Journal of Mathematical Physics: Most Cited articles
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Most cited articles from Journal of Mathematical Physicsen-usTue, 30 Nov 2021 12:45:07 GMTAtypon® Literatum™http://validator.w3.org/feed/docs/rss2.html10080Journal of Mathematical Physics: Most Cited articleshttps://aip.scitation.org/na101/home/literatum/publisher/aip/journals/covergifs/jmp/cover.jpg
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Completely positive dynamical semigroups of N‐level systems
https://aip.scitation.org/doi/10.1063/1.522979?feed=most-cited
https://aip.scitation.org/doi/10.1063/1.522979?feed=most-citedWe establish the general form of the generator of a completely positive dynamical semigroup of an N‐level quantum system, and we apply the result to derive explicit inequalities among the physical parameters characterizing the Markovian evolution of a 2‐level system.Vittorio Gorini, Andrzej Kossakowski, and E. C. G. SudarshanThu, 28 Aug 2008 07:00:00 GMTThe Einstein Tensor and Its Generalizations
https://aip.scitation.org/doi/10.1063/1.1665613?feed=most-cited
https://aip.scitation.org/doi/10.1063/1.1665613?feed=most-citedThe Einstein tensor Gij is symmetric, divergence free, and a concomitant of the metric tensor gab together with its first two derivatives. In this paper all tensors of valency two with these properties are displayed explicitly. The number of independent tensors of this type depends crucially on the dimension of the space, and, in the four dimensional case, the only tensors with these properties are the metric and the Einstein tensors.David LovelockTue, 28 Oct 2003 08:00:00 GMTThe world as a hologram
https://aip.scitation.org/doi/10.1063/1.531249?feed=most-cited
https://aip.scitation.org/doi/10.1063/1.531249?feed=most-citedAccording to ’t Hooft the combination of quantum mechanics and gravity requires the three‐dimensional world to be an image of data that can be stored on a two‐dimensional projection much like a holographic image. The two‐dimensional description only requires one discrete degree of freedom per Planck area and yet it is rich enough to describe all three‐dimensional phenomena. After outlining ’t Hooft’s proposal we give a preliminary informal description of how it may be implemented. One finds a basic requirement that particles must grow in size as their momenta are increased far above the Planck scale. The consequences for high‐energyLeonard SusskindThu, 04 Jun 1998 07:00:00 GMTRandom Walks on Lattices. II
https://aip.scitation.org/doi/10.1063/1.1704269?feed=most-cited
https://aip.scitation.org/doi/10.1063/1.1704269?feed=most-citedFormulas are obtained for the mean first passage times (as well as their dispersion) in random walks from the origin to an arbitrary lattice point on a periodic space lattice with periodic boundary conditions. Generally this time is proportional to the number of lattice points. The number of distinct points visited after n steps on a k‐dimensional lattice (with k ≥ 3) when n is large is a1n + a2n½ + a3 + a4n−½ + …. The constants a1 − a4 have been obtained for walks on a simple cubic lattice when k = 3 and a1 and a2 areElliott W. Montroll and George H. WeissWed, 22 Dec 2004 08:00:00 GMTTime‐Dependent Statistics of the Ising Model
https://aip.scitation.org/doi/10.1063/1.1703954?feed=most-cited
https://aip.scitation.org/doi/10.1063/1.1703954?feed=most-citedThe individual spins of the Ising model are assumed to interact with an external agency (e.g., a heat reservoir) which causes them to change their states randomly with time. Coupling between the spins is introduced through the assumption that the transition probabilities for any one spin depend on the values of the neighboring spins. This dependence is determined, in part, by the detailed balancing condition obeyed by the equilibrium state of the model. The Markoff process which describes the spin functions is analyzed in detail for the case of a closed N‐member chain. The expectation values of the individual spinsRoy J. GlauberWed, 22 Dec 2004 08:00:00 GMTPseudo-Hermiticity versus PT symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
https://aip.scitation.org/doi/10.1063/1.1418246?feed=most-cited
