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Asymptotic behavior for a semilinear Bresse system with variable coefficients and locally distributed nonlinear dissipation J. Math. Phys. (IF 1.3) Pub Date : 2024-04-24 Sabeur Mansouri
In this paper, we consider a semilinear Bresse system in one dimensional bounded non homogeneous medium. We investigate stability issues for such a problem with a nonlinear damping acting in all three wave equations. We prove, firstly, the existence and uniqueness of the solutions by using the nonlinear semigroup method. Afterwords, we establish an uniform decay rates of the energy for these solutions
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Large-time lump patterns of Kadomtsev-Petviashvili I equation in a plasma analyzed via vector one-constraint method J. Math. Phys. (IF 1.3) Pub Date : 2024-04-24 Huian Lin, Liming Ling
In plasma physics, the Kadomtsev–Petviashvili I (KPI) equation is a fundamental model for investigating the evolution characteristics of nonlinear waves. For the KPI equation, the constraint method is an effective tool for generating solitonic or rational solutions from the solutions of lower-dimensional integrable systems. In this work, various nonsingular, rational lump solutions of the KPI equation
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Isometric spectral subtriples J. Math. Phys. (IF 1.3) Pub Date : 2024-04-19 A. Watcharangkool, W. Sucpikarnon, P. Bertozzini
We investigate the notion of subsystem in the framework of spectral triple as a generalized notion of noncommutative submanifold. In the case of manifolds, we consider several conditions on Dirac operators which turn embedded submanifolds into isometric submanifolds. We then suggest a definition of spectral subtriple based on the notion of submanifold algebra and the already existing notions of Riemannian
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Normalized solutions for Kirchhoff–Choquard type equations with different potentials J. Math. Phys. (IF 1.3) Pub Date : 2024-04-19 Min Liu, Rui Sun
In this paper, we are concerned with a Kirchhoff-Choquard type equation with L2-prescribed mass. Under different cases of the potential, we prove the existence of normalized ground state solutions to this equation. To obtain the boundedness from below of the energy functional and the compactness of the minimizing sequence, we apply the Gagliardo-Nirenberg inequality with the Riesz potential and the
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The Vladimirov operator with variable coefficients on finite adeles and the Feynman formulas for the Schrödinger equation J. Math. Phys. (IF 1.3) Pub Date : 2024-04-19 Roman Urban
We construct the Hamiltonian Feynman, Lagrangian Feynman, and Feynman–Kac formulas for the solution of the Cauchy problem with the Schrödinger operator −MgDα − V, where Dα is the Vladimirov operator and Mg is the operator of multiplication by a real-valued function g defined on the d-dimensional space AKd of finite adeles over the algebraic number field K.
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Positive rupture solutions of steady states for thin-film-type equations J. Math. Phys. (IF 1.3) Pub Date : 2024-04-18 Zongming Guo, Fangshu Wan
Positive radial and non-radial rupture solutions of steady states for thin-film-type equations are constructed via the asymptotic expansions up to arbitrary orders near the isolated rupture of prescribed positive rupture solutions of the equation. Some new types of rupture solutions for elliptic equations with negative exponents are provided.
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Ambient-space variational calculus for gauge fields on constant-curvature spacetimes J. Math. Phys. (IF 1.3) Pub Date : 2024-04-18 Xavier Bekaert, Nicolas Boulanger, Yegor Goncharov, Maxim Grigoriev
We propose a systematic generating procedure to construct free Lagrangians for massive, massless and partially massless, totally-symmetric tensor fields on AdSd+1 starting from the Becchi–Rouet–Stora–Tyutin (BRST) Lagrangian description of massless fields in the flat ambient space Rd,2. A novelty is that the Lagrangian is described by a d + 1 form on Rd,2 whose pullback to AdSd+1 gives the genuine
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On a nonlocal integral operator commuting with the Laplacian and the Sturm–Liouville problem: Low rank perturbations of the operator J. Math. Phys. (IF 1.3) Pub Date : 2024-04-17 Lotfi Hermi, Naoki Saito
We reformulate all general real coupled self-adjoint boundary value problems as integral operators and show that they are all finite rank perturbations of the free space Green’s function on the real line. This free space Green’s function corresponds to the nonlocal boundary value problem proposed earlier by Saito [Appl. Comput. Harmon. Anal. 25, 68–97 (2008)]. We prove these perturbations to be polynomials
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Exact periodic solution family of the complex cubic-quintic Ginzburg–Landau equation with intrapulse Raman scattering J. Math. Phys. (IF 1.3) Pub Date : 2024-04-17 Yuqian Zhou, Qiuyan Zhang, Jibin Li, Mengke Yu
In this paper, we consider the exact solutions of the complex cubic-quintic Ginzburg–Landau equation. By investigating the dynamical behavior of solutions of the corresponding traveling wave system of this PDE, we derive exact explicit parametric representations of the periodic wave solutions under given parameter conditions.
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Multiplicity and limit of solutions for logarithmic Schrödinger equations on graphs J. Math. Phys. (IF 1.3) Pub Date : 2024-04-17 Mengqiu Shao, Yunyan Yang, Liang Zhao
Let Ω be a finite connected subset of a locally finite graph G = (V, E) with the vertex set V and the edge set E. We investigate the logarithmic Schrödinger equation on Ω with the nonlinear term |u|p−2u log u2. For p > 2, through two different approaches which are the Brouwer degree theory and mountain-pass theorem, we obtain the existence of ground state solutions. We also apply the Brouwer degree
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Nonhydrostatic internal waves in the presence of mean currents and rotation J. Math. Phys. (IF 1.3) Pub Date : 2024-04-17 Jordan McCarney
In this paper we present a new exact solution that represents a Pollard-like, three-dimensional, nonlinear internal wave propagating on a non-uniform zonal current in a nonhydrostatic ocean model. The solution is presented in Lagrangian coordinates, and in the process we derive a dispersion relation for the internal wave which is subjected to a perturbative analysis which reveals the existence of two
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On the physical vacuum free boundary problem of the 1D shallow water equations coupled with the Poisson equation J. Math. Phys. (IF 1.3) Pub Date : 2024-04-17 Kelin Li, Yuexun Wang
This paper is concerned with the vacuum free boundary problem of the 1D shallow water equations coupled with the Poisson equation. We establish the local-in-time well-posedness of classical solutions to this system, and the solutions possess higher-order regularity all the way to the vacuum free boundary, though the density degenerates near the vacuum boundary. To deal with the force term generated
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New spinorial mass-quasilocal angular momentum inequality for initial data with marginally future trapped surface J. Math. Phys. (IF 1.3) Pub Date : 2024-04-16 Jarosław Kopiński, Alberto Soria, Juan A. Valiente Kroon
We prove a new geometric inequality that relates the Arnowitt–Deser–Misner mass of initial data to a quasilocal angular momentum of a marginally outer trapped surface (MOTS) inner boundary. The inequality is expressed in terms of a 1-spinor, which satisfies an intrinsic first-order Dirac-type equation. Furthermore, we show that if the initial data is axisymmetric, then the divergence-free vector used
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Self-adjoint momentum operator for a particle confined in a multi-dimensional cavity J. Math. Phys. (IF 1.3) Pub Date : 2024-04-16 A. Mariani, U.-J. Wiese
Based on the recent construction of a self-adjoint momentum operator for a particle confined in a one-dimensional interval, we extend the construction to arbitrarily shaped regions in any number of dimensions. Different components of the momentum vector do not commute with each other unless very special conditions are met. As such, momentum measurements should be considered one direction at a time
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Topological insulators and K-theory J. Math. Phys. (IF 1.3) Pub Date : 2024-04-12 Ralph M. Kaufmann, Dan Li, Birgit Wehefritz–Kaufmann
We analyze topological invariants, in particular Z2 invariants, which characterize time reversal invariant topological insulators, in the framework of index theory and K-theory. After giving a careful study of the underlying geometry and K-theory, we formalize topological invariants as elements of KR theory. To be precise, the strong topological invariants lie in the higher KR groups of spheres; KR̃−j−1(SD+1
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Representations of the affine ageing algebra agê(1) J. Math. Phys. (IF 1.3) Pub Date : 2024-04-11 Huaimin Li, Qing Wang
In this paper, we investigate the affine ageing algebra agê(1), which is a central extension of the loop algebra of the one-spatial ageing algebra age(1). Certain Verma-type modules including Verma modules and imaginary Verma modules of agê(1) are studied. Particularly, the simplicity of these modules are characterized and their irreducible quotient modules are determined. We also study the restricted
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On the first eigenvalue of the Laplacian for polygons J. Math. Phys. (IF 1.3) Pub Date : 2024-04-10 Emanuel Indrei
A 2006 conjecture of Antunes and Freitas is addressed connecting the scaling-invariant polygonal isoperimetric and principal frequency deficits for triangles. This yields a quantitative polygonal Faber–Krahn inequality for triangles with an explicit constant. Furthermore, a problem mentioned in the 1951 book “Isoperimetric Inequalities In Mathematical Physics” by Pólya and Szegö is addressed: a formula
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Irreducible modules over N = 2 superconformal algebras arising from algebraic D-modules J. Math. Phys. (IF 1.3) Pub Date : 2024-04-08 Haibo Chen, Xiansheng Dai, Dong Liu, Yufeng Pei
In this paper, we introduce a family of functors denoted as Fb, which act on algebraic D-modules and produce modules over N = 2 superconformal algebras. We demonstrate that these functors preserve irreducibility for all values of b, except for explicitly outlined cases. Moreover, we establish the necessary and sufficient conditions for determining the natural isomorphism between two such functors.
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On the existence and stability of stationary solutions for the compressible micropolar fluids J. Math. Phys. (IF 1.3) Pub Date : 2024-04-08 Wanchen Cui, Hong Cai
We consider the existence, uniqueness and nonlinear stability of stationary solutions for the three-dimensional compressible micropolar fluids with the external force of general form. More precisely, with the weighted L2 and L∞ estimates on solutions to the linearized problem, we show the existence and uniqueness of stationary solutions in some suitable function space by the contraction mapping principle
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Global well-posedness of three-dimensional incompressible Boussinesq system with temperature-dependent viscosity J. Math. Phys. (IF 1.3) Pub Date : 2024-04-08 Dongjuan Niu, Lu Wang
In this paper, we focus on the global well-posedness of solutions to three-dimensional incompressible Boussinesq equations with temperature-dependent viscosity under the smallness assumption of initial velocity fields u0 in the critical space Ḃ3,10. The key ingredients here lie in the decomposition of the velocity fields and the regularity theory of the Stokes system, which are crucial to get rid
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Connecting exceptional orthogonal polynomials of different kind J. Math. Phys. (IF 1.3) Pub Date : 2024-04-04 C. Quesne
The known asymptotic relations interconnecting Jacobi, Laguerre, and Hermite classical orthogonal polynomials are generalized to the corresponding exceptional orthogonal polynomials of codimension m. It is proved that Xm-Laguerre exceptional orthogonal polynomials of type I, II, or III can be obtained as limits of Xm-Jacobi exceptional orthogonal polynomials of the same type. Similarly, Xm-Hermite
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On α-z-Rényi divergence in the von Neumann algebra setting J. Math. Phys. (IF 1.3) Pub Date : 2024-04-04 Shinya Kato
We will investigate the α-z-Rényi divergence in the general von Neumann algebra setting based on Haagerup non-commutative Lp-spaces. In particular, we establish almost all its expected properties when 0 < α < 1 and some of them when α > 1. In an Appendix we also give an equality condition for generalized Hölder’s inequality in Haagerup non-commutative Lp-spaces.
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On the vanishing viscosity limit for the viscous and resistive 3D magnetohydrodynamic system with axisymmetric data J. Math. Phys. (IF 1.3) Pub Date : 2024-04-03 Youssouf Maafa, Oussama Melkemi
The current paper aims to explore the three-dimensional axisymmetric viscous and resistive magnetohydrodynamic system. This article is concerned with two outcomes, in the first result we prove the global existence of a unique solution for this system under initial data lying in the Sobolev spaces Hs × Hs−2 with s>52, furthermore, we obtain uniform estimates with respect to the viscosity. The second
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On approximating the symplectic spectrum of infinite-dimensional operators J. Math. Phys. (IF 1.3) Pub Date : 2024-04-03 V. B. Kiran Kumar, Anmary Tonny
The symplectic eigenvalues play a significant role in the finite-mode quantum information theory, and Williamson’s normal form proves to be a valuable tool in this area. Understanding the symplectic spectrum of a Gaussian Covariance Operator is a crucial task. Recently, in 2018, an infinite-dimensional analogue of Williamson’s Normal form was discovered, which has been instrumental in studying the
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On the Poisson equation for nonreversible Markov jump processes J. Math. Phys. (IF 1.3) Pub Date : 2024-04-02 Faezeh Khodabandehlou, Christian Maes, Karel Netočný
We study the solution V of the Poisson equation LV + f = 0 where L is the backward generator of an irreducible (finite) Markov jump process and f is a given centered state function. Bounds on V are obtained using a graphical representation derived from the Matrix Forest Theorem and using a relation with mean first-passage times. Applications include estimating time-accumulated differences during relaxation
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One-dimensional Schrödinger operator with decaying white noise potential J. Math. Phys. (IF 1.3) Pub Date : 2024-04-02 Nariyuki Minami
In this paper, we consider a random one-dimensional Schrödinger operator Hω on the half line which has, as its potential term, Gaussian white noise multiplied by a decaying factor. Although the potential term is not an ordinary function, but a distribution, it is possible to realize Hω as a symmetric operator in L2([0, ∞); dt) as was pointed out by the present author [Minami, Lect. Notes Math. 1299
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Uniqueness of conservative solutions to the modified Camassa-Holm equation via characteristics J. Math. Phys. (IF 1.3) Pub Date : 2024-04-01 Zhen He, Zhaoyang Yin
In this paper, for a given conservative solution, we introduce a set of auxiliary variables tailored to this particular solution, and prove that these variables satisfy a particular semilinear system having unique solutions. In turn, we get the uniqueness of the conservative solution in the original variables.
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Cucker–Smale type flocking models on a sphere J. Math. Phys. (IF 1.3) Pub Date : 2024-04-01 Sun-Ho Choi, Dohyun Kwon, Hyowon Seo
We present a Cucker–Smale type flocking model on a sphere including three terms: a centripetal force, multi-agent interactions on a sphere, and inter-particle bonding forces. We consider a rotation operator to compare velocity vectors on different tangent spaces. Due to the geometric restriction, the rotation operator is singular at antipodal points and the relative velocity between two agents located
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Asymptotics for the semi-dissipative 2D Boussinesq system J. Math. Phys. (IF 1.3) Pub Date : 2024-03-29 Jinfang He, Jijun Wang, Yandong Zhao
In this article, we consider the convergence from the semi-dissipative 2D Boussinesq equations to the 2D Navier–Stokes equations in some sense. When the temperature variable θ tends to 0, we prove that the component uθ of the solution of the semi-dissipative 2D Boussinesq equations is converging to the solution u of the 2D Navier–Stokes equations in the space H and uθ is asymptotically converging to
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The non-holonomic Herglotz variational problem J. Math. Phys. (IF 1.3) Pub Date : 2024-03-28 Enrico Massa, Enrico Pagani
The geometric approach to the study of the Herglotz problem developed in Massa and Pagani [J. Math. Phys. 64, 102902 (2023)] is extended to the case in which the evolution of the system is subject to a set of non-holonomic constraints. The original setup is suitably adapted to the case in study. Various aspects of the problem are considered: the direct derivation of the evolution equations; the super-lagrangian
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Inverse problems for Dirac operators with constant delay less than half of the interval J. Math. Phys. (IF 1.3) Pub Date : 2024-03-27 Feng Wang, Chuan-Fu Yang
In this work, we consider Dirac-type operators with a constant delay of less than half of the interval and not less than two-fifths of the interval. For our considered Dirac-type operators, two inverse spectral problems are studied. Specifically, reconstruction of two complex L2-potentials is studied from complete spectra of two boundary value problems with one common boundary condition y1(0) = 0 or
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Pointwise modulus of continuity of the Lyapunov exponent and integrated density of states for analytic multi-frequency quasi-periodic M(2,C) cocycles J. Math. Phys. (IF 1.3) Pub Date : 2024-03-27 M. Powell
It is known that the Lyapunov exponent for multifrequency analytic cocycles is weak-Hölder continuous in cocycle for certