nontrivial isotropy groups
10.1063/5.0134596
Journal of Mathematical Physics
20230324T10:09:40Z
© 2023 Author(s).
D. D. McNutt
A. A. Coley
R. J. van den Hoogen

Explicit formulas and decay rates for the solution of the wave equation in cosmological spacetimes
https://aip.scitation.org/doi/10.1063/5.0135092?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/64/3">Volume 64, Issue 3</a>, March 2023. <br/>We obtain explicit formulas for the solution of the wave equation in certain Friedmann–Lemaître–Robertson–Walker (FLRW) spacetimes. Our method, pioneered by Klainerman and Sarnak, consists in finding differential operators that map solutions of the wave equation in these FLRW spacetimes to solutions of the conformally invariant wave equation in simpler, ultrastatic spacetimes, for which spherical mean formulas are available. In addition to recovering the formulas for the dustfilled flat and hyperbolic FLRW spacetimes originally derived by Klainerman and Sarnak and generalizing them to the spherical case, we obtain new formulas for the radiationfilled FLRW spacetimes and also for the de Sitter, antide Sitter, and Milne universes. We use these formulas to study the solutions with respect to the Huygens principle and the decay rates and to formulate conjectures about the general decay rates in flat and hyperbolic FLRW spacetimes. The positive resolution of the conjecture in the flat case is seen to follow from known results in the literature.
Journal of Mathematical Physics, Volume 64, Issue 3, March 2023. <br/>We obtain explicit formulas for the solution of the wave equation in certain Friedmann–Lemaître–Robertson–Walker (FLRW) spacetimes. Our method, pioneered by Klainerman and Sarnak, consists in finding differential operators that map solutions of the wave equation in these FLRW spacetimes to solutions of the conformally invariant wave equation in simpler, ultrastatic spacetimes, for which spherical mean formulas are available. In addition to recovering the formulas for the dustfilled flat and hyperbolic FLRW spacetimes originally derived by Klainerman and Sarnak and generalizing them to the spherical case, we obtain new formulas for the radiationfilled FLRW spacetimes and also for the de Sitter, antide Sitter, and Milne universes. We use these formulas to study the solutions with respect to the Huygens principle and the decay rates and to formulate conjectures about the general decay rates in flat and hyperbolic FLRW spacetimes. The positive resolution of the conjecture in the flat case is seen to follow from known results in the literature.
Explicit formulas and decay rates for the solution of the wave equation in cosmological spacetimes
10.1063/5.0135092
Journal of Mathematical Physics
20230327T10:06:07Z
© 2023 Author(s).
José Natário
Flavio Rossetti

Quasiperiodic solutions to nonlinear random Schrödinger equations at fixed potential realizations
https://aip.scitation.org/doi/10.1063/5.0134120?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/64/3">Volume 64, Issue 3</a>, March 2023. <br/>In this paper, we study the discrete nonlinear random Schrödinger equation [math] on [math], where 0 < ɛ, δ ≪ 1, Δ is the discrete Laplacian, and V is the random potential. We fix the random potential V in a good set. Then, we use small amplitudes as parameters to construct quasiperiodic solutions of the nonlinear random Schrödinger equation.
Journal of Mathematical Physics, Volume 64, Issue 3, March 2023. <br/>In this paper, we study the discrete nonlinear random Schrödinger equation [math] on [math], where 0 < ɛ, δ ≪ 1, Δ is the discrete Laplacian, and V is the random potential. We fix the random potential V in a good set. Then, we use small amplitudes as parameters to construct quasiperiodic solutions of the nonlinear random Schrödinger equation.
Quasiperiodic solutions to nonlinear random Schrödinger equations at fixed potential realizations
10.1063/5.0134120
Journal of Mathematical Physics
20230308T11:04:55Z
© 2023 Author(s).
Jiansheng Geng
Yingnan Sun
W.M. Wang

General theory of the higherorder linear quaternion qdifference equations through the quaternion determinant algorithm and the characteristic polynomial
https://aip.scitation.org/doi/10.1063/5.0071865?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/64/3">Volume 64, Issue 3</a>, March 2023. <br/>The general theory of quaternion qdifference equations is completely different from traditional qdifference equations in the complex space for the special algebraic structure of the quaternion space, such as the noncommutativity of multiplication among elements. In this paper, some properties of basic quaternion qdiscrete functions, such as the quaternion qexponential function, are obtained. The existence, uniqueness, and extension theorems of the solution for higherorder linear quaternion qdifference equations (QQDCEs) are established through constructing quaternion qstepwise approximation sequences, and the equivalent variable transform between higherorder linear QQDCEs and quaternion linear qdifference equations is given. Moreover, some basic results, such as the Wronskian formula, Liouville formula, and general solution structure theorems of higherorder linear QQDCEs with constant and variable coefficients, are established by applying the quaternion characteristic polynomial and the quaternion determinant algorithm. In addition, some particular and general solution formulas of nonhomogeneous QQDCEs are obtained under the noncommutative condition of quaternion elements. Finally, several examples are provided to illustrate the feasibility of our obtained results.
Journal of Mathematical Physics, Volume 64, Issue 3, March 2023. <br/>The general theory of quaternion qdifference equations is completely different from traditional qdifference equations in the complex space for the special algebraic structure of the quaternion space, such as the noncommutativity of multiplication among elements. In this paper, some properties of basic quaternion qdiscrete functions, such as the quaternion qexponential function, are obtained. The existence, uniqueness, and extension theorems of the solution for higherorder linear quaternion qdifference equations (QQDCEs) are established through constructing quaternion qstepwise approximation sequences, and the equivalent variable transform between higherorder linear QQDCEs and quaternion linear qdifference equations is given. Moreover, some basic results, such as the Wronskian formula, Liouville formula, and general solution structure theorems of higherorder linear QQDCEs with constant and variable coefficients, are established by applying the quaternion characteristic polynomial and the quaternion determinant algorithm. In addition, some particular and general solution formulas of nonhomogeneous QQDCEs are obtained under the noncommutative condition of quaternion elements. Finally, several examples are provided to illustrate the feasibility of our obtained results.
General theory of the higherorder linear quaternion qdifference equations through the quaternion determinant algorithm and the characteristic polynomial
10.1063/5.0071865
Journal of Mathematical Physics
20230310T11:02:45Z
© 2023 Author(s).
Desu Chen
Chao Wang
Zhien Li

When action is not least for systems with actiondependent Lagrangians
https://aip.scitation.org/doi/10.1063/5.0099612?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/64/3">Volume 64, Issue 3</a>, March 2023. <br/>The dynamics of some nonconservative and dissipative systems can be derived by calculating the first variation of an actiondependent action according to the variational principle of Herglotz. This is directly analogous to the variational principle of Hamilton commonly used to derive the dynamics of conservative systems. In a similar fashion, just as the second variation of a conservative system’s action can be used to infer whether that system’s possible trajectories are dynamically stable, so too can the second variation of the actiondependent action be used to infer whether the possible trajectories of nonconservative and dissipative systems are dynamically stable. In this paper, I show, generalizing earlier analyses of the second variation of the action for conservative systems, how to calculate the second variation of the actiondependent action and how to apply it to two physically important systems: a timeindependent harmonic oscillator and a timedependent harmonic oscillator.
Journal of Mathematical Physics, Volume 64, Issue 3, March 2023. <br/>The dynamics of some nonconservative and dissipative systems can be derived by calculating the first variation of an actiondependent action according to the variational principle of Herglotz. This is directly analogous to the variational principle of Hamilton commonly used to derive the dynamics of conservative systems. In a similar fashion, just as the second variation of a conservative system’s action can be used to infer whether that system’s possible trajectories are dynamically stable, so too can the second variation of the actiondependent action be used to infer whether the possible trajectories of nonconservative and dissipative systems are dynamically stable. In this paper, I show, generalizing earlier analyses of the second variation of the action for conservative systems, how to calculate the second variation of the actiondependent action and how to apply it to two physically important systems: a timeindependent harmonic oscillator and a timedependent harmonic oscillator.
When action is not least for systems with actiondependent Lagrangians
10.1063/5.0099612
Journal of Mathematical Physics
20230320T11:14:15Z
© 2023 Author(s).
Joseph Ryan

Markov properties of partially open quantum random walks
https://aip.scitation.org/doi/10.1063/5.0087222?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/64/3">Volume 64, Issue 3</a>, March 2023. <br/>In this paper, we first construct (nonhomogeneous) quantum Markov chains (QMCs, for short) associated with partially open quantum random walks (POQRWs, for short). We then focus on the study of the analogs of irreducibility, period, and ergodic behavior of POQRWs by QMCs. Moreover, we get the characterization of invariant states of POQRWs via QMCs.
Journal of Mathematical Physics, Volume 64, Issue 3, March 2023. <br/>In this paper, we first construct (nonhomogeneous) quantum Markov chains (QMCs, for short) associated with partially open quantum random walks (POQRWs, for short). We then focus on the study of the analogs of irreducibility, period, and ergodic behavior of POQRWs by QMCs. Moreover, we get the characterization of invariant states of POQRWs via QMCs.
Markov properties of partially open quantum random walks
10.1063/5.0087222
Journal of Mathematical Physics
20230310T11:02:46Z
© 2023 Author(s).
Yuan Bao Kang

Canonical and canonoid transformations for Hamiltonian systems on (co)symplectic and (co)contact manifolds
https://aip.scitation.org/doi/10.1063/5.0135045?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/64/3">Volume 64, Issue 3</a>, March 2023. <br/>In this paper, we present canonical and canonoid transformations considered as global geometrical objects for Hamiltonian systems. Under the mathematical formalisms of symplectic, cosymplectic, contact, and cocontact geometries, the canonoid transformations are defined for (co)symplectic and (co)contact Hamiltonian systems. The local characterizations of these transformations are derived explicitly, and it is demonstrated that for a given canonoid transformation, there exist constants of motion associated with it.
Journal of Mathematical Physics, Volume 64, Issue 3, March 2023. <br/>In this paper, we present canonical and canonoid transformations considered as global geometrical objects for Hamiltonian systems. Under the mathematical formalisms of symplectic, cosymplectic, contact, and cocontact geometries, the canonoid transformations are defined for (co)symplectic and (co)contact Hamiltonian systems. The local characterizations of these transformations are derived explicitly, and it is demonstrated that for a given canonoid transformation, there exist constants of motion associated with it.
Canonical and canonoid transformations for Hamiltonian systems on (co)symplectic and (co)contact manifolds
10.1063/5.0135045
Journal of Mathematical Physics
20230301T11:04:46Z
© 2023 Author(s).
R. Azuaje
A. M. EscobarRuiz

Lowdimensional bihamiltonian structures of topological type
https://aip.scitation.org/doi/10.1063/5.0130899?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/64/3">Volume 64, Issue 3</a>, March 2023. <br/>We construct local bihamiltonian structures from classical Walgebras associated with nonregular nilpotent elements of regular semisimple type in Lie algebras of types A2 and A3. They form exact Poisson pencils and admit a dispersionless limit, and their leading terms define logarithmic or trivial Dubrovin–Frobenius manifolds. We calculate the corresponding central invariants, which are expected to be constants. In particular, we get Dubrovin–Frobenius manifolds associated with the focused Schrödinger equation and Hurwitz space M0;1,0 and the corresponding bihamiltonian structures of topological type.
Journal of Mathematical Physics, Volume 64, Issue 3, March 2023. <br/>We construct local bihamiltonian structures from classical Walgebras associated with nonregular nilpotent elements of regular semisimple type in Lie algebras of types A2 and A3. They form exact Poisson pencils and admit a dispersionless limit, and their leading terms define logarithmic or trivial Dubrovin–Frobenius manifolds. We calculate the corresponding central invariants, which are expected to be constants. In particular, we get Dubrovin–Frobenius manifolds associated with the focused Schrödinger equation and Hurwitz space M0;1,0 and the corresponding bihamiltonian structures of topological type.
Lowdimensional bihamiltonian structures of topological type
10.1063/5.0130899
Journal of Mathematical Physics
20230313T11:20:38Z
© 2023 Author(s).
Yassir Dinar

A new light on the FKMM invariant and its consequences
https://aip.scitation.org/doi/10.1063/5.0135106?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/64/3">Volume 64, Issue 3</a>, March 2023. <br/>“Quaternionic” vector bundles are the objects that describe topological phases of quantum systems subjected to an odd timereversal symmetry (class AII). In this work, we prove that the Furuta–Kametani–Matsue–Minami (FKMM) invariant provides the correct fundamental characteristic class for the classification of “Quaternionic” vector bundles in dimension less than or equal to three (low dimension). The new insight is provided by the interpretation of the FKMM invariant from the viewpoint of the Bredon equivariant cohomology. This fact, along with basic results in equivariant homotopy theory, allows us to achieve the expected result.
Journal of Mathematical Physics, Volume 64, Issue 3, March 2023. <br/>“Quaternionic” vector bundles are the objects that describe topological phases of quantum systems subjected to an odd timereversal symmetry (class AII). In this work, we prove that the Furuta–Kametani–Matsue–Minami (FKMM) invariant provides the correct fundamental characteristic class for the classification of “Quaternionic” vector bundles in dimension less than or equal to three (low dimension). The new insight is provided by the interpretation of the FKMM invariant from the viewpoint of the Bredon equivariant cohomology. This fact, along with basic results in equivariant homotopy theory, allows us to achieve the expected result.
A new light on the FKMM invariant and its consequences
10.1063/5.0135106
Journal of Mathematical Physics
20230315T10:09:00Z
© 2023 Author(s).
Giuseppe De Nittis
Kiyonori Gomi

Singularity analysis and bilinear approach to some Bogoyavlensky equations
https://aip.scitation.org/doi/10.1063/5.0124393?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/64/3">Volume 64, Issue 3</a>, March 2023. <br/>We discuss singularity analysis and bilinear integrability of four Bogoyavlensky differentialdifference equations. Three of them are completely integrable, and the fourth is, to our knowledge, a new one. Blending the singularity confinement with the Painlevé property reveals strictly confining and anticonfining (weakly confining) singularity patterns. Strictly confining patterns are extremely useful because they provide the nonlinear substitution needed for Hirota bilinear forms. For the new proposed equation, we also get the bilinear form and multisoliton solution, being a good candidate for a new integrable system. In addition, using the bilinear formalism, we recover integrable timediscretizations of the first three systems.
Journal of Mathematical Physics, Volume 64, Issue 3, March 2023. <br/>We discuss singularity analysis and bilinear integrability of four Bogoyavlensky differentialdifference equations. Three of them are completely integrable, and the fourth is, to our knowledge, a new one. Blending the singularity confinement with the Painlevé property reveals strictly confining and anticonfining (weakly confining) singularity patterns. Strictly confining patterns are extremely useful because they provide the nonlinear substitution needed for Hirota bilinear forms. For the new proposed equation, we also get the bilinear form and multisoliton solution, being a good candidate for a new integrable system. In addition, using the bilinear formalism, we recover integrable timediscretizations of the first three systems.
Singularity analysis and bilinear approach to some Bogoyavlensky equations
10.1063/5.0124393
Journal of Mathematical Physics
20230317T10:30:41Z
© 2023 Author(s).
A. S. Carstea

