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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Asymptotic behavior of the stationary magnetohydrodynamic equations in an exterior domain
https://aip.scitation.org/doi/10.1063/5.0058652?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/62/11">Volume 62, Issue 11</a>, November 2021. <br/>In this paper, we study the asymptotic behavior of solutions to the incompressible magnetohydrodynamic (MHD) equations in an exterior domain. We will show that, under some assumption, any nontrivial velocity field u and magnetic field h obey a minimal decaying rate exp(−Cx2 log x) at infinity. Our proof is based on appropriate Carleman estimates. As a consequence, we establish a Liouvilletype result for the three dimensional incompressible MHDs in an exterior domain.
Journal of Mathematical Physics, Volume 62, Issue 11, November 2021. <br/>In this paper, we study the asymptotic behavior of solutions to the incompressible magnetohydrodynamic (MHD) equations in an exterior domain. We will show that, under some assumption, any nontrivial velocity field u and magnetic field h obey a minimal decaying rate exp(−Cx2 log x) at infinity. Our proof is based on appropriate Carleman estimates. As a consequence, we establish a Liouvilletype result for the three dimensional incompressible MHDs in an exterior domain.
Asymptotic behavior of the stationary magnetohydrodynamic equations in an exterior domain
10.1063/5.0058652
Journal of Mathematical Physics
20211101T09:58:46Z
© 2021 Author(s).
Huiying Fan
Meng Wang

Dispersive estimates for nonlinear Schrödinger equations with external potentials
https://aip.scitation.org/doi/10.1063/5.0055911?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/62/11">Volume 62, Issue 11</a>, November 2021. <br/>We consider the long time dynamics of nonlinear Schrödinger equations with an external potential. More precisely, we look at Hartree type equations in three or higher dimensions with small initial data. We prove an optimal decay estimate, which is comparable to the decay of free solutions. Our proof relies on good control on a high Sobolev norm of the solution to estimate the terms in Duhamel’s formula.
Journal of Mathematical Physics, Volume 62, Issue 11, November 2021. <br/>We consider the long time dynamics of nonlinear Schrödinger equations with an external potential. More precisely, we look at Hartree type equations in three or higher dimensions with small initial data. We prove an optimal decay estimate, which is comparable to the decay of free solutions. Our proof relies on good control on a high Sobolev norm of the solution to estimate the terms in Duhamel’s formula.
Dispersive estimates for nonlinear Schrödinger equations with external potentials
10.1063/5.0055911
Journal of Mathematical Physics
20211102T10:30:21Z
© 2021 Author(s).
Charlotte Dietze

The Neumann and Robin problems for the Korteweg–de Vries equation on the halfline
https://aip.scitation.org/doi/10.1063/5.0064147?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/62/11">Volume 62, Issue 11</a>, November 2021. <br/>The wellposedness of the Neumann and Robin problems for the Korteweg–de Vries equation is studied with data in Sobolev spaces. Using the Fokas unified transform method, the corresponding linear problems with forcing are solved and solution estimates are derived. Then, using these, an iteration map is defined, and it is proved to be a contraction in appropriate solution spaces after the needed bilinear estimates are derived.
Journal of Mathematical Physics, Volume 62, Issue 11, November 2021. <br/>The wellposedness of the Neumann and Robin problems for the Korteweg–de Vries equation is studied with data in Sobolev spaces. Using the Fokas unified transform method, the corresponding linear problems with forcing are solved and solution estimates are derived. Then, using these, an iteration map is defined, and it is proved to be a contraction in appropriate solution spaces after the needed bilinear estimates are derived.
The Neumann and Robin problems for the Korteweg–de Vries equation on the halfline
10.1063/5.0064147
Journal of Mathematical Physics
20211104T09:57:57Z
© 2021 Author(s).
A. Alexandrou Himonas
Carlos Madrid
Fangchi Yan

Local weak solution of the isentropic compressible Navier–Stokes equations
https://aip.scitation.org/doi/10.1063/5.0054450?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/62/11">Volume 62, Issue 11</a>, November 2021. <br/>Whether the three dimensional isentropic compressible Navier–Stokes equations admit weak solutions for arbitrary initial data with adiabatic exponent γ > 1 remains a challenging problem. The only available results under γ > 1 were achieved by either assuming the initial data with small energy due to Hoff [J. Differ. Equations 120(1), 215–254 (1995)] or under the spherically symmetric condition by Jiang and Zhang [Commun. Math. Phys. 215, 559–581 (2001)] and Huang [J. Differ. Equations 262, 1341–1358 (2017)]. In this paper, we establish the existence of weak solutions with higher regularity of the threedimensional periodic compressible isentropic Navier–Stokes equations in small time for the adiabatic exponent γ > 1 in the presence of vacuum. It can be viewed as a local version of Hoff’s work and also extends the result of Desjardins [Commun. Partial Differ. Equations 22(5–6), 977–1008 (1997)] by removing the assumption of γ > 3.
Journal of Mathematical Physics, Volume 62, Issue 11, November 2021. <br/>Whether the three dimensional isentropic compressible Navier–Stokes equations admit weak solutions for arbitrary initial data with adiabatic exponent γ > 1 remains a challenging problem. The only available results under γ > 1 were achieved by either assuming the initial data with small energy due to Hoff [J. Differ. Equations 120(1), 215–254 (1995)] or under the spherically symmetric condition by Jiang and Zhang [Commun. Math. Phys. 215, 559–581 (2001)] and Huang [J. Differ. Equations 262, 1341–1358 (2017)]. In this paper, we establish the existence of weak solutions with higher regularity of the threedimensional periodic compressible isentropic Navier–Stokes equations in small time for the adiabatic exponent γ > 1 in the presence of vacuum. It can be viewed as a local version of Hoff’s work and also extends the result of Desjardins [Commun. Partial Differ. Equations 22(5–6), 977–1008 (1997)] by removing the assumption of γ > 3.
Local weak solution of the isentropic compressible Navier–Stokes equations
10.1063/5.0054450
Journal of Mathematical Physics
20211108T11:12:39Z
© 2021 Author(s).
Xiangdi Huang
Wei Yan