https://aip.scitation.org/doi/10.1063/1.1418246?feed=most-citedWe introduce the notion of pseudo-Hermiticity and show that every Hamiltonian with a real spectrum is pseudo-Hermitian. We point out that all the -symmetric non-Hermitian Hamiltonians studied in the literature belong to the class of pseudo-Hermitian Hamiltonians, and argue that the basic structure responsible for the particular spectral properties of these Hamiltonians is their pseudo-Hermiticity. We explore the basic properties of general pseudo-Hermitian Hamiltonians, develop pseudosupersymmetric quantum mechanics, and study some concrete examples, namely the Hamiltonian of the two-component Wheeler–DeWitt equation for the FRW-models coupled to a real massive scalar field and a class of pseudo-Hermitian Hamiltonians with a realAli MostafazadehTue, 18 Dec 2001 08:00:00 GMTAn Exact Quantum Theory of the Time‐Dependent Harmonic Oscillator and of a Charged Particle in a Time‐Dependent Electromagnetic Field
https://aip.scitation.org/doi/10.1063/1.1664991?feed=most-cited
https://aip.scitation.org/doi/10.1063/1.1664991?feed=most-citedThe theory of explicitly time‐dependent invariants is developed for quantum systems whose Hamiltonians are explicitly time dependent. The central feature of the discussion is the derivation of a simple relation between eigenstates of such an invariant and solutions of the Schrödinger equation. As a specific well‐posed application of the general theory, the case of a general Hamiltonian which settles into constant operators in the sufficiently remote past and future is treated and, in particular, the transition amplitude connecting any initial state in the remote past to any final state in the remote future is calculated in terms of eigenstates ofH. R. Lewis Jr. and W. B. RiesenfeldTue, 04 Nov 2003 08:00:00 GMTAn Approach to Gravitational Radiation by a Method of Spin Coefficients
https://aip.scitation.org/doi/10.1063/1.1724257?feed=most-cited
https://aip.scitation.org/doi/10.1063/1.1724257?feed=most-citedA new approach to general relativity by means of a tetrad or spinor formalism is presented. The essential feature of this approach is the consistent use of certain complex linear combinations of Ricci rotation coefficients which give, in effect, the spinor affine connection. It is applied to two problems in radiation theory; a concise proof of a theorem of Goldberg and Sachs and a description of the asymptotic behavior of the Riemann tensor and metric tensor, for outgoing gravitational radiation.Ezra Newman and Roger PenroseWed, 22 Dec 2004 08:00:00 GMTTopological quantum memory
https://aip.scitation.org/doi/10.1063/1.1499754?feed=most-cited
https://aip.scitation.org/doi/10.1063/1.1499754?feed=most-citedWe analyze surface codes, the topological quantum error-correcting codes introduced by Kitaev. In these codes, qubits are arranged in a two-dimensional array on a surface of nontrivial topology, and encoded quantum operations are associated with nontrivial homology cycles of the surface. We formulate protocols for error recovery, and study the efficacy of these protocols. An order-disorder phase transition occurs in this system at a nonzero critical value of the error rate; if the error rate is below the critical value (the accuracy threshold), encoded information can be protected arbitrarily well in the limit of a large code block. This phaseEric Dennis, Alexei Kitaev, Andrew Landahl, and John PreskillTue, 20 Aug 2002 07:00:00 GMTThe Zeno’s paradox in quantum theory
https://aip.scitation.org/doi/10.1063/1.523304?feed=most-cited
https://aip.scitation.org/doi/10.1063/1.523304?feed=most-citedWe seek a quantum‐theoretic expression for the probability that an unstable particle prepared initially in a well defined state ρ will be found to decay sometime during a given interval. It is argued that probabilities like this which pertain to continuous monitoring possess operational meaning. A simple natural approach to this problem leads to the conclusion that an unstable particle which is continuously observed to see whether it decays will never be found to decay!. Since recording the track of an unstable particle (which can be distinguished from its decay products) approximately realizes such continuous observations, the above conclusion seemsB. Misra and E. C. G. SudarshanTue, 26 Aug 2008 07:00:00 GMTTwo‐dimensional lumps in nonlinear dispersive systems