Classification of degenerate nonhomogeneous Hamiltonian operators
https://aip.scitation.org/doi/10.1063/5.0135134?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/64/3">Volume 64, Issue 3</a>, March 2023. <br/>We investigate nonhomogeneous Hamiltonian operators composed of a first order Dubrovin–Novikov operator and an ultralocal one. The study of such operators turns out to be fundamental for the inverted system of equations associated with a class of Hamiltonian scalar equations. Often, the involved operators are degenerate in the first order term. For this reason, a complete classification of the operators with a degenerate leading coefficient in systems with two and three components is presented.
Journal of Mathematical Physics, Volume 64, Issue 3, March 2023. <br/>We investigate nonhomogeneous Hamiltonian operators composed of a first order Dubrovin–Novikov operator and an ultralocal one. The study of such operators turns out to be fundamental for the inverted system of equations associated with a class of Hamiltonian scalar equations. Often, the involved operators are degenerate in the first order term. For this reason, a complete classification of the operators with a degenerate leading coefficient in systems with two and three components is presented.
Classification of degenerate nonhomogeneous Hamiltonian operators
10.1063/5.0135134
Journal of Mathematical Physics
20230320T11:14:14Z
© 2023 Author(s).
Marta Dell’Atti
Pierandrea Vergallo

Revisiting the Coulomb problem: A novel representation of the confluent hypergeometric function as an infinite sum of discrete Bessel functions
https://aip.scitation.org/doi/10.1063/5.0082567?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/64/3">Volume 64, Issue 3</a>, March 2023. <br/>We use the tridiagonal representation approach to solve the radial Schrödinger equation for the continuum scattering states of the Coulomb problem in a complete basis set of discrete Bessel functions. Consequently, we obtain a new representation of the confluent hypergeometric function as an infinite sum of Bessel functions, which is numerically very stable and more rapidly convergent than another wellknown formula.
Journal of Mathematical Physics, Volume 64, Issue 3, March 2023. <br/>We use the tridiagonal representation approach to solve the radial Schrödinger equation for the continuum scattering states of the Coulomb problem in a complete basis set of discrete Bessel functions. Consequently, we obtain a new representation of the confluent hypergeometric function as an infinite sum of Bessel functions, which is numerically very stable and more rapidly convergent than another wellknown formula.
Revisiting the Coulomb problem: A novel representation of the confluent hypergeometric function as an infinite sum of discrete Bessel functions
10.1063/5.0082567
Journal of Mathematical Physics
20230322T11:23:39Z
© 2023 Author(s).
A. D. Alhaidari

Nonautonomous kcontact field theories
https://aip.scitation.org/doi/10.1063/5.0131110?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/64/3">Volume 64, Issue 3</a>, March 2023. <br/>This paper provides a new geometric framework to describe nonconservative field theories with explicit dependence on the space–time coordinates by combining the kcosymplectic and kcontact formulations. This geometric framework, the kcocontact geometry, permits the development of Hamiltonian and Lagrangian formalisms for these field theories. We also compare this new formulation in the autonomous case with the previous kcontact formalism. To illustrate the theory, we study the nonlinear damped wave equation with external timedependent forcing.
Journal of Mathematical Physics, Volume 64, Issue 3, March 2023. <br/>This paper provides a new geometric framework to describe nonconservative field theories with explicit dependence on the space–time coordinates by combining the kcosymplectic and kcontact formulations. This geometric framework, the kcocontact geometry, permits the development of Hamiltonian and Lagrangian formalisms for these field theories. We also compare this new formulation in the autonomous case with the previous kcontact formalism. To illustrate the theory, we study the nonlinear damped wave equation with external timedependent forcing.
Nonautonomous kcontact field theories
10.1063/5.0131110
Journal of Mathematical Physics
20230322T11:23:42Z
© 2023 Author(s).
Xavier Rivas