Fractional Kirchhofftype equation with singular potential and critical exponent
https://aip.scitation.org/doi/10.1063/5.0061144?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/62/11">Volume 62, Issue 11</a>, November 2021. <br/>In this paper, we study a class of critical fractional Kirchhofftype equations with singular potential. With a range of parameters, we propose several existence results. Our work extends the results of Li and Su [Z. Angew. Math. Phys. 66, 3147 (2015)].
Journal of Mathematical Physics, Volume 62, Issue 11, November 2021. <br/>In this paper, we study a class of critical fractional Kirchhofftype equations with singular potential. With a range of parameters, we propose several existence results. Our work extends the results of Li and Su [Z. Angew. Math. Phys. 66, 3147 (2015)].
Fractional Kirchhofftype equation with singular potential and critical exponent
10.1063/5.0061144
Journal of Mathematical Physics
20211109T12:32:53Z
© 2021 Author(s).
Senli Liu
Haibo Chen

Schrödinger [math]–Laplace equations in [math] involving indefinite weights and critical growth
https://aip.scitation.org/doi/10.1063/5.0054557?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/62/11">Volume 62, Issue 11</a>, November 2021. <br/>We study a class of critical Schrödinger [math]–Laplace equations in [math], with reaction terms of the concave–convex type and involving indefinite weights. The class of potentials used in this study is different from that in most existing studies on Schrödinger equations in [math]. We establish a concentrationcompactness principle for weighted Sobolev spaces with variable exponents involving the potentials. By employing this concentrationcompactness principle and the Nehari manifold method, we obtain existence and multiplicity results for the solution to our problem.
Journal of Mathematical Physics, Volume 62, Issue 11, November 2021. <br/>We study a class of critical Schrödinger [math]–Laplace equations in [math], with reaction terms of the concave–convex type and involving indefinite weights. The class of potentials used in this study is different from that in most existing studies on Schrödinger equations in [math]. We establish a concentrationcompactness principle for weighted Sobolev spaces with variable exponents involving the potentials. By employing this concentrationcompactness principle and the Nehari manifold method, we obtain existence and multiplicity results for the solution to our problem.
Schrödinger [math]–Laplace equations in [math] involving indefinite weights and critical growth
10.1063/5.0054557
Journal of Mathematical Physics
20211111T12:20:06Z
© 2021 Author(s).
Ky Ho
YunHo Kim
Jongrak Lee

Upper semicontinuity of random attractors and existence of invariant measures for nonlocal stochastic Swift–Hohenberg equation with multiplicative noise
https://aip.scitation.org/doi/10.1063/5.0039187?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/62/11">Volume 62, Issue 11</a>, November 2021. <br/>In this paper, we mainly study the longtime dynamical behaviors of 2D nonlocal stochastic Swift–Hohenberg equations with multiplicative noise from two perspectives. First, by adopting the analytic semigroup theory, we prove the upper semicontinuity of random attractors in the Sobolev space [math], as the coefficient of the multiplicative noise approaches zero. Then, we extend the classical “stochastic Gronwall’s lemma,” making it more convenient in applications. Based on this improvement, we are allowed to use the analytic semigroup theory to establish the existence of ergodic invariant measures.
Journal of Mathematical Physics, Volume 62, Issue 11, November 2021. <br/>In this paper, we mainly study the longtime dynamical behaviors of 2D nonlocal stochastic Swift–Hohenberg equations with multiplicative noise from two perspectives. First, by adopting the analytic semigroup theory, we prove the upper semicontinuity of random attractors in the Sobolev space [math], as the coefficient of the multiplicative noise approaches zero. Then, we extend the classical “stochastic Gronwall’s lemma,” making it more convenient in applications. Based on this improvement, we are allowed to use the analytic semigroup theory to establish the existence of ergodic invariant measures.
Upper semicontinuity of random attractors and existence of invariant measures for nonlocal stochastic Swift–Hohenberg equation with multiplicative noise
10.1063/5.0039187
Journal of Mathematical Physics
20211116T11:06:33Z
© 2021 Author(s).
Jintao Wang
Chunqiu Li
Lu Yang
Mo Jia

