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Journal of Mathematical Physics
Journal Prestige (SJR): 0.644  Citation Impact (citeScore): 1 Number of Followers: 25  Hybrid journal (It can contain Open Access articles)ISSN (Print) 0022-2488 - ISSN (Online) 1089-7658 Published by AIP  [27 journals]
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- Asymptotic estimate of weak solutions in a fourth-order parabolic equation
with logarithm-
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Authors: Bingchen Liu, Ke Li, Fengjie Li
Abstract: Journal of Mathematical Physics, Volume 64, Issue 1, January 2023.
This paper deals with an initial-boundary problem of the fourth-order parabolic equation involving two logarithm terms. First, we give some results for blow-up or global solutions through classifying the initial energy and the Nehari energy. Second, we show asymptotic estimates about blow-up time and a large time estimate of solutions, respectively.
Citation: Journal of Mathematical Physics
PubDate: 2023-01-26T11:16:57Z
DOI: 10.1063/5.0088490
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- Exact solution and coherent states of an asymmetric oscillator with
position-dependent mass-
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Authors: Bruno G. da Costa, Ignacio S. Gomez, Biswanath Rath
Abstract: Journal of Mathematical Physics, Volume 64, Issue 1, January 2023.
We revisit the problem of the deformed oscillator with position-dependent mass [da Costa et al., J. Math. Phys. 62, 092101 (2021)] in the classical and quantum formalisms by introducing the effect of the mass function in both kinetic and potential energies. The resulting Hamiltonian is mapped into a Morse oscillator by means of a point canonical transformation from the usual phase space (x, p) to a deformed one (xγ, Πγ). Similar to the Morse potential, the deformed oscillator presents bound trajectories in phase space corresponding to an anharmonic oscillatory motion in classical formalism and, therefore, bound states with a discrete spectrum in quantum formalism. On the other hand, open trajectories in phase space are associated with scattering states and continuous energy spectrum. Employing the factorization method, we investigate the properties of the coherent states, such as the time evolution and their uncertainties. A fast localization, classical and quantum, is reported for the coherent states due to the asymmetrical position-dependent mass. An oscillation of the time evolution of the uncertainty relationship is also observed, whose amplitude increases as the deformation increases.
Citation: Journal of Mathematical Physics
PubDate: 2023-01-26T11:16:54Z
DOI: 10.1063/5.0094564
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- Exact thresholds for global existence to the nonlinear beam equations with
and without a damping-
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Authors: Yiyin Yuan, Shuai Tian, Jun Qing, Shihui Zhu
Abstract: Journal of Mathematical Physics, Volume 64, Issue 1, January 2023.
In this paper, we study the Cauchy problem for focusing nonlinear beam equations with and without a damping term. By constructing two pairs of invariant flows, we obtain the exact thresholds for the global existence and blow-up to the above equations in the sense that both thresholds are explicitly expressed by the L2-norm of the fourth-order nonlinear elliptic equation without any damping.
Citation: Journal of Mathematical Physics
PubDate: 2023-01-26T11:16:53Z
DOI: 10.1063/5.0103472
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- Problems involving the fractional g-Laplacian with lack of compactness
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Authors: Sabri Bahrouni, Hichem Ounaies, Olfa Elfalah
Abstract: Journal of Mathematical Physics, Volume 64, Issue 1, January 2023.
In this paper, we prove compact embedding of a subspace of the fractional Orlicz–Sobolev space [math] consisting of radial functions; our target embedding spaces are of Orlicz type. In addition, we prove a Lions and Lieb type results for [math] that works together in a particular way to get a sequence whose weak limit is non-trivial. As an application, we study the existence of solutions to quasilinear elliptic problems in the whole space [math] involving the fractional g-Laplacian operator, where the conjugated function [math] of G does not satisfy the Δ2-condition.
Citation: Journal of Mathematical Physics
PubDate: 2023-01-26T11:16:52Z
DOI: 10.1063/5.0105895
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- Fully developed, doubly periodic, viscous flows in infinite space-periodic
pipes under general time-periodic total fluxes-
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Authors: Hugo Beirão da Veiga, Jiaqi Yang
Abstract: Journal of Mathematical Physics, Volume 64, Issue 1, January 2023.
We study the motion of a viscous incompressible fluid in an n + 1-dimensional infinite pipe Λ with an L-periodic shape in the z = xn+1 direction. We denote by Σz the cross-section of the pipe at the level z and by vz the (n + 1)th component of the velocity. We look for fully developed solutions v(x, z, t) with a given T-time periodic total flux [math], which should be simultaneously T-periodic with respect to time and L-space-periodic with respect to z. We prove the existence and uniqueness of the above problem. The results extend those proved in the study by Beirão da Veiga [Arch. Ration. Mech. Anal. 178(3), 301–325 (2005)], where the cross-sections were independent of z.