https://aip.scitation.org/doi/10.1063/1.524208?feed=most-cited
https://aip.scitation.org/doi/10.1063/1.524208?feed=most-citedTwo‐dimensional lump solutions which decay to a uniform state in all directions are obtained for the Kadomtsev–Petviashvili and a two‐dimensional nonlinear Schrödinger type equation. The amplitude of these solutions is rational in its independent variables. These solutions are constructed by taking a ’’long wave’’ limit of the corresponding N‐soliton solutions obtained by direct methods. The solutions describing multiple collisions of lumps are also presented.J. Satsuma and M. J. AblowitzTue, 29 Jul 2008 07:00:00 GMTBrownian Motion of a Quantum Oscillator
https://aip.scitation.org/doi/10.1063/1.1703727?feed=most-cited
https://aip.scitation.org/doi/10.1063/1.1703727?feed=most-citedAn action principle technique for the direct computation of expectation values is described and illustrated in detail by a special physical example, the effect on an oscillator of another physical system. This simple problem has the advantage of combining immediate physical applicability (e.g., resistive damping or maser amplification of a single electromagnetic cavity mode) with a significant idealization of the complex problems encountered in many‐particle and relativistic field theory. Successive sections contain discussions of the oscillator subjected to external forces, the oscillator loosely coupled to the external system, an improved treatment of this problem and, finally, there is a briefJulian SchwingerWed, 22 Dec 2004 08:00:00 GMTStatistical Theory of the Energy Levels of Complex Systems. I
https://aip.scitation.org/doi/10.1063/1.1703773?feed=most-cited
https://aip.scitation.org/doi/10.1063/1.1703773?feed=most-citedNew kinds of statistical ensemble are defined, representing a mathematical idealization of the notion of ``all physical systems with equal probability.'' Three such ensembles are studied in detail, based mathematically upon the orthogonal, unitary, and symplectic groups. The orthogonal ensemble is relevant in most practical circumstances, the unitary ensemble applies only when time‐reversal invariance is violated, and the symplectic ensemble applies only to odd‐spin systems without rotational symmetry. The probability‐distributions for the energy levels are calculated in the three cases. Repulsion between neighboring levels is strongest in the symplectic ensemble and weakest in the orthogonal ensemble. An exact mathematical correspondenceFreeman J. DysonWed, 22 Dec 2004 08:00:00 GMTSymmetric informationally complete quantum measurements
https://aip.scitation.org/doi/10.1063/1.1737053?feed=most-cited
https://aip.scitation.org/doi/10.1063/1.1737053?feed=most-citedWe consider the existence in arbitrary finite dimensions of a positive operator valued measure (POVM) comprised of rank-one operators all of whose operator inner products are equal. Such a set is called a “symmetric, informationally complete” POVM (SIC–POVM) and is equivalent to a set of equiangular lines in SIC–POVMs are relevant for quantum state tomography, quantum cryptography, and foundational issues in quantum mechanics. We construct SIC–POVMs in dimensions two, three, and four. We further conjecture that a particular kind of group-covariant SIC–POVM exists in arbitrary dimensions, providing numerical results up to dimension 45 to bolster this claim.Joseph M. Renes, Robin Blume-Kohout, A. J. Scott, and Carlton M. CavesThu, 06 May 2004 07:00:00 GMTPT-symmetric quantum mechanics
https://aip.scitation.org/doi/10.1063/1.532860?feed=most-cited
https://aip.scitation.org/doi/10.1063/1.532860?feed=most-citedThis paper proposes to broaden the canonical formulation of quantum mechanics. Ordinarily, one imposes the condition on the Hamiltonian, where † represents the mathematical operation of complex conjugation and matrix transposition. This conventional Hermiticity condition is sufficient to ensure that the Hamiltonian H has a real spectrum. However, replacing this mathematical condition by the weaker and more physical requirement where ‡ represents combined parity reflection and time reversal PT, one obtains new classes of complex Hamiltonians whose spectra are still real and positive. This generalization of Hermiticity is investigated using a complex deformation of the harmonic oscillator Hamiltonian, where εCarl M. Bender, Stefan Boettcher, and Peter N. MeisingerThu, 22 Apr 1999 07:00:00 GMTExact envelope‐soliton solutions of a nonlinear wave equation