Power law logarithmic bounds of moments for long range operators in arbitrary dimension
https://aip.scitation.org/doi/10.1063/5.0138325?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/64/3">Volume 64, Issue 3</a>, March 2023. <br/>We show that the sublinear bound of the bad Green’s functions implies explicit logarithmic bounds of moments for long range operators in arbitrary dimension.
Journal of Mathematical Physics, Volume 64, Issue 3, March 2023. <br/>We show that the sublinear bound of the bad Green’s functions implies explicit logarithmic bounds of moments for long range operators in arbitrary dimension.
Power law logarithmic bounds of moments for long range operators in arbitrary dimension
10.1063/5.0138325
Journal of Mathematical Physics
20230323T10:34:50Z
© 2023 Author(s).
Wencai Liu

Double interlacing in random tiling models
https://aip.scitation.org/doi/10.1063/5.0093542?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/64/3">Volume 64, Issue 3</a>, March 2023. <br/>Random tilings of very large domains will typically lead to a solid, a liquid, and a gas phase. In the twophase case, the solid–liquid boundary (arctic curve) is smooth, possibly with singularities. At the point of tangency of the arctic curve with the domain boundary, for largesized domains, the tiles of a certain shape form a singly interlacing set, fluctuating according to the eigenvalues of the principal minors of a Gaussian unitary ensemblematrix. Introducing nonconvexities in large domains may lead to the appearance of several interacting liquid regions: They can merely touch, leading to either a split tacnode (hard tacnode), with two distinct adjacent frozen phases descending into the tacnode, or a soft tacnode. For appropriate scaling of the nonconvex domains and probing about such split tacnodes, filaments, evolving in a bricklike sea of dimers of another type, will connect the liquid patches. Nearby, the tiling fluctuations are governed by a discrete tacnode kernel—i.e., a determinantal point process on a doubly interlacing set of dots belonging to a discrete array of parallel lines. This kernel enables us to compute the joint distribution of the dots along those lines. This kernel appears in two very different models: (i) domino tilings of skewAztec rectangles and (ii) lozenge tilings of hexagons with cuts along opposite edges. Soft tacnodes appear when two arctic curves gently touch each other amid a bricklike sea of dimers of one type, unlike the split tacnode. We hope that this largely expository paper will provide a view on the subject and be accessible to a wider audience.
Journal of Mathematical Physics, Volume 64, Issue 3, March 2023. <br/>Random tilings of very large domains will typically lead to a solid, a liquid, and a gas phase. In the twophase case, the solid–liquid boundary (arctic curve) is smooth, possibly with singularities. At the point of tangency of the arctic curve with the domain boundary, for largesized domains, the tiles of a certain shape form a singly interlacing set, fluctuating according to the eigenvalues of the principal minors of a Gaussian unitary ensemblematrix. Introducing nonconvexities in large domains may lead to the appearance of several interacting liquid regions: They can merely touch, leading to either a split tacnode (hard tacnode), with two distinct adjacent frozen phases descending into the tacnode, or a soft tacnode. For appropriate scaling of the nonconvex domains and probing about such split tacnodes, filaments, evolving in a bricklike sea of dimers of another type, will connect the liquid patches. Nearby, the tiling fluctuations are governed by a discrete tacnode kernel—i.e., a determinantal point process on a doubly interlacing set of dots belonging to a discrete array of parallel lines. This kernel enables us to compute the joint distribution of the dots along those lines. This kernel appears in two very different models: (i) domino tilings of skewAztec rectangles and (ii) lozenge tilings of hexagons with cuts along opposite edges. Soft tacnodes appear when two arctic curves gently touch each other amid a bricklike sea of dimers of one type, unlike the split tacnode. We hope that this largely expository paper will provide a view on the subject and be accessible to a wider audience.
Double interlacing in random tiling models
10.1063/5.0093542
Journal of Mathematical Physics
20230328T10:26:42Z
© 2023 Author(s).
Mark Adler
Pierre van Moerbeke