Citation: Journal of Mathematical Physics
PubDate: 2023-01-26T11:16:50Z
DOI: 10.1063/5.0094333
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- Dirac reductions and classical W-algebras
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Authors: Gahng Sahn Lee, Arim Song, Uhi Rinn Suh
Abstract: Journal of Mathematical Physics, Volume 64, Issue 1, January 2023.
In the first part of this paper, we generalize the Dirac reduction to the extent of non-local Poisson vertex superalgebra and non-local SUSY Poisson vertex algebra cases. Next, we modify this reduction so that we explain the structures of classical W-superalgebras and SUSY classical W-algebras in terms of the modified Dirac reduction.
Citation: Journal of Mathematical Physics
PubDate: 2023-01-26T11:16:49Z
DOI: 10.1063/5.0126205
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- Critical inhomogeneous coupled Schrödinger equations
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Authors: Tarek Saanouni, Radhia Ghanmi
Abstract: Journal of Mathematical Physics, Volume 64, Issue 1, January 2023.
This work develops a local theory of the inhomogeneous coupled Schrödinger equations [math]. Here, one treats the critical Sobolev regime [math], where [math] is the index of the invariant Sobolev norm under the dilatation [math]. To the authors’ knowledge, the technique used in order to prove the existence of an energy local solution to the above-mentioned problem in the sub-critical regime s < sc, which consists of dividing the integrals on the unit ball of [math] and its complementary, is no more applicable for s = sc. In order to overcome this difficulty, one uses two different methods. The first one consists of using Lorentz spaces with the fact that [math], which allows us to handle the inhomogeneous term. In the second method, one uses some weighted Lebesgue spaces, which seem to be suitable to deal with the inhomogeneous term x −γ. In order to avoid a singularity of the source term, one considers the case p ≥ 2, which restricts the space dimensions to N ≤ 3.
Citation: Journal of Mathematical Physics
PubDate: 2023-01-25T12:46:52Z
DOI: 10.1063/5.0097741
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- From the Nash–Kuiper theorem of isometric embeddings to the Euler
equations for steady fluid motions: Analogues, examples, and extensions-
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Authors: Siran Li, Marshall Slemrod
Abstract: Journal of Mathematical Physics, Volume 64, Issue 1, January 2023.
Direct linkages between regular or irregular isometric embeddings of surfaces and steady compressible or incompressible fluid dynamics are investigated in this paper. For a surface (M, g) isometrically embedded in [math], we construct a mapping that sends the second fundamental form of the embedding to the density, velocity, and pressure of steady fluid flows on (M, g). From a Partial Differential Equations perspective, this mapping sends solutions to the Gauss–Codazzi equations to the steady Euler equations. Several families of special solutions of physical or geometrical significance are studied in detail, including the Chaplygin gas on standard and flat tori as well as the irregular isometric embeddings of the flat torus. We also discuss tentative extensions to multiple dimensions.
Citation: Journal of Mathematical Physics
PubDate: 2023-01-25T12:46:52Z
DOI: 10.1063/5.0100212
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- The null distance encodes causality
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Authors: A. Sakovich, C. Sormani
Abstract: Journal of Mathematical Physics, Volume 64, Issue 1, January 2023.
A Lorentzian manifold, N, endowed with a time function, τ, can be converted into a metric space using the null distance, [math], defined by Sormani and Vega [Classical Quant. Grav. 33(8), 085001 (2016)]. We show that if the time function is a regular cosmological time function as studied by Andersson, Galloway, and Howard [Classical Quant. Grav. 15(2), 309–322 (1998)], and also by Wald and Yip [J. Math. Phys. 22, 2659–2665 (1981)], or if, more generally, it satisfies the anti-Lipschitz condition of Chruściel, Grant, and Minguzzi [Ann. Henri Poincare 17(10), 2801–2824 (2016)], then the causal structure is encoded by the null distance in the following sense: for any p ∈ N, there is an open neighborhood Up such that for any q ∈ Up, we have [math] if and only if q lies in the causal future of p. The local encoding of causality can be applied to prove the global encoding of causality in a variety of settings, including spacetimes N where τ is a proper function. As a consequence, in dimension n + 1, n ≥ 2, we prove that if there is a bijective map between two such spacetimes, F : M1 → M2, which preserves the cosmological time function, τ2(F(p)) = τ1(p) for any p ∈ M1, and preserves the null distance, [math] for any p, q ∈ M1, then there is a Lorentzian isometry between them, F∗g1 = g2. This yields a canonical procedure allowing us to convert large classes of spacetimes into unique metric spaces with causal structures and time functions. This will be applied in our upcoming work to define spacetime intrinsic flat convergence.