https://aip.scitation.org/doi/10.1063/1.1666399?feed=most-cited
https://aip.scitation.org/doi/10.1063/1.1666399?feed=most-citedExact N‐envelope‐soliton solutions have been obtained for the following nonlinear wave equation, i∂ψ/∂t + i3α|ψ|2 ∂ψ/∂x + β∂2ψ/∂x2 + iγ∂3ψ/∂x3 + δ|ψ|2ψ = 0, where α, β, γ and δ are real positive constants with the relation αβ = γδ. In one limit of α = γ = 0, the equation reduces to the nonlinear Schrödinger equation which describes a plane self‐focusing and one‐dimensional self‐modulation of waves in nonlinear dispersive media. In another limit, β = δ = 0, the equation for real Ψ, reduces to the modified Korteweg‐de Vries equation. Hence, the solutions reveal the close relation between classicalRyogo HirotaMon, 03 Nov 2003 08:00:00 GMTAn exact solution for a derivative nonlinear Schrödinger equation
https://aip.scitation.org/doi/10.1063/1.523737?feed=most-cited
https://aip.scitation.org/doi/10.1063/1.523737?feed=most-citedA method of solution for the ’’derivative nonlinear Schrödinger equation’’ iqt=−qxx±i (q*q2)x is presented. The appropriate inverse scattering problem is solved, and the one‐soliton solution is obtained, as well as the infinity of conservation laws. Also, we note that this equation can also possess ’’algebraic solitons.’’David J. Kaup and Alan C. NewellMon, 11 Aug 2008 07:00:00 GMTThe Painlevé property for partial differential equations
https://aip.scitation.org/doi/10.1063/1.525721?feed=most-cited
https://aip.scitation.org/doi/10.1063/1.525721?feed=most-citedIn this paper we define the Painlevé property for partial differential equations and show how it determines, in a remarkably simple manner, the integrability, the Bäcklund transforms, the linearizing transforms, and the Lax pairs of three well‐known partial differential equations (Burgers’ equation, KdV equation, and the modified KdV equation). This indicates that the Painlevé property may provide a unified description of integrable behavior in dynamical systems (ordinary and partial differential equations), while, at the same time, providing an efficient method for determining the integrability of particular systems.John Weiss, M. Tabor, and George CarnevaleThu, 04 Jun 1998 07:00:00 GMTPainless nonorthogonal expansions
https://aip.scitation.org/doi/10.1063/1.527388?feed=most-cited
https://aip.scitation.org/doi/10.1063/1.527388?feed=most-citedIn a Hilbert space H, discrete families of vectors {hj} with the property that f=∑j〈hj‖ f〉hj for every f in H are considered. This expansion formula is obviously true if the family is an orthonormal basis of H, but also can hold in situations where the hj are not mutually orthogonal and are ‘‘overcomplete.’’ The two classes of examples studied here are (i) appropriate sets of Weyl–Heisenberg coherent states, based on certain (non‐Gaussian) fiducial vectors, and (ii) analogous families of affine coherent states. It is believed, that such ‘‘quasiorthogonal expansions’’ will be a useful tool in many areas of theoretical physicsIngrid Daubechies, A. Grossmann, and Y. MeyerThu, 04 Jun 1998 07:00:00 GMTRelationship between Systems of Impenetrable Bosons and Fermions in One Dimension
https://aip.scitation.org/doi/10.1063/1.1703687?feed=most-cited
https://aip.scitation.org/doi/10.1063/1.1703687?feed=most-citedA rigorous one‐one correspondence is established between one‐dimensional systems of bosons and of spinless fermions. This correspondence holds irrespective of the nature of the interparticle interactions, subject only to the restriction that the interaction have an impenetrable core. It is shown that the Bose and Fermi eigenfunctions are related by ψB=ψFA, where A(x1 … xn) is +1 or −1 according as the order pq … r, when the particle coordinates xj are arranged in the order xp<xq< … <xr, is an even or an odd permutation of 1 … n. The energy spectra of the two systems are identical, asM. GirardeauWed, 22 Dec 2004 08:00:00 GMT