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Journal of Mathematical Physics
Journal Prestige (SJR): 0.644  Citation Impact (citeScore): 1 Number of Followers: 26  Hybrid journal (It can contain Open Access articles)ISSN (Print) 0022-2488 - ISSN (Online) 1089-7658 Published by AIP  [28 journals]
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- A nonvanishing spectral gap for AKLT models on generalized decorated
graphs-
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Authors: Angelo Lucia, Amanda Young
Abstract: Journal of Mathematical Physics, Volume 64, Issue 4, April 2023.
We consider the spectral gap question for Affleck, Kennedy, Lieb, and Tasaki models defined on decorated versions of simple, connected graphs G. This class of decorated graphs, which are defined by replacing all edges of G with a chain of n sites, in particular includes any decorated multi-dimensional lattice. Using the Tensor Network States approach from [Abdul-Rahman et al., Analytic Trends in Mathematical Physics, Contemporary Mathematics (American Mathematical Society, 2020), Vol. 741, p. 1.], we prove that if the decoration parameter is larger than a linear function of the maximal vertex degree, then the decorated model has a nonvanishing spectral gap above the ground state energy.
Citation: Journal of Mathematical Physics
PubDate: 2023-04-17T11:57:17Z
DOI: 10.1063/5.0139706
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- Integrable heat conduction model
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Authors: Chiara Franceschini, Rouven Frassek, Cristian Giardinà
Abstract: Journal of Mathematical Physics, Volume 64, Issue 4, April 2023.
We consider a stochastic process of heat conduction where energy is redistributed along a chain between nearest neighbor sites via an improper beta distribution. Similar to the well-known Kipnis–Marchioro–Presutti (KMP) model, the finite chain is coupled at its ends with two reservoirs that break the conservation of energy when working at different temperatures. At variance with KMP, the model considered here is integrable, and one can write in a closed form the n-point correlation functions of the non-equilibrium steady state. As a consequence of the exact solution one, can directly prove that the system is in “local equilibrium,” which is described at the macro-scale by a product measure. Integrability manifests itself through the description of the model via the open Heisenberg chain with non-compact spins. The algebraic formulation of the model allows us to interpret its duality relation with a purely absorbing particle system as a change of representation.
Citation: Journal of Mathematical Physics
PubDate: 2023-04-17T11:57:15Z
DOI: 10.1063/5.0138013
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- Monotonic multi-state quantum f-divergences
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Authors: Keiichiro Furuya, Nima Lashkari, Shoy Ouseph
Abstract: Journal of Mathematical Physics, Volume 64, Issue 4, April 2023.
We use the Tomita–Takesaki modular theory and the Kubo–Ando operator mean to write down a large class of multi-state quantum f-divergences and prove that they satisfy the data processing inequality. For two states, this class includes the (α, z)-Rényi divergences, the f-divergences of Petz, and the Rényi Belavkin-Staszewski relative entropy as special cases. The method used is the interpolation theory of non-commutative [math] spaces, and the result applies to general von Neumann algebras, including the local algebra of quantum field theory. We conjecture that these multi-state Rényi divergences have operational interpretations in terms of the optimal error probabilities in asymmetric multi-state quantum state discrimination.
Citation: Journal of Mathematical Physics
PubDate: 2023-04-14T11:11:48Z
DOI: 10.1063/5.0125505
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- Study of stationary rigidly rotating anisotropic cylindrical fluids with
new exact interior solutions of GR. III. Azimuthal pressure-
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Authors: M.-N. Célérier
Abstract: Journal of Mathematical Physics, Volume 64, Issue 4, April 2023.
The investigation of interior spacetimes sourced by stationary cylindrical anisotropic fluids is pursued and specialized here to rigidly rotating fluids with an azimuthally directed pressure. Based on the occurrence of an extra degree of freedom in the equations, two general methods for constructing different classes of exact solutions to the field equations are proposed. Exemplifying such recipes, a bunch of solutions are constructed. Axisymmetry and regularity conditions on the axis are examined, and the spacetimes are properly matched to a vacuum exterior. A number of classes and subclasses are thus studied, and an analysis of their features leads to sorting out three classes whose appropriate mathematical and physical properties are discussed. This work is part of a larger study of the influence of anisotropic pressure in general relativity, using cylindrical symmetry as a simplifying assumption, and considering, in turn, each principal stress direction. It has been initiated in companion Papers I and II, where the pressure was assumed to be axially directed, and is followed by Paper IV considering radial pressure and Paper V contrasting the previous results with the corresponding dust and perfect fluid solutions.
Citation: Journal of Mathematical Physics
PubDate: 2023-04-14T11:11:47Z
DOI: 10.1063/5.0121169
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- Connected (n, m)-point functions of diagonal 2-BKP tau-functions and spin
double Hurwitz numbers-
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Authors: Zhiyuan Wang, Chenglang Yang
Abstract: Journal of Mathematical Physics, Volume 64, Issue 4, April 2023.
We derive an explicit formula for connected (n, m)-point functions associated with an arbitrary diagonal tau-function of the 2-BKP hierarchy using the computation of neutral fermions and boson–fermion correspondence of type B and then apply this formula to the computation of connected spin double Hurwitz numbers. This is the type B analog of Wang and Yang [arXiv:2210.08712 (2022)].
Citation: Journal of Mathematical Physics
PubDate: 2023-04-13T11:00:26Z
DOI: 10.1063/5.0136839
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- Quadratic symplectic Lie superalgebras with a filiform module as an odd
part-
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Authors: Elisabete Barreiro, Saïd Benayadi, Rosa M. Navarro, José M. Sánchez
Abstract: Journal of Mathematical Physics, Volume 64, Issue 4, April 2023.
The present work studies deeply quadratic symplectic Lie superalgebras, obtaining, in particular, that they are all nilpotent. Consequently, we provide classifications in low dimensions and identify the double extensions that maintain symplectic structures. By means of both elementary odd double extensions and generalized double extensions of quadratic symplectic Lie superalgebras, we obtain an inductive description of quadratic symplectic Lie superalgebras of filiform type.
Citation: Journal of Mathematical Physics
PubDate: 2023-04-13T11:00:26Z
DOI: 10.1063/5.0142935
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- Quantum tomographic Aubry–Mather theory
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Authors: A. Shabani, F. Khellat
Abstract: Journal of Mathematical Physics, Volume 64, Issue 4, April 2023.
In this paper, we study the quantum analog of the Aubry–Mather theory from a tomographic point of view. In order to have a well-defined real distribution function for the quantum phase space, which can be a solution for variational action minimizing problems, we reconstruct quantum Mather measures by means of inverse Radon transform and prove that the resulting tomograms, which are fair and non-negative distribution functions, are also solutions of the quantum Mather problem and, in the semi-classical sense, converge to the classical Mather measures.
Citation: Journal of Mathematical Physics
PubDate: 2023-04-13T11:00:25Z
DOI: 10.1063/5.0127998
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- The existence of dyon solutions for generalized Weinberg–Salam model
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Authors: Shouxin Chen, Yilu Xu
Abstract: Journal of Mathematical Physics, Volume 64, Issue 4, April 2023.
The generalized Weinberg–Salam model, which is presented in a recent study of Kimm, Yoon, and Cho [Eur. Phys. J. C 75, 67 (2015)], is arising in electroweak theory. In this paper, we prove the existence and asymptotic behaviors at infinity of static and radially symmetric dyon solutions to the boundary-value problem of this model. Moreover, as a by-product, the qualitative properties of dyon solutions are also obtained. The methods used here are the extremum principle, the Schauder fixed point theory, and the shooting approach depending on one shooting parameter. We provide an effective framework for constructing the dyon solutions in general dimensions and develop the existing results.
Citation: Journal of Mathematical Physics
PubDate: 2023-04-12T11:27:25Z
DOI: 10.1063/5.0130660
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- Free energy subadditivity for symmetric random Hamiltonians
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Authors: Mark Sellke
Abstract: Journal of Mathematical Physics, Volume 64, Issue 4, April 2023.
We consider a random Hamiltonian [math] defined on a compact space Σ that admits a transitive action by a compact group [math]. When the law of H is [math]-invariant, we show its expected free energy relative to the unique [math]-invariant probability measure on Σ, which obeys a subadditivity property in the law of H itself. The bound is often tight for weak disorder and relates free energies at different temperatures when H is a Gaussian process. Many examples are discussed, including branching random walks, several spin glasses, random constraint satisfaction problems, and the random field Ising model. We also provide a generalization to quantum Hamiltonians with applications to the quantum Sherrington–Kirkpatrick and Sachdev–Ye–Kitaev models.
Citation: Journal of Mathematical Physics
PubDate: 2023-04-12T11:27:24Z
DOI: 10.1063/5.0124718
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- Residual entropy of a two-dimensional Ising model with crossing and
four-spin interactions-
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Authors: De-Zhang Li, Yu-Jun Zhao, Yao Yao, Xiao-Bao Yang
Abstract: Journal of Mathematical Physics, Volume 64, Issue 4, April 2023.
We study the residual entropy of a two-dimensional Ising model with crossing and four-spin interactions, both in the case of a zero magnetic field and in an imaginary magnetic field [math]. The spin configurations of this Ising model can be mapped into the hydrogen configurations of square ice with the defined standard direction of the hydrogen bonds. Making use of the equivalence of this Ising system with the exactly solved eight-vertex model and taking the low temperature limit, we obtain the residual entropy. Two soluble cases in the zero field and one soluble case in the imaginary field are examined. In the case that the free-fermion condition holds in zero field, we find that the ground states in the low temperature limit include the configurations disobeying the ice rules. In another case in zero field where the four-spin interactions are −∞ and another case in imaginary field where the four-spin interactions are 0, the residual entropy exactly agrees with the result of square ice determined by Lieb in 1967. In the solutions to the latter two cases, we have shown alternative approaches to the residual entropy problem of square ice.
Citation: Journal of Mathematical Physics
PubDate: 2023-04-12T11:27:23Z
DOI: 10.1063/5.0086299
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- On the universality and membership problems for quantum gates
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Authors: Lorenzo Mattioli, Adam Sawicki
Abstract: Journal of Mathematical Physics, Volume 64, Issue 4, April 2023.
We study the universality and membership problems for gate sets consisting of a finite number of quantum gates. Our approach relies on the techniques from compact Lie group theory. We also introduce an auxiliary problem called the subgroup universality problem, which helps in solving some instances of the membership problem and can be of interest on its own. The resulting theorems are mainly formulated in terms of centralizers and the adjoint representations of a given set of quantum gates.
Citation: Journal of Mathematical Physics
PubDate: 2023-04-11T11:22:12Z
DOI: 10.1063/5.0106615
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- On topology of the moduli space of gapped Hamiltonians for topological
phases-
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Authors: Po-Shen Hsin, Zhenghan Wang
Abstract: Journal of Mathematical Physics, Volume 64, Issue 4, April 2023.
The moduli space of gapped Hamiltonians that are in the same topological phase is an intrinsic object that is associated with the topological order. The topology of these moduli spaces has been used recently in the construction of Floquet codes. We propose a systematical program to study the topology of these moduli spaces. In particular, we use effective field theory to study the cohomology classes of these spaces, which includes and generalizes the Berry phase. We discuss several applications for studying phase transitions. We show that a nontrivial family of gapped systems with the same topological order can protect isolated phase transitions in the phase diagram, and we argue that the phase transitions are characterized by screening of topological defects. We argue that the family of gapped systems obeys bulk-boundary correspondence. We show that a family of gapped systems in the bulk with the same topological order can rule out a family of gapped systems on the boundary with the topological order given by the topological boundary condition, constraining phase transitions on the boundary.