Blowup vs boundedness in a twospecies attraction–repulsion chemotaxis system with two chemicals
https://aip.scitation.org/doi/10.1063/5.0069180?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/62/11">Volume 62, Issue 11</a>, November 2021. <br/>We consider the attraction–repulsion chemotaxis system in a smoothly bounded domain [math]. When the system is parabolic–elliptic–parabolic–elliptic, we establish the finite time blowup conditions of nonradial solutions by making a differential inequality on the moment of solutions. Apart from that, in some special cases, the solutions of the system are globally bounded without blowup. Our results extend some known conclusions in the literature.
Journal of Mathematical Physics, Volume 62, Issue 11, November 2021. <br/>We consider the attraction–repulsion chemotaxis system in a smoothly bounded domain [math]. When the system is parabolic–elliptic–parabolic–elliptic, we establish the finite time blowup conditions of nonradial solutions by making a differential inequality on the moment of solutions. Apart from that, in some special cases, the solutions of the system are globally bounded without blowup. Our results extend some known conclusions in the literature.
Blowup vs boundedness in a twospecies attraction–repulsion chemotaxis system with two chemicals
10.1063/5.0069180
Journal of Mathematical Physics
20211117T11:04:13Z
© 2021 Author(s).
Aichao Liu
Binxiang Dai

Asymptotically periodic quasilinear Schrödinger equations with critical exponential growth
https://aip.scitation.org/doi/10.1063/5.0053794?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/62/11">Volume 62, Issue 11</a>, November 2021. <br/>In this work, we study the existence of a positive solution for a class of quasilinear Schrödinger equations involving a potential that behaves like a periodic function at infinity and the nonlinear term may exhibit critical exponential growth. In order to prove our main result, we combine minimax methods with a version of the Trudinger–Moser inequality. These equations appear naturally in mathematical physics and have been derived as models of several physical phenomena.
Journal of Mathematical Physics, Volume 62, Issue 11, November 2021. <br/>In this work, we study the existence of a positive solution for a class of quasilinear Schrödinger equations involving a potential that behaves like a periodic function at infinity and the nonlinear term may exhibit critical exponential growth. In order to prove our main result, we combine minimax methods with a version of the Trudinger–Moser inequality. These equations appear naturally in mathematical physics and have been derived as models of several physical phenomena.
Asymptotically periodic quasilinear Schrödinger equations with critical exponential growth
10.1063/5.0053794
Journal of Mathematical Physics
20211117T11:04:14Z
© 2021 Author(s).
Uberlandio B. Severo
Diogo de S. Germano

On the attraction–repulsion chemotaxis system with volumefilling effect
https://aip.scitation.org/doi/10.1063/5.0051198?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/62/11">Volume 62, Issue 11</a>, November 2021. <br/>In this paper, we consider the attraction–repulsion Keller–Segel system with volumefilling effect under homogeneous Neumann boundary conditions in a smooth boundary bounded domain with n ≥ 2. We study the global existence and asymptotic behavior of the classical solution to the system in various ranges of parameter values.
Journal of Mathematical Physics, Volume 62, Issue 11, November 2021. <br/>In this paper, we consider the attraction–repulsion Keller–Segel system with volumefilling effect under homogeneous Neumann boundary conditions in a smooth boundary bounded domain with n ≥ 2. We study the global existence and asymptotic behavior of the classical solution to the system in various ranges of parameter values.
On the attraction–repulsion chemotaxis system with volumefilling effect
10.1063/5.0051198
Journal of Mathematical Physics
20211122T11:39:52Z
© 2021 Author(s).
Hongyun Peng

An index for twodimensional SPT states
https://aip.scitation.org/doi/10.1063/5.0055704?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/62/11">Volume 62, Issue 11</a>, November 2021. <br/>We define an index for 2D Ginvariant invertible states of bosonic lattice systems in the thermodynamic limit for a finite symmetry group G with a unitary action. We show that this index is an invariant of the symmetry protected phase.
Journal of Mathematical Physics, Volume 62, Issue 11, November 2021. <br/>We define an index for 2D Ginvariant invertible states of bosonic lattice systems in the thermodynamic limit for a finite symmetry group G with a unitary action. We show that this index is an invariant of the symmetry protected phase.
An index for twodimensional SPT states
10.1063/5.0055704
Journal of Mathematical Physics
20211101T11:04:40Z
© 2021 Author(s).
Nikita Sopenko

An algebraic approach of nonselfadjoint Hamiltonians in Krein spaces
https://aip.scitation.org/doi/10.1063/5.0061797?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/62/11">Volume 62, Issue 11</a>, November 2021. <br/>Through our series of studies, we have constructed some physical operators such as nonselfadjoint Hamiltonians H, lowering operators A, and raising operators B and their adjoint H†, A†, and B† from generalized Riesz systems. However, we cannot consider the [math]algebraic structure of their operators because even the sum H + H† is not welldefined. Our purpose of this paper is to introduce the [math]algebra structure of all their operators by defining a certain Krein space.
Journal of Mathematical Physics, Volume 62, Issue 11, November 2021. <br/>Through our series of studies, we have constructed some physical operators such as nonselfadjoint Hamiltonians H, lowering operators A, and raising operators B and their adjoint H†, A†, and B† from generalized Riesz systems. However, we cannot consider the [math]algebraic structure of their operators because even the sum H + H† is not welldefined. Our purpose of this paper is to introduce the [math]algebra structure of all their operators by defining a certain Krein space.
An algebraic approach of nonselfadjoint Hamiltonians in Krein spaces
10.1063/5.0061797
Journal of Mathematical Physics
20211101T09:58:47Z
© 2021 Author(s).
Hiroshi Inoue