Citation: Journal of Mathematical Physics
PubDate: 2023-01-24T11:13:36Z
DOI: 10.1063/5.0118979
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- Strong traveling wave solutions for a nonlocal diffusive
susceptible–infectious–recovered model with spatiotemporal delay-
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Authors: Ran Zhang, Hongyong Zhao
Abstract: Journal of Mathematical Physics, Volume 64, Issue 1, January 2023.
In general, a Lyapunov functional is one of the main approaches to show the existence of strong traveling wave solutions. However, introducing a spatiotemporal delay into a nonlocal diffusive epidemic model will bring great difficulties to the construction of a Lyapunov functional. In this paper, a new Lyapunov functional will be constructed to solve the problem of strong traveling wave solutions for a nonlocal diffusive SIR model with a spatiotemporal delay. Our results improve some known results in Wu et al. [J. Math. Phys. 61, 061512 (2020)] and Yang et al. [Appl. Anal. (in press)] by removing an a priori condition.
Citation: Journal of Mathematical Physics
PubDate: 2023-01-24T11:13:36Z
DOI: 10.1063/5.0108745
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- Quasi-periodic solutions for one dimensional Schrödinger equation with
quasi-periodic forcing and Dirichlet boundary condition-
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Authors: Min Zhang, Yi Wang, Jie Rui
Abstract: Journal of Mathematical Physics, Volume 64, Issue 1, January 2023.
This paper is concerned with a one-dimensional quasi-periodically forced nonlinear Schrödinger equation under Dirichlet boundary conditions. The existence of the quasi-periodic solutions for the equation is verified. By infinitely many symplectic transformations of coordinates, the Hamiltonian of the linear part of the equation can be reduced to an autonomous system. By utilizing the measure estimation of small divisors, there exists a symplectic change of coordinate transformation of the Hamiltonian of the equation into a nice Birkhoff normal form. By an abstract KAM (Kolmogorov-Arnold-Moser) theorem, the existence of a class of small-amplitude quasi-periodic solutions for the above equation is verified.
Citation: Journal of Mathematical Physics
PubDate: 2023-01-24T11:13:35Z
DOI: 10.1063/5.0093668
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- Computing the R-matrix of the quantum toroidal algebra
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Authors: Alexandr Garbali, Andrei Neguţ
Abstract: Journal of Mathematical Physics, Volume 64, Issue 1, January 2023.
We consider the problem of the R-matrix of the quantum toroidal algebra [math] in the Fock representation. Using the connection between the R-matrix R(u) (u being the spectral parameter) and the theory of Macdonald operators, we obtain explicit formulas for R(u) in the operator and matrix forms. These formulas are expressed in terms of the eigenvalues of a certain Macdonald operator, which completely describe the functional dependence of R(u) on the spectral parameter u. We then consider the geometric R-matrix (obtained from the theory of K-theoretic stable bases on moduli spaces of framed sheaves), which is expected to coincide with R(u) and thus gives another approach to the study of the poles of the R-matrix as a function of u.
Citation: Journal of Mathematical Physics
PubDate: 2023-01-24T11:13:34Z
DOI: 10.1063/5.0120003
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- Limiting behavior of center manifolds for stochastic evolutionary
equations with delay in varying phase spaces-
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Authors: Juan Yang, Jiaxin Gong, Longyu Wu, Ji Shu
Abstract: Journal of Mathematical Physics, Volume 64, Issue 1, January 2023.
In this article, we consider random center manifolds for a class of stochastic evolutionary equations with delay driven by multiplicative white noise. We first prove the existence and Ck smoothness of random center manifolds for the equations with delay. Then, we show the Ck smooth convergence of the center manifolds as the phase spaces approach to their singular limit.
Citation: Journal of Mathematical Physics
PubDate: 2023-01-23T11:03:54Z
DOI: 10.1063/5.0082575
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- Formation of delta shock and vacuum state for the pressureless
hydrodynamic model under the small disturbance of traffic pressure-
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Authors: Yixuan Wang, Meina Sun
Abstract: Journal of Mathematical Physics, Volume 64, Issue 1, January 2023.
The formation of delta shock and vacuum state for the pressureless hydrodynamic model is investigated in detail under the small disturbance of traffic pressure. Exact Riemann solutions for the perturbed system can be constructed explicitly for four different possible structures. Asymptotically, the perturbed Riemann solution involving two shocks will collapse to a single delta shock, and the perturbed Riemann solution involving two rarefaction waves will degenerate into a solution containing two contact discontinuities along with the vacuum state between them when the perturbed parameter goes to zero. It should be stressed here that the internal state in each of the two rarefaction wave-fans turns out to be the vacuum state gradually in such a limiting case, which differs obviously from the previous result that each of the two rarefaction wave-fans is compressed globally to be a single contact discontinuity. Additionally, some typical numerical results exhibiting the formation process of delta shock and vacuum state are presented to verify our theoretic results.
Citation: Journal of Mathematical Physics
PubDate: 2023-01-23T11:03:52Z
DOI: 10.1063/5.0129937
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- Convergence from power-law to logarithm-law in nonlinear fractional
Schrödinger equations-
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Authors: Xiaoming An, Xian Yang
Abstract: Journal of Mathematical Physics, Volume 64, Issue 1, January 2023.
In this paper, we show a connection between fractional Schrödinger equations with power-law nonlinearity and fractional Schrödinger equations with logarithm-law nonlinearity. We prove that ground state solutions of power-law fractional equations, as p → 2+, converge to a ground state solution of logarithm-law fractional equations. In particular, we provide a new proof to the existence of a ground state of logarithm-law fractional Schrödinger equations.
Citation: Journal of Mathematical Physics
PubDate: 2023-01-20T12:04:15Z
DOI: 10.1063/5.0096488
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- Analysis of a stochastic Lotka–Volterra competitive system with infinite
delays and Ornstein–Uhlenbeck process-
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Authors: Qun Liu
Abstract: Journal of Mathematical Physics, Volume 64, Issue 1, January 2023.
In this paper, we construct and analyze a stochastic Lotka–Volterra competitive model with the Ornstein–Uhlenbeck process and infinite delays. First, we verify the existence and uniqueness of the global solution of the system with any initial value. Then, we investigate the pth moment boundedness, asymptotic pathwise estimation, and asymptotic behavior of the solutions of the stochastic system in turn. In addition, we develop sufficient conditions for the existence of a stationary distribution of positive solutions to the stochastic system by establishing a series of suitable Lyapunov functions. Finally, by solving the corresponding six-dimensional Fokker–Planck equation, we obtain the accurate expression of the local density function of the linear system corresponding to the stochastic system.
Citation: Journal of Mathematical Physics
PubDate: 2023-01-20T12:04:14Z
DOI: 10.1063/5.0099936
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- Small solutions of the Einstein–Boltzmann-scalar field system with
Bianchi symmetry-
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Authors: Ho Lee, Jiho Lee, Ernesto Nungesser
Abstract: Journal of Mathematical Physics, Volume 64, Issue 1, January 2023.
We show that small homogeneous solutions to the Einstein–Boltzmann-scalar field system exist globally toward the future and tend to the de Sitter solution in a suitable sense. More specifically, we assume that the spacetime is of Bianchi type I–VIII, that the matter is described by Israel particles and that there exists a scalar field with a potential which has a positive lower bound. This represents a generalization of the work [H. Lee and E. Nungesser, Classical Quantum Gravity 35, 025001 (2018)], where a cosmological constant was considered, and a generalization of [H. Lee and J. Lee, J. Math. Phys. 63, 031502 (2022)], where a spatially flat FLRW spacetime was considered. We obtain the global existence and asymptotic behavior of classical solutions to the Einstein–Boltzmann-scalar field system for small initial data.
Citation: Journal of Mathematical Physics
PubDate: 2023-01-20T12:04:13Z
DOI: 10.1063/5.0125996
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- Chemical diffusion master equation: Formulations of reaction–diffusion
processes on the molecular level-
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Authors: Mauricio J. del Razo, Stefanie Winkelmann, Rupert Klein, Felix Höfling
Abstract: Journal of Mathematical Physics, Volume 64, Issue 1, January 2023.
The chemical diffusion master equation (CDME) describes the probabilistic dynamics of reaction–diffusion systems at the molecular level [del Razo et al., Lett. Math. Phys. 112, 49 (2022)]; it can be considered as the master equation for reaction–diffusion processes. The CDME consists of an infinite ordered family of Fokker–Planck equations, where each level of the ordered family corresponds to a certain number of particles and each particle represents a molecule. The equations at each level describe the spatial diffusion of the corresponding set of particles, and they are coupled to each other via reaction operators—linear operators representing chemical reactions. These operators change the number of particles in the system and, thus, transport probability between different levels in the family. In this work, we present three approaches to formulate the CDME and show the relations between them. We further deduce the non-trivial combinatorial factors contained in the reaction operators, and we elucidate the relation to the original formulation of the CDME, which is based on creation and annihilation operators acting on many-particle probability density functions. Finally, we discuss applications to multiscale simulations of biochemical systems among other future prospects.
Citation: Journal of Mathematical Physics
PubDate: 2023-01-20T12:04:13Z
DOI: 10.1063/5.0129620
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- Global existence and wave breaking for a stochastic two-component
Camassa–Holm system-
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Authors: Yajie Chen, Yingting Miao, Shijie Shi
Abstract: Journal of Mathematical Physics, Volume 64, Issue 1, January 2023.