Citation: Journal of Mathematical Physics
PubDate: 2023-04-10T02:02:38Z
DOI: 10.1063/5.0136906
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- Ergodicity of unlabeled dynamics of Dyson’s model in infinite
dimensions-
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Authors: Hirofumi Osada, Shota Osada
Abstract: Journal of Mathematical Physics, Volume 64, Issue 4, April 2023.
Dyson’s model in infinite dimensions is a system of Brownian particles that interact via a logarithmic potential with an inverse temperature of β = 2. The stochastic process can be represented by the solution to an infinite-dimensional stochastic differential equation. The associated unlabeled dynamics (diffusion process) are given by the Dirichlet form with the sine2 point process as a reference measure. In a previous study, we proved that Dyson’s model in infinite dimensions is irreducible, but left the ergodicity of the unlabeled dynamics as an open problem. In this paper, we prove that the unlabeled dynamics of Dyson’s model in infinite dimensions are ergodic.
Citation: Journal of Mathematical Physics
PubDate: 2023-04-10T02:02:37Z
DOI: 10.1063/5.0086873
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- Spectral inequality for Dirac right triangles
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Authors: Tuyen Vu
Abstract: Journal of Mathematical Physics, Volume 64, Issue 4, April 2023.
We consider a Dirac operator on right triangles, subject to infinite-mass boundary conditions. We conjecture that the lowest positive eigenvalue is minimized by the isosceles right triangle under the area or perimeter constraints. We prove this conjecture under extra geometric hypotheses relying on a recent approach of Briet and Krejčiřík [J. Math. Phys. 63, 013502 (2022)].
Citation: Journal of Mathematical Physics
PubDate: 2023-04-10T02:02:34Z
DOI: 10.1063/5.0147732
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- Hochschild cohomology of the Weyl conformal algebra with coefficients in
finite modules-
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Authors: H. Alhussein, P. Kolesnikov
Abstract: Journal of Mathematical Physics, Volume 64, Issue 4, April 2023.
In this work, we find Hochschild cohomology groups of the Weyl associative conformal algebra with coefficients in all finite modules. The Weyl conformal algebra is the universal associative conformal envelope of the Virasoro Lie conformal algebra relative to the locality N = 2. In order to obtain this result, we adjust the algebraic discrete Morse theory to the case of differential algebras.
Citation: Journal of Mathematical Physics
PubDate: 2023-04-05T04:03:38Z
DOI: 10.1063/5.0146223
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- Analytic theory of coupled-cavity traveling wave tubes
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Authors: Alexander Figotin
Abstract: Journal of Mathematical Physics, Volume 64, Issue 4, April 2023.
Coupled-cavity traveling wave tube (CCTWT) is a high power microwave vacuum electronic device used to amplify radio frequency signals. CCTWTs have numerous applications, including radar, radio navigation, space communication, television, radio repeaters, and charged particle accelerators. Microwave-generating interactions in CCTWTs take place mostly in coupled resonant cavities positioned periodically along the electron beam axis. Operational features of a CCTWT, particularly the amplification mechanism, are similar to those of a multicavity klystron. We advance here a Lagrangian field theory of CCTWTs with the space being represented by one-dimensional continuum. The theory integrates into it the space-charge effects, including the so-called debunching (electron-to-electron repulsion). The corresponding Euler–Lagrange field equations are ordinary differential equations with coefficients varying periodically in the space. Utilizing the system periodicity, we develop instrumental features of the Floquet theory, including the monodromy matrix and its Floquet multipliers. We use them to derive closed form expressions for a number of physically significant quantities. Those include, in particular, dispersion relations and the frequency dependent gain foundational to the RF signal amplification. Serpentine (folded, corrugated) traveling wave tubes are very similar to CCTWTs, and our theory applies to them also.