Manifold topology, observables, and gauge group
https://aip.scitation.org/doi/10.1063/5.0048336?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/62/11">Volume 62, Issue 11</a>, November 2021. <br/>The relation between the manifold topology, observables, and gauge group is clarified on the basis of the classification of the representations of the algebra of observables associated with positions and displacements on the manifold. The guiding, physically motivated, principles are (i) locality, i.e., the generating role of the algebras localized in small, topologically trivial, regions, (ii) diffeomorphism covariance, which guarantees the intrinsic character of the analysis, and (iii) the exclusion of additional local degrees of freedom with respect to the Schrödinger representation. The locally normal representations of the resulting observable algebra are classified by unitary representations of the fundamental group of the manifold, which actually generate an observable, “topological,” subalgebra. The result is confronted with the standard approach based on the introduction of the universal covering [math] of [math] and on the decomposition of [math] according to the spectrum of the fundamental group, which plays the role of a gauge group. It is shown that in this way one obtains all the representations of the observables iff the fundamental group is amenable. The implications on the observability of the permutation group in particle statistics are discussed.
Journal of Mathematical Physics, Volume 62, Issue 11, November 2021. <br/>The relation between the manifold topology, observables, and gauge group is clarified on the basis of the classification of the representations of the algebra of observables associated with positions and displacements on the manifold. The guiding, physically motivated, principles are (i) locality, i.e., the generating role of the algebras localized in small, topologically trivial, regions, (ii) diffeomorphism covariance, which guarantees the intrinsic character of the analysis, and (iii) the exclusion of additional local degrees of freedom with respect to the Schrödinger representation. The locally normal representations of the resulting observable algebra are classified by unitary representations of the fundamental group of the manifold, which actually generate an observable, “topological,” subalgebra. The result is confronted with the standard approach based on the introduction of the universal covering [math] of [math] and on the decomposition of [math] according to the spectrum of the fundamental group, which plays the role of a gauge group. It is shown that in this way one obtains all the representations of the observables iff the fundamental group is amenable. The implications on the observability of the permutation group in particle statistics are discussed.
Manifold topology, observables, and gauge group
10.1063/5.0048336
Journal of Mathematical Physics
20211119T11:21:28Z
© 2021 Author(s).
G. Morchio
F. Strocchi

Rigorous computerassisted bounds on the period doubling renormalization fixed point and eigenfunctions in maps with critical point of degree 4
https://aip.scitation.org/doi/10.1063/5.0054823?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/62/11">Volume 62, Issue 11</a>, November 2021. <br/>We gain tight rigorous bounds on the renormalization fixed point for period doubling in families of unimodal maps with degree 4 critical point. We use a contraction mapping argument to bound essential eigenfunctions and eigenvalues for the linearization of the operator and for the operator controlling the scaling of added noise. Multiprecision arithmetic with rigorous directed rounding is used to bound operations in a space of analytic functions yielding tight bounds on power series coefficients and universal constants to over 320 significant figures.
Journal of Mathematical Physics, Volume 62, Issue 11, November 2021. <br/>We gain tight rigorous bounds on the renormalization fixed point for period doubling in families of unimodal maps with degree 4 critical point. We use a contraction mapping argument to bound essential eigenfunctions and eigenvalues for the linearization of the operator and for the operator controlling the scaling of added noise. Multiprecision arithmetic with rigorous directed rounding is used to bound operations in a space of analytic functions yielding tight bounds on power series coefficients and universal constants to over 320 significant figures.
Rigorous computerassisted bounds on the period doubling renormalization fixed point and eigenfunctions in maps with critical point of degree 4
10.1063/5.0054823
Journal of Mathematical Physics
20211103T10:07:59Z
© 2021 Author(s).
Andrew D. Burbanks
Andrew H. Osbaldestin
Judi A. Thurlby

Random invariant manifolds of stochastic evolution equations driven by Gaussian and nonGaussian noises
https://aip.scitation.org/doi/10.1063/5.0065640?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/62/11">Volume 62, Issue 11</a>, November 2021. <br/>The goal of this work is to compare the invariant manifold of the stochastic evolution equation driven by an αstable process with the invariant manifold of the stochastic evolution equation forced by Brownian motion. First, we show that the solution of the Marcus stochastic evolution equation driven by a type of αstable process converges to the solution of the related Stratonovich stochastic evolution equation forced by Brownian motion. Then, we study the invariant stable manifold of the stochastic evolution equation driven by an αstable process. Finally, we prove that the invariant stable manifold of the Marcus stochastic evolution equation driven by an αstable process converges in probability to the invariant stable manifold of the Stratonovich stochastic evolution equation forced by Brownian motion. The connection between the random dynamical system driven by nonGaussian noise and the random dynamical system driven by Gaussian noise is established.
Journal of Mathematical Physics, Volume 62, Issue 11, November 2021. <br/>The goal of this work is to compare the invariant manifold of the stochastic evolution equation driven by an αstable process with the invariant manifold of the stochastic evolution equation forced by Brownian motion. First, we show that the solution of the Marcus stochastic evolution equation driven by a type of αstable process converges to the solution of the related Stratonovich stochastic evolution equation forced by Brownian motion. Then, we study the invariant stable manifold of the stochastic evolution equation driven by an αstable process. Finally, we prove that the invariant stable manifold of the Marcus stochastic evolution equation driven by an αstable process converges in probability to the invariant stable manifold of the Stratonovich stochastic evolution equation forced by Brownian motion. The connection between the random dynamical system driven by nonGaussian noise and the random dynamical system driven by Gaussian noise is established.
Random invariant manifolds of stochastic evolution equations driven by Gaussian and nonGaussian noises
10.1063/5.0065640
Journal of Mathematical Physics
20211103T10:07:57Z
© 2021 Author(s).
Xianming Liu

Multiple periodic solutions for an asymptotically linear wave equation with xdependent coefficients
https://aip.scitation.org/doi/10.1063/5.0048205?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/62/11">Volume 62, Issue 11</a>, November 2021. <br/>In this paper, we investigate the existence of multiple nontrivial periodic solutions for an asymptotically linear wave equation with xdependent coefficients. Such a mathematical model can be derived from the forced vibrations of a nonhomogeneous string and propagation of seismic waves in nonisotropic media. By constructing a suitable function space, we characterize the problem as a variational problem, and then we prove that there are at least three nontrivial periodic solutions via variational methods.
Journal of Mathematical Physics, Volume 62, Issue 11, November 2021. <br/>In this paper, we investigate the existence of multiple nontrivial periodic solutions for an asymptotically linear wave equation with xdependent coefficients. Such a mathematical model can be derived from the forced vibrations of a nonhomogeneous string and propagation of seismic waves in nonisotropic media. By constructing a suitable function space, we characterize the problem as a variational problem, and then we prove that there are at least three nontrivial periodic solutions via variational methods.
Multiple periodic solutions for an asymptotically linear wave equation with xdependent coefficients
10.1063/5.0048205
Journal of Mathematical Physics
20211103T10:07:57Z
© 2021 Author(s).
Hui Wei
Mu Ma
Shuguan Ji

New methods of isochrone mechanics
https://aip.scitation.org/doi/10.1063/5.0056957?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/62/11">Volume 62, Issue 11</a>, November 2021. <br/>Isochrone potentials are spherically symmetric potentials within which a particle orbits with a radial period that is independent of its angular momentum. Whereas all previous results on isochrone mechanics have been established using classical analysis and geometry, in this article, we revisit the isochrone problem of motion using tools from Hamiltonian dynamical systems. In particular, we (1) solve the problem of motion using a welladapted set of angleaction coordinates and generalize the notion of eccentric anomaly to all isochrone orbits, and (2) we construct the Birkhoff normal form for a particle orbiting a generic radial potential and examine its Birkhoff invariants to prove that the class of isochrone potentials is in correspondence with parabolas in the plane. Along the way, several fundamental results of celestial mechanics, such as the Bertrand theorem or the Kepler equation and laws, are obtained as special cases of more general properties characterizing isochrone mechanics.
Journal of Mathematical Physics, Volume 62, Issue 11, November 2021. <br/>Isochrone potentials are spherically symmetric potentials within which a particle orbits with a radial period that is independent of its angular momentum. Whereas all previous results on isochrone mechanics have been established using classical analysis and geometry, in this article, we revisit the isochrone problem of motion using tools from Hamiltonian dynamical systems. In particular, we (1) solve the problem of motion using a welladapted set of angleaction coordinates and generalize the notion of eccentric anomaly to all isochrone orbits, and (2) we construct the Birkhoff normal form for a particle orbiting a generic radial potential and examine its Birkhoff invariants to prove that the class of isochrone potentials is in correspondence with parabolas in the plane. Along the way, several fundamental results of celestial mechanics, such as the Bertrand theorem or the Kepler equation and laws, are obtained as special cases of more general properties characterizing isochrone mechanics.
New methods of isochrone mechanics
10.1063/5.0056957
Journal of Mathematical Physics
20211105T09:45:00Z
© 2021 Author(s).
Paul Ramond
Jérôme Perez

Dynamical invariants for timedependent real and complex Hamiltonian systems
https://aip.scitation.org/doi/10.1063/5.0061119?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/62/11">Volume 62, Issue 11</a>, November 2021. <br/>The Struckmeier and Riedel (SR) approach is extended in real space to isolate dynamical invariants for one and twodimensional timedependent Hamiltonian systems. We further develop the SRformalism in [math] complex phase space characterized by z = x + iy and [math] and construct invariants for some physical systems. The obtained quadratic invariants contain a function f2(t), which is a solution of a linear thirdorder differential equation. We further explore this approach into extended complex phase space defined by x = x1 + ip2 and p = p1 + ix2 to construct a quadratic invariant for a timedependent quadratic potential. The derived invariants may be of interest in the realm of numerical simulations of explicitly timedependent Hamiltonian systems.
Journal of Mathematical Physics, Volume 62, Issue 11, November 2021. <br/>The Struckmeier and Riedel (SR) approach is extended in real space to isolate dynamical invariants for one and twodimensional timedependent Hamiltonian systems. We further develop the SRformalism in [math] complex phase space characterized by z = x + iy and [math] and construct invariants for some physical systems. The obtained quadratic invariants contain a function f2(t), which is a solution of a linear thirdorder differential equation. We further explore this approach into extended complex phase space defined by x = x1 + ip2 and p = p1 + ix2 to construct a quadratic invariant for a timedependent quadratic potential. The derived invariants may be of interest in the realm of numerical simulations of explicitly timedependent Hamiltonian systems.
Dynamical invariants for timedependent real and complex Hamiltonian systems
10.1063/5.0061119
Journal of Mathematical Physics
20211108T11:12:40Z
© 2021 Author(s).
Narender Kumar
S. B. Bhardwaj
Vinod Kumar
Ram Mehar Singh
Fakir Chand

On the number of equilibria balancing Newtonian point masses with a central force
https://aip.scitation.org/doi/10.1063/5.0060237?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/62/11">Volume 62, Issue 11</a>, November 2021. <br/>We consider the critical points (equilibria) of a planar potential generated by n Newtonian point masses augmented with a quadratic term (such as arises from a centrifugal effect). Particular cases of this problem have been considered previously in studies of the circularrestricted nbody problem. We show that the number of equilibria is finite for a generic set of parameters, and we establish estimates for the number of equilibria. We prove that the number of equilibria is bounded below by n + 1, and we provide examples to show that this lower bound is sharp. We prove an upper bound on the number of equilibria that grows exponentially in n. In order to establish a lower bound on the maximum number of equilibria, we analyze a class of examples, referred to as “ring configurations,” consisting of n − 1 equal masses positioned at vertices of a regular polygon with an additional mass located at the center. Previous numerical observations indicate that these configurations can produce as many as 5n − 5 equilibria. We verify analytically that the ring configuration has at least 5n − 5 equilibria when the central mass is sufficiently small. We conjecture that the maximum number of equilibria grows linearly with the number of point masses. We also discuss some mathematical similarities to other equilibrium problems in mathematical physics, namely, Maxwell’s problem from electrostatics and the image counting problem from gravitational lensing.
Journal of Mathematical Physics, Volume 62, Issue 11, November 2021. <br/>We consider the critical points (equilibria) of a planar potential generated by n Newtonian point masses augmented with a quadratic term (such as arises from a centrifugal effect). Particular cases of this problem have been considered previously in studies of the circularrestricted nbody problem. We show that the number of equilibria is finite for a generic set of parameters, and we establish estimates for the number of equilibria. We prove that the number of equilibria is bounded below by n + 1, and we provide examples to show that this lower bound is sharp. We prove an upper bound on the number of equilibria that grows exponentially in n. In order to establish a lower bound on the maximum number of equilibria, we analyze a class of examples, referred to as “ring configurations,” consisting of n − 1 equal masses positioned at vertices of a regular polygon with an additional mass located at the center. Previous numerical observations indicate that these configurations can produce as many as 5n − 5 equilibria. We verify analytically that the ring configuration has at least 5n − 5 equilibria when the central mass is sufficiently small. We conjecture that the maximum number of equilibria grows linearly with the number of point masses. We also discuss some mathematical similarities to other equilibrium problems in mathematical physics, namely, Maxwell’s problem from electrostatics and the image counting problem from gravitational lensing.
On the number of equilibria balancing Newtonian point masses with a central force
10.1063/5.0060237
Journal of Mathematical Physics
20211123T11:09:06Z
© 2021 Author(s).
Nickolas Arustamyan
Christopher Cox
Erik Lundberg
Sean Perry
Zvi Rosen

Critical fluctuations in renewal models of statistical mechanics
https://aip.scitation.org/doi/10.1063/5.0049786?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/62/11">Volume 62, Issue 11</a>, November 2021. <br/>We investigate the sharp asymptotic behavior at criticality of the large fluctuations of extensive observables in renewal models of statistical mechanics, such as the Poland–Scheraga model of DNA denaturation, the Fisher–Felderhof model of fluids, the Wako–Saitô–Muñoz–Eaton model of protein folding, and the Tokar–Dreyssé model of strained epitaxy. These models amount to Gibbs changes of measure of a classical renewal process and can be identified with a constrained pinning model of polymers. The extensive observables that enter the thermodynamic description turn out to be cumulative rewards corresponding to deterministic rewards that are uniquely determined by the waiting time and grow no faster than it. The probability decay with the system size of their fluctuations switches from exponential to subexponential at criticality, which is a regime corresponding to a discontinuous pinning–depinning phase transition. We describe such decay by proposing a precise large deviation principle under the assumption that the subexponential correction term to the waiting time distribution is regularly varying. This principle is, in particular, used to characterize the fluctuations of the number of renewals, which measures the DNAbound monomers in the Poland–Scheraga model, the particles in the Fisher–Felderhof model and the Tokar–Dreyssé model, and the native peptide bonds in the Wako–Saitô–Muñoz–Eaton model.
Journal of Mathematical Physics, Volume 62, Issue 11, November 2021. <br/>We investigate the sharp asymptotic behavior at criticality of the large fluctuations of extensive observables in renewal models of statistical mechanics, such as the Poland–Scheraga model of DNA denaturation, the Fisher–Felderhof model of fluids, the Wako–Saitô–Muñoz–Eaton model of protein folding, and the Tokar–Dreyssé model of strained epitaxy. These models amount to Gibbs changes of measure of a classical renewal process and can be identified with a constrained pinning model of polymers. The extensive observables that enter the thermodynamic description turn out to be cumulative rewards corresponding to deterministic rewards that are uniquely determined by the waiting time and grow no faster than it. The probability decay with the system size of their fluctuations switches from exponential to subexponential at criticality, which is a regime corresponding to a discontinuous pinning–depinning phase transition. We describe such decay by proposing a precise large deviation principle under the assumption that the subexponential correction term to the waiting time distribution is regularly varying. This principle is, in particular, used to characterize the fluctuations of the number of renewals, which measures the DNAbound monomers in the Poland–Scheraga model, the particles in the Fisher–Felderhof model and the Tokar–Dreyssé model, and the native peptide bonds in the Wako–Saitô–Muñoz–Eaton model.
Critical fluctuations in renewal models of statistical mechanics
10.1063/5.0049786
Journal of Mathematical Physics
20211110T12:52:43Z
© 2021 Author(s).
Marco Zamparo