In this paper, we study the stochastic two-component Camassa–Holm shallow water system on [math] and [math]. We first establish the existence, uniqueness, and blow-up criterion of the pathwise strong solution to the initial value problem with nonlinear noise. Then, we consider the impact of noise on preventing blow-up. In both nonlinear and linear noise cases, we establish global existence. In the nonlinear noise case, the global existence holds true with probability 1 if a Lyapunov-type condition is satisfied. In the linear noise case, we provide a lower bound for the probability that the solution exists globally. Furthermore, in the linear noise and the periodic case, we formulate a precise condition on initial data that leads to blow-up of strong solutions with a positive probability, and the lower bound for this probability is also estimated.
Citation: Journal of Mathematical Physics
PubDate: 2023-01-19T11:03:09Z
DOI: 10.1063/5.0100733
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- Asymptotic stability of the 2D MHD equations without resistivity on a flat
strip domain-
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Authors: Dongxiang Chen, Xiaoli Li, Xiaoli Chen
Abstract: Journal of Mathematical Physics, Volume 64, Issue 1, January 2023.
In this paper, we establish the asymptotic stability of certain stationary solution to 2D magnetohydrodynamic flow without resistivity in the infinite flat strip [math]. In addition, some explicit decay rates are also established.
Citation: Journal of Mathematical Physics
PubDate: 2023-01-18T11:09:08Z
DOI: 10.1063/5.0129193
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- On the Cauchy problem for Boltzmann equation modeling a polyatomic gas
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Authors: Irene M. Gamba, Milana Pavić-Čolić
Abstract: Journal of Mathematical Physics, Volume 64, Issue 1, January 2023.
In the present article, we consider the Boltzmann equation that models a polyatomic gas by introducing one additional continuous variable, referred to as microscopic internal energy. We establish existence and uniqueness theory in the space homogeneous setting for the full non-linear case, under an extended Grad-type assumption on transition probability rates, which comprises hard potentials for both the relative speed and internal energy with the rate in the interval [math], multiplied by an integrable angular part and integrable partition functions. The Cauchy problem is resolved by means of an abstract ordinary differential equation (ODE) theory in Banach spaces for the initial data with finite and strictly positive gas mass and energy, finite momentum, and additionally finite [math] polynomial moment, with [math] depending on the rate of the transition probability and the structure of a polyatomic molecule or its internal degrees of freedom. Moreover, we prove that polynomially and exponentially weighted Banach space norms associated with the solution are both generated and propagated uniformly in time.
Citation: Journal of Mathematical Physics
PubDate: 2023-01-13T11:08:11Z
DOI: 10.1063/5.0103621
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- Quiver Yangians and crystal meltings: A concise summary
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Authors: Masahito Yamazaki
Abstract: Journal of Mathematical Physics, Volume 64, Issue 1, January 2023.
The goal of this short article is to summarize some of the recent developments in quiver Yangians and crystal meltings. This article is based on a lecture delivered by the author at International Congress on Mathematical Physics (ICMP), Geneva, 2021.
Citation: Journal of Mathematical Physics
PubDate: 2023-01-12T11:17:47Z
DOI: 10.1063/5.0089785
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- Topology vs localization in synthetic dimensions
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Authors: Domenico Monaco, Thaddeus Roussigné
Abstract: Journal of Mathematical Physics, Volume 64, Issue 1, January 2023.
Motivated by recent developments in quantum simulation of synthetic dimensions, e.g., in optical lattices of ultracold atoms, we discuss here d-dimensional periodic, gapped quantum systems for d ≤ 4, with a focus on the topology of the occupied energy states. We perform this analysis by asking whether the spectral subspace below the gap can be spanned by smooth and periodic Bloch functions, corresponding to localized Wannier functions in position space. By constructing these Bloch functions inductively in the dimension, we show that if they are required to be orthonormal, then, in general, their existence is obstructed by the first two Chern classes of the underlying Bloch bundle, with the second Chern class characterizing, in particular, the four-dimensional situation. If the orthonormality constraint is relaxed, we show how m occupied energy bands can be spanned by a Parseval frame comprising at most m + 2 Bloch functions.
Citation: Journal of Mathematical Physics
PubDate: 2023-01-12T11:17:47Z
DOI: 10.1063/5.0130240
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- Strict monotonicity, continuity, and bounds on the Kertész line for the
random-cluster model on [math]-
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Authors: Ulrik Thinggaard Hansen, Frederik Ravn Klausen
Abstract: Journal of Mathematical Physics, Volume 64, Issue 1, January 2023.
Ising and Potts models can be studied using the Fortuin–Kasteleyn representation through the Edwards–Sokal coupling. This adapts to the setting where the models are exposed to an external field of strength h> 0. In this representation, which is also known as the random-cluster model, the Kertész line is the curve that separates two regions of the parameter space defined according to the existence of an infinite cluster in [math]. This signifies a geometric phase transition between the ordered and disordered phases even in cases where a thermodynamic phase transition does not occur. In this article, we prove strict monotonicity and continuity of the Kertész line. Furthermore, we give new rigorous bounds that are asymptotically correct in the limit h → 0 complementing the bounds from the work of Ruiz and Wouts [J. Math. Phys. 49, 053303 (2008)], which were asymptotically correct for h → ∞. Finally, using a cluster expansion, we investigate the continuity of the Kertész line phase transition.