Citation: Journal of Mathematical Physics
PubDate: 2023-04-05T04:03:36Z
DOI: 10.1063/5.0102701
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- Spectral invariants of the magnetic Dirichlet-to-Neumann map on Riemannian
manifolds-
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Authors: Genqian Liu, Xiaoming Tan
Abstract: Journal of Mathematical Physics, Volume 64, Issue 4, April 2023.
This paper is devoted to investigating the heat trace asymptotic expansion associated with the magnetic Steklov problem on a smooth compact Riemannian manifold (Ω, g) with smooth boundary ∂Ω. By computing the full symbol of the magnetic Dirichlet-to-Neumann map [math], we establish an effective procedure, by which we can calculate all the coefficients a0, a1, …, an−1 of the asymptotic expansion. In particular, we explicitly give the first four coefficients a0, a1, a2, and a3. They are spectral invariants, which provide precise information concerning the volume and curvatures of the boundary ∂Ω and some physical quantities.
Citation: Journal of Mathematical Physics
PubDate: 2023-04-05T04:03:35Z
DOI: 10.1063/5.0088549
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- Algebraic approach to annihilation and repulsion of bound states in the
continuum in finite systems-
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Authors: N. M. Shubin
Abstract: Journal of Mathematical Physics, Volume 64, Issue 4, April 2023.
We present an algebraic approach to the description of bound states in the continuum (BICs) in finite systems with a discrete energy spectrum coupled to several decay channels. General estimations and bounds on the number of linearly independent BICs are derived. We show that the algebraic point of view provides straightforward and illustrative interpretations of typical well-known results, including the Friedrich–Wintgen mechanism and the Pavlov-Verevkin model. Pair-wise annihilation and repulsion of BICs in the energy–parameter space are discussed within generic two- and three-level models. An illustrative algebraic interpretation of such phenomena in Hilbert space is presented.
Citation: Journal of Mathematical Physics
PubDate: 2023-04-05T04:03:34Z
DOI: 10.1063/5.0142892
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- Arithmetic phase transitions for mosaic Maryland model
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Authors: Jiawei He, Xu Xia
Abstract: Journal of Mathematical Physics, Volume 64, Issue 4, April 2023.
We give a precise description of spectral types of the mosaic Maryland model with any irrational frequency, which provides a quasi-periodic unbounded model with non-monotone potential having arithmetic phase transition.
Citation: Journal of Mathematical Physics
PubDate: 2023-04-05T04:03:34Z
DOI: 10.1063/5.0123576
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- Relation of stability and bifurcation properties between continuous and
ultradiscrete dynamical systems via discretization with positivity: One
dimensional cases-
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Authors: Shousuke Ohmori, Yoshihiro Yamazaki
Abstract: Journal of Mathematical Physics, Volume 64, Issue 4, April 2023.
The stability and bifurcation properties of one-dimensional discrete dynamical systems with positivity, which are derived from continuous ones by tropical discretization, are studied. The discretized time interval is introduced as a bifurcation parameter in the discrete dynamical systems, and the emergence condition of an additional bifurcation, flip bifurcation, is identified. The correspondence between the discrete dynamical systems with positivity and the ultradiscrete ones derived from them is discussed. It is found that the derived ultradiscrete max-plus dynamical systems can retain the bifurcations of the original continuous ones via tropical discretization and ultradiscretization.
Citation: Journal of Mathematical Physics
PubDate: 2023-04-03T04:18:59Z
DOI: 10.1063/5.0137636
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- Some perturbation results for quasi-bases and other sequences of vectors
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Authors: Fabio Bagarello, Rosario Corso
Abstract: Journal of Mathematical Physics, Volume 64, Issue 4, April 2023.
We discuss some perturbation results concerning certain pairs of sequences of vectors in a Hilbert space [math] and producing new sequences, which share, with the original ones, reconstruction formulas on a dense subspace of [math] or on the whole space. We also propose some preliminary results on the same issue, but in a distributional settings.