Uncertainty principles for the Fourier and the shorttime Fourier transforms
https://aip.scitation.org/doi/10.1063/5.0047191?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/62/11">Volume 62, Issue 11</a>, November 2021. <br/>The aim of this paper is to establish a few uncertainty principles for the Fourier and the shorttime Fourier transforms. In addition, we discuss an analog of the Donoho–Stark uncertainty principle and provide some estimates for the size of the essential support of the shorttime Fourier transform.
Journal of Mathematical Physics, Volume 62, Issue 11, November 2021. <br/>The aim of this paper is to establish a few uncertainty principles for the Fourier and the shorttime Fourier transforms. In addition, we discuss an analog of the Donoho–Stark uncertainty principle and provide some estimates for the size of the essential support of the shorttime Fourier transform.
Uncertainty principles for the Fourier and the shorttime Fourier transforms
10.1063/5.0047191
Journal of Mathematical Physics
20211101T11:04:41Z
© 2021 Author(s).
Anirudha Poria

Contractivity properties of Ornstein–Uhlenbeck semigroup for mixed qAraki–Woods von Neumann algebras
https://aip.scitation.org/doi/10.1063/5.0057987?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/62/11">Volume 62, Issue 11</a>, November 2021. <br/>We study certain nontracial von Neumann algebras generated by some selfadjoint operators satisfying mixed qcommutation relations. Such algebras are discussed in the work of Bikram et al. [“Mixed qdeformed ArakiWoods von Neumann algebras,” (submitted)]. We prove the analog of Nelson’s hypercontractivity inequality for the mixed qOrnstein–Uhlenbeck semigroup. We also show that the mixed qOrnstein–Uhlenbeck semigroup is ultracontractive.
Journal of Mathematical Physics, Volume 62, Issue 11, November 2021. <br/>We study certain nontracial von Neumann algebras generated by some selfadjoint operators satisfying mixed qcommutation relations. Such algebras are discussed in the work of Bikram et al. [“Mixed qdeformed ArakiWoods von Neumann algebras,” (submitted)]. We prove the analog of Nelson’s hypercontractivity inequality for the mixed qOrnstein–Uhlenbeck semigroup. We also show that the mixed qOrnstein–Uhlenbeck semigroup is ultracontractive.
Contractivity properties of Ornstein–Uhlenbeck semigroup for mixed qAraki–Woods von Neumann algebras
10.1063/5.0057987
Journal of Mathematical Physics
20211101T09:58:46Z
© 2021 Author(s).
Panchugopal Bikram
Rajeeb R. Mohanta

The Robin problem on rectangles
https://aip.scitation.org/doi/10.1063/5.0061763?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/62/11">Volume 62, Issue 11</a>, November 2021. <br/>We study the statistics and the arithmetic properties of the Robin spectrum of a rectangle. A number of results are obtained for the multiplicities in the spectrum depending on the Diophantine nature of the aspect ratio. In particular, it is shown that for the square, unlike the case of Neumann eigenvalues where there are unbounded multiplicities of arithmetic origin, there are no multiplicities in the Robin spectrum for a sufficiently small (but nonzero) Robin parameter except a systematic symmetry. In addition, uniform lower and upper bounds are established for the Robin–Neumann gaps in terms of their limiting mean spacing. Finally, the pair correlation function of the Robin spectrum on a Diophantine rectangle is shown to be Poissonian.
Journal of Mathematical Physics, Volume 62, Issue 11, November 2021. <br/>We study the statistics and the arithmetic properties of the Robin spectrum of a rectangle. A number of results are obtained for the multiplicities in the spectrum depending on the Diophantine nature of the aspect ratio. In particular, it is shown that for the square, unlike the case of Neumann eigenvalues where there are unbounded multiplicities of arithmetic origin, there are no multiplicities in the Robin spectrum for a sufficiently small (but nonzero) Robin parameter except a systematic symmetry. In addition, uniform lower and upper bounds are established for the Robin–Neumann gaps in terms of their limiting mean spacing. Finally, the pair correlation function of the Robin spectrum on a Diophantine rectangle is shown to be Poissonian.
The Robin problem on rectangles
10.1063/5.0061763
Journal of Mathematical Physics
20211101T09:58:45Z
© 2021 Author(s).
Zeév Rudnick
Igor Wigman