Citation: Journal of Mathematical Physics
PubDate: 2023-01-12T11:17:45Z
DOI: 10.1063/5.0105283
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- Construction of exact solutions to Nahm’s equations for the
multimonopole-
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Authors: H. W. Braden, Sergey A. Cherkis, Jason M. Quinones
Abstract: Journal of Mathematical Physics, Volume 64, Issue 1, January 2023.
We construct high rank solutions to Nahm’s equations for boundary conditions that correspond to the Dirac multimonopole. Here, the spectral curve is explicitly known, and we achieve the integration by constructing a basis of polynomial tuples that forms a frame for the flow of the eigenline bundle over the curve.
Citation: Journal of Mathematical Physics
PubDate: 2023-01-11T12:16:46Z
DOI: 10.1063/5.0098288
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- Derivation of the Maxwell–Schrödinger equations: A note on the infrared
sector of the radiation field-
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Authors: Marco Falconi, Nikolai Leopold
Abstract: Journal of Mathematical Physics, Volume 64, Issue 1, January 2023.
We slightly extend prior results about the derivation of the Maxwell–Schrödinger equations from the bosonic Pauli–Fierz Hamiltonian. More concretely, we show that the findings from Leopold and Pickl [SIAM J. Math. Anal. 52(5), 4900–4936 (2020)] about the coherence of the quantized electromagnetic field also hold for soft photons with small energies. This is achieved with the help of an estimate from Ammari et al. [arXiv:2202.05015 (2022)], which proves that the domain of the number of photon operator is invariant during the time evolution generated by the Pauli–Fierz Hamiltonian.
Citation: Journal of Mathematical Physics
PubDate: 2023-01-10T11:22:26Z
DOI: 10.1063/5.0093786
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- The variational principle, conformal and disformal transformations, and
the degrees of freedom-
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Authors: Alexey Golovnev
Abstract: Journal of Mathematical Physics, Volume 64, Issue 1, January 2023.
Conformal and disformal transformations are now being very intensively studied in the context of various modified gravity theories. In particular, some special classes of them can be used for constructing mimetic dark matter models. Recently, it has been shown that many more transformations of this type, if not virtually all of them when the coefficients depend on the scalar kinetic term, can produce new solutions with mimetic properties. The aim of this paper is to explain how it works at the level of the variational principle, and to express some worries about the viability of these models.
Citation: Journal of Mathematical Physics
PubDate: 2023-01-06T10:39:30Z
DOI: 10.1063/5.0120079
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- Cubic first integrals of autonomous dynamical systems in E2 by an
algorithmic approach-
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Authors: Antonios Mitsopoulos, Michael Tsamparlis
Abstract: Journal of Mathematical Physics, Volume 64, Issue 1, January 2023.
In a recent paper of Mitsopoulos and Tsamparlis [J. Geom. Phys. 170, 104383 (2021)], a general theorem is given, which provides an algorithmic method for the computation of first integrals (FIs) of autonomous dynamical systems in terms of the symmetries of the kinetic metric defined by the dynamical equations of the system. In the present work, we apply this theorem to compute the cubic FIs of autonomous conservative Newtonian dynamical systems with two degrees of freedom. We show that the known results on this topic, which have been obtained by means of various divertive methods, and the additional ones derived in this work can be obtained by the single algorithmic method provided by this theorem. The results are collected in Tables I–IV, which can be used as an updated reference for these types of integrable and superintegrable potentials. The results we find are for special values of free parameters; therefore, using the methods developed here, other researchers by a different suitable choice of the parameters will be able to find new integrable and superintegrable potentials.
Citation: Journal of Mathematical Physics
PubDate: 2023-01-06T10:39:28Z
DOI: 10.1063/5.0097329
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- Affine geometric description of thermodynamics
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Authors: Shin-itiro Goto
Abstract: Journal of Mathematical Physics, Volume 64, Issue 1, January 2023.
Thermodynamics provides a unified perspective of the thermodynamic properties of various substances. To formulate thermodynamics in the language of sophisticated mathematics, thermodynamics is described by a variety of differential geometries, including contact and symplectic geometries. Meanwhile, affine geometry is a branch of differential geometry and is compatible with information geometry, where information geometry is known to be compatible with thermodynamics. By combining above, it is expected that thermodynamics is compatible with affine geometry and is expected that several affine geometric tools can be introduced in the analysis of thermodynamic systems. In this paper, affine geometric descriptions of equilibrium and nonequilibrium thermodynamics are proposed. For equilibrium systems, it is shown that several thermodynamic quantities can be identified with geometric objects in affine geometry and that several geometric objects can be introduced in thermodynamics. Examples of these include the following: specific heat is identified with the affine fundamental form and a flat connection is introduced in thermodynamic phase space. For nonequilibrium systems, two classes of relaxation processes are shown to be described in the language of an extension of affine geometry. Finally, this affine geometric description of thermodynamics for equilibrium and nonequilibrium systems is compared with a contact geometric description.
Citation: Journal of Mathematical Physics
PubDate: 2023-01-06T10:39:26Z
DOI: 10.1063/5.0124768
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- Analysis of a stochastic HIV model with cell-to-cell transmission and
Ornstein–Uhlenbeck process-
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Authors: Qun Liu
Abstract: Journal of Mathematical Physics, Volume 64, Issue 1, January 2023.
In this paper, we establish and analyze a stochastic human immunodeficiency virus model with both virus-to-cell and cell-to-cell transmissions and Ornstein–Uhlenbeck process, in which we suppose that the virus-to-cell infection rate and the cell-to-cell infection rate satisfy the Ornstein–Uhlenbeck process. First, we validate that there exists a unique global solution to the stochastic model with any initial value. Then, we adopt a stochastic Lyapunov function technique to develop sufficient criteria for the existence of a stationary distribution of positive solutions to the stochastic system, which reflects the strong persistence of all CD4+ T cells and free viruses. In particular, under the same conditions as the existence of a stationary distribution, we obtain the specific form of the probability density around the quasi-chronic infection equilibrium of the stochastic system. Finally, numerical simulations are conducted to validate these analytical results. Our results suggest that the methods used in this paper can be applied to study other viral infection models in which the infected CD4+ T cells are divided into latently infected and actively infected subgroups.
Citation: Journal of Mathematical Physics
PubDate: 2023-01-06T10:39:25Z
DOI: 10.1063/5.0127775
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- Asymptotic stability of the 2D MHD equations without magnetic diffusion
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Authors: Lihua Dong, Xiaoxia Ren
Abstract: Journal of Mathematical Physics, Volume 64, Issue 1, January 2023.
We investigate the asymptotic stability of certain steady solution to the 2D MHD equations without magnetic diffusion in an infinite strip domain. Decay rates of smooth solution to that system are also given.
Citation: Journal of Mathematical Physics
PubDate: 2023-01-05T11:33:44Z
DOI: 10.1063/5.0112577
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- Lie algebraic Carroll/Galilei duality
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Authors: José Figueroa-O’Farrill
Abstract: Journal of Mathematical Physics, Volume 64, Issue 1, January 2023.
We characterize Lie groups with bi-invariant bargmannian, galilean, or carrollian structures. Localizing at the identity, we show that Lie algebras with ad-invariant bargmannian, carrollian, or galilean structures are actually determined by the same data: a metric Lie algebra with a skew-symmetric derivation. This is the same data defining a one-dimensional double extension of the metric Lie algebra and, indeed, bargmannian Lie algebras coincide with such double extensions, containing carrollian Lie algebras as an ideal and projecting to galilean Lie algebras. This sets up a canonical correspondence between carrollian and galilean Lie algebras mediated by bargmannian Lie algebras. This reformulation allows us to use the structure theory of metric Lie algebras to give a list of bargmannian, carrollian, and galilean Lie algebras in the positive-semidefinite case. We also characterize Lie groups admitting a bi-invariant (ambient) leibnizian structure. Leibnizian Lie algebras extend the class of bargmannian Lie algebras and also set up a non-canonical correspondence between carrollian and galilean Lie algebras.
Citation: Journal of Mathematical Physics
PubDate: 2023-01-04T11:01:37Z
DOI: 10.1063/5.0132661
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- Blow-up solutions for a class of divergence Schrödinger equations with
intercritical inhomogeneous nonlinearity-
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Authors: Bowen Zheng, Tohru Ozawa, Jian Zhai
Abstract: Journal of Mathematical Physics, Volume 64, Issue 1, January 2023.
In this article, we study a class of divergence Schrödinger equations with intercritical inhomogeneous nonlinearity [math] where 2 − n < b < 2, c ≥ b − 2, and 2(2 − b) − bp < np − 2c < (2 − b)(p + 2). We prove the blow-up of radial solutions for the negative energy by using a virial-type estimate. In addition, we derive a generalized Gagliardo–Nirenberg inequality and use it to establish the general blow-up criteria for radial solutions with non-negative energy.
Citation: Journal of Mathematical Physics
PubDate: 2023-01-04T11:01:32Z
DOI: 10.1063/5.0098298
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- Exploring wave–particle behaviors of entangled Bragg diffracted
neutral atoms-
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Authors: Izma Qureshi, Tasawar Abbas, Muhammad Imran, Rameez-ul Islam
Abstract: Journal of Mathematical Physics, Volume 64, Issue 1, January 2023.
In this paper, we theoretically study the concept of the wave–particle duality of two entangled neutral Bragg diffracted atoms. This is an extension of a recent study where the same idea was proposed in the photonic setup [Man et al., Sci. Rep. 7, 42539 (2017)] using two independent Mach–Zehnder interferometers. Now, we propose a similar scheme using the cavity-QED based setup, which comprises two independent atomic de Broglie Mach–Zehnder–Bragg interferometers, a source cavity that generates two external momenta state entangled atoms. Once the atoms pass through the source cavity initially prepared in the superposition of zero and one photon, they emerge out of the cavity in entangled momenta state such that if one atom is transmitted to the upper interferometer, then the second atom must traverse the lower interferometer, and vice versa. The final atomic de Broglie beam splitter at the top interferometer is prepared in the superposition of zero and one photon and facilitates observing the wave or particle aspect in a single setting. This entire setup functions in off-resonant Bragg diffraction and the proposed schematics are shown to be experimentally feasible under contemporary research scenarios.
Citation: Journal of Mathematical Physics
PubDate: 2023-01-04T11:01:27Z
DOI: 10.1063/5.0102512
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- The full viscous quantum hydrodynamic system in one dimensional space
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Authors: Wenlong Sun, Yeping Li, Xiaoying Han
Abstract: Journal of Mathematical Physics, Volume 64, Issue 1, January 2023.
A viscous quantum hydrodynamic system for particle density, current density, energy density, and electrostatic potential, coupled with a Poisson equation, is studied in spatial one dimensional real line. The system is self-consistent in the sense that the electric field, which forms a forcing term in the momentum and energy equations, is determined by the coupled Poisson equation. First, the existence and uniqueness of the stationary solution is proved in an appropriate Sobolev space. Then, exponential stability of the stationary solution is established by constructing an a priori estimate. Since the techniques for classical hydrodynamic equations are not applicable here due to the quantum term, the existence of a local-in-time solution is obtained by showing the existence of local-in-time solutions of a reformulated system via the iteration method.
Citation: Journal of Mathematical Physics
PubDate: 2023-01-03T01:51:46Z
DOI: 10.1063/5.0125284
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- Quantum field presentation for generalized Hall–Littlewood functions
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Authors: Fang Huang, Chuanzhong Li
Abstract: Journal of Mathematical Physics, Volume 64, Issue 1, January 2023.
In this paper, we give the definition and quantum field presentation for a generalized Hall–Littlewood function using vertex operators, which is an extension of the Hall–Littlewood function. Furthermore, these generalized Hall–Littlewood functions can be deduced to universal characters at t = 0 and generalized Schur Q-functions at t = −1.
Citation: Journal of Mathematical Physics
PubDate: 2023-01-03T01:51:45Z
DOI: 10.1063/5.0093505
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- 2D Toda τ functions, weighted Hurwitz numbers and the Cayley graph:
Determinant representation and recursion formula-
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Authors: Xiang-Mao Ding, Xiang Li
Abstract: Journal of Mathematical Physics, Volume 64, Issue 1, January 2023.
We generalize the determinant representation of the Kadomtsev–Petviashvili τ functions to the case of the 2D Toda τ functions. The generating functions for the weighted Hurwitz numbers are a parametric family of 2D Toda τ functions, for which we give a determinant representation of weighted Hurwitz numbers. Then, we can get a finite-dimensional equation system for the weighted Hurwitz numbers [math] with the same dimension σ = ω = n. Using this equation system, we calculated the value of the weighted Hurwitz numbers with dimension 0, 1, 2, 3 and give a recursion formula for calculating the higher dimensional weighted Hurwitz numbers. Finally, we get a matrix representation for the Hurwitz numbers and obtain a determinant representation of weighted paths in the Cayley graph.
Citation: Journal of Mathematical Physics
PubDate: 2023-01-03T01:51:45Z
DOI: 10.1063/5.0127097
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- Comment on “Noether’s-type theorems on time scales” [J. Math. Phys.
61, 113502 (2020)]-
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Authors: Delfim F. M. Torres
Abstract: Journal of Mathematical Physics, Volume 64, Issue 1, January 2023.
We comment on the validity of Noether’s theorem and on the conclusions of Anerot et al. [J. Math. Phys. 61(11), 113502 (2020)].
Citation: Journal of Mathematical Physics
PubDate: 2023-01-03T01:51:43Z
DOI: 10.1063/5.0108477
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- Erratum: “Metastability for the degenerate Potts model with negative
external magnetic field under Glauber dynamics” [J. Math. Phys. 63,
123303 (2022)]-
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Authors: Gianmarco Bet, Anna Gallo, Francesca R. Nardi
Abstract: Journal of Mathematical Physics, Volume 64, Issue 1, January 2023.
Citation: Journal of Mathematical Physics
PubDate: 2023-01-03T01:51:42Z
DOI: 10.1063/5.0138999
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