Citation: Journal of Mathematical Physics
PubDate: 2023-04-03T04:18:59Z
DOI: 10.1063/5.0131314
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- Commutators on Fock spaces
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Authors: Daniel Alpay, Paula Cerejeiras, Uwe Kähler, Trevor Kling
Abstract: Journal of Mathematical Physics, Volume 64, Issue 4, April 2023.
Given a weighted ℓ2 space with weights associated with an entire function, we consider pairs of weighted shift operators, whose commutators are diagonal operators, when considered as operators over a general Fock space. We establish a calculus for the algebra of these commutators and apply it to the general case of Gelfond–Leontiev derivatives. This general class of operators includes many known examples, such as classic fractional derivatives and Dunkl operators. This allows us to establish a general framework, which goes beyond the classic Weyl–Heisenberg algebra. Concrete examples for its application are provided.
Citation: Journal of Mathematical Physics
PubDate: 2023-04-03T04:18:58Z
DOI: 10.1063/5.0080723
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- Programming of channels in generalized probabilistic theories
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Authors: Takayuki Miyadera, Ryo Takakura
Abstract: Journal of Mathematical Physics, Volume 64, Issue 4, April 2023.
For a given target system and apparatus described by quantum theory, the so-called quantum no-programming theorem indicates that a family of states called programs in the apparatus with a fixed unitary operation on total system programs distinct unitary dynamics to the target system only if the initial programs are orthogonal to each other. The current study aims at revealing whether a similar behavior can be observed in generalized probabilistic theories (GPTs). Generalizing the programming scheme to GPTs, we derive a similar theorem to the quantum no-programming theorem. We, furthermore, demonstrate that programming of reversible dynamics is closely related to a curious structure named a quasi-classical structure on the state space. Programming of irreversible dynamics, i.e., channels, in GPTs is also investigated.
Citation: Journal of Mathematical Physics
PubDate: 2023-04-03T04:18:58Z
DOI: 10.1063/5.0101198
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- Wong–Zakai approximations for non-autonomous stochastic parabolic
equations with X-elliptic operators in higher regular spaces-
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Authors: Lili Gao, Ming Huang, Lu Yang
Abstract: Journal of Mathematical Physics, Volume 64, Issue 4, April 2023.
In this paper, we consider the regularity of Wong–Zakai approximations of the non-autonomous stochastic degenerate parabolic equations with X-elliptic operators. We first establish the pullback random attractors for the random degenerate parabolic equations with a general diffusion. Then, we prove the convergence of solutions and the upper semi-continuity of random attractors of the Wong–Zakai approximation equations in Lp(DN) ∩ H.
Citation: Journal of Mathematical Physics
PubDate: 2023-04-03T04:18:57Z
DOI: 10.1063/5.0111876
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- The general structure of the decoherence-free subalgebra for uniformly
continuous quantum Markov semigroups-
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Authors: Emanuela Sasso, Veronica Umanità
Abstract: Journal of Mathematical Physics, Volume 64, Issue 4, April 2023.
By using the decomposition of the decoherence-free subalgebra [math] in direct integrals of factors, we obtain a structure theorem for every uniformly continuous quantum Markov semigroup. Moreover, we prove that when there exists a faithful normal invariant state, [math] has to be atomic and decoherence takes place.
Citation: Journal of Mathematical Physics
PubDate: 2023-04-03T04:18:57Z
DOI: 10.1063/5.0092998
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- Ulam–Hyers stability for second-order non-instantaneous impulsive
fractional neutral stochastic differential equations-
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Authors: Dhanalakshmi K., Balasubramaniam P.
Abstract: Journal of Mathematical Physics, Volume 64, Issue 4, April 2023.
In this paper, sufficient conditions are established for the Ulam–Hyers stability of second-order non-instantaneous impulsive fractional neutral stochastic differential equations (NIIFNSDEs) with supremum norm in the pth means square sense. The existence of solution of NIIFNSDEs is derived by using the cosine family of linear operator, It[math]’s formula, and M[math]nch fixed point theorem in infinite-dimensional space. Finally, an example is demonstrated to illustrate the obtained theoretical results.