Tight conformation of 2bridge knots using superhelices
https://aip.scitation.org/doi/10.1063/5.0059298?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/62/11">Volume 62, Issue 11</a>, November 2021. <br/>The ropelength is a mathematical quantity that regulates the tightness of flexible strands in the threedimensional space. The superhelical conformation of long twisted strands is known to be more efficient in terms of ropelength compared with the circular double helical conformation. In this paper, we present a conformation of 2bridge knots by using ropelengthminimizing superhelical curves and derive an upper bound on the ropelength of 2bridge knots. Our superhelical model of 2bridge knots is shown to be more efficient than the standard double helical one if the iterative twisted parts are long enough.
Journal of Mathematical Physics, Volume 62, Issue 11, November 2021. <br/>The ropelength is a mathematical quantity that regulates the tightness of flexible strands in the threedimensional space. The superhelical conformation of long twisted strands is known to be more efficient in terms of ropelength compared with the circular double helical conformation. In this paper, we present a conformation of 2bridge knots by using ropelengthminimizing superhelical curves and derive an upper bound on the ropelength of 2bridge knots. Our superhelical model of 2bridge knots is shown to be more efficient than the standard double helical one if the iterative twisted parts are long enough.
Tight conformation of 2bridge knots using superhelices
10.1063/5.0059298
Journal of Mathematical Physics
20211101T09:58:49Z
© 2021 Author(s).
Youngsik Huh
Hyoungjun Kim
Seungsang Oh

Angularradial integrability of Coulomblike potentials in Dirac equations
https://aip.scitation.org/doi/10.1063/5.0055250?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/62/11">Volume 62, Issue 11</a>, November 2021. <br/>We consider the Dirac equation, written in polar formalism, in the presence of general Coulomblike potentials, that is, potentials arising from the time component of the vector potential and depending only on the radial coordinate, in order to study the conditions of integrability, given as some specific form for the solution: we find that the angular dependence can always be integrated, while the radial dependence is reduced to finding the solution of a Riccati equation so that it is always possible, at least in principle. We exhibit the known case of the Coulomb potential and one special generalization as examples to show the versatility of the method.
Journal of Mathematical Physics, Volume 62, Issue 11, November 2021. <br/>We consider the Dirac equation, written in polar formalism, in the presence of general Coulomblike potentials, that is, potentials arising from the time component of the vector potential and depending only on the radial coordinate, in order to study the conditions of integrability, given as some specific form for the solution: we find that the angular dependence can always be integrated, while the radial dependence is reduced to finding the solution of a Riccati equation so that it is always possible, at least in principle. We exhibit the known case of the Coulomb potential and one special generalization as examples to show the versatility of the method.
Angularradial integrability of Coulomblike potentials in Dirac equations
10.1063/5.0055250
Journal of Mathematical Physics
20211101T09:58:48Z
© 2021 Author(s).
Luca Fabbri
Andre G. Campos

Spectral type of a class of random Jacobi operators
https://aip.scitation.org/doi/10.1063/5.0055683?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/62/11">Volume 62, Issue 11</a>, November 2021. <br/>In this paper, we use the generalized Prüfer variables to study the spectral type of a class of random Jacobi operators [math] in which the decay speed of the parameters an is n−α for some α > 0. We will show that the operator has an absolutely continuous spectrum for [math], a pure point spectrum for [math], and a transition from a singular continuous spectrum to a pure point spectrum in [math].
Journal of Mathematical Physics, Volume 62, Issue 11, November 2021. <br/>In this paper, we use the generalized Prüfer variables to study the spectral type of a class of random Jacobi operators [math] in which the decay speed of the parameters an is n−α for some α > 0. We will show that the operator has an absolutely continuous spectrum for [math], a pure point spectrum for [math], and a transition from a singular continuous spectrum to a pure point spectrum in [math].
Spectral type of a class of random Jacobi operators
10.1063/5.0055683
Journal of Mathematical Physics
20211102T10:30:19Z
© 2021 Author(s).
Zhengqi Fu
Xiong Li

Erratum: “Dispersion relations for the timefractional Cattaneo–Maxwell heat equation” [J. Math. Phys. 59, 013506 (2018)]
https://aip.scitation.org/doi/10.1063/5.0075270?af=R&feed=mostrecent
Journal of Mathematical Physics, <a href="https://aip.scitation.org/toc/jmp/62/11">Volume 62, Issue 11</a>, November 2021. <br/>
Journal of Mathematical Physics, Volume 62, Issue 11, November 2021. <br/>
Erratum: “Dispersion relations for the timefractional Cattaneo–Maxwell heat equation” [J. Math. Phys. 59, 013506 (2018)]
10.1063/5.0075270
Journal of Mathematical Physics
20211105T09:45:01Z
© 2021 Author(s).
Andrea Giusti