Citation: Journal of Mathematical Physics
PubDate: 2023-04-03T04:18:56Z
DOI: 10.1063/5.0088040
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- On the Hochstadt–Lieberman theorem for the fourth-order binomial
operator-
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Authors: Lu Chen, Guoliang Shi, Jun Yan
Abstract: Journal of Mathematical Physics, Volume 64, Issue 4, April 2023.
A method of recovering the potential of the fourth-order binomial operator on a half-interval [1/2, 1] using a known potential on another half-interval [0, 1/2] and the eigenvalues of the self-adjoint boundary problem on the whole interval [0, 1] is proposed.
Citation: Journal of Mathematical Physics
PubDate: 2023-04-03T04:18:56Z
DOI: 10.1063/5.0107145
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- An application of Heun functions in the quantum mechanics of a constrained
particle-
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Authors: Alexandre G. M. Schmidt, Matheus E. Pereira
Abstract: Journal of Mathematical Physics, Volume 64, Issue 4, April 2023.
Using the thin-layer quantization, we formulate the problem of a Schrödinger particle constrained to move along a coordinate surface of the bi-spherical coordinate system. In three-dimensional space, the free Schrödinger equation is not separable in this coordinate system. However, when we consider the equation for a particle constrained to a given surface, there are only two degrees of freedom. One has to introduce a geometrical potential to attach the particle to the surface. This well-known potential has two contributions: one from Gauss’ curvature and the other from the mean curvature. The Schrödinger equation leads to a general Heun equation. We solve it exactly and present the eigenfunctions and plots of the probability densities, and, as an application of this methodology, we study the problem of an electric charge propagating along these coordinate surfaces in the presence of a uniform magnetic field.
Citation: Journal of Mathematical Physics
PubDate: 2023-04-03T04:18:55Z
DOI: 10.1063/5.0135385
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- Resonant collisions of high-order localized waves in the Maccari system
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Authors: Yulei Cao, Yi Cheng, Jingsong He
Abstract: Journal of Mathematical Physics, Volume 64, Issue 4, April 2023.
Exploring new nonlinear wave solutions to integrable systems has always been an open issue in physics, applied mathematics, and engineering. In this paper, the Maccari system, a two-dimensional analog of nonlinear Schr[math]dinger equation, is investigated. The system is derived from the Kadomtsev–Petviashvili (KP) equation and is widely used in nonlinear optics, plasma physics, and water waves. A large family of semi-rational solutions of the Maccari system are proposed with the KP hierarchy reduction method and Hirota bilinear method. These semi-rational solutions reduce to the breathers of elastic collision and resonant collision under special parameters. In case of resonant collisions between breathers and rational waves, these semi-rational solutions describe lumps fusion into breathers, or lumps fission from breathers, or a mixture of these fusion and fission. The resonant collisions of semi-rational solutions are semi-localized in time (i.e., lumps exist only when t → +∞ or t → −∞), and we also discuss their dynamics and asymptotic behaviors.
Citation: Journal of Mathematical Physics
PubDate: 2023-04-03T04:18:54Z
DOI: 10.1063/5.0141546
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- Discrete and zeta-regularized determinants of the Laplacian on polygonal
domains with Dirichlet boundary conditions-
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Authors: Rafael L. Greenblatt
Abstract: Journal of Mathematical Physics, Volume 64, Issue 4, April 2023.
For [math], a connected, open, bounded set whose boundary is a finite union of disjoint polygons whose vertices have integer coordinates, the logarithm of the discrete Laplacian on [math] with Dirichlet boundary conditions has an asymptotic expression for large L involving the zeta-regularized determinant of the associated continuum Laplacian. When Π is not simply connected, this result extends to Laplacians acting on two-valued functions with a specified monodromy class.
Citation: Journal of Mathematical Physics
PubDate: 2023-04-03T04:18:53Z
DOI: 10.1063/5.0062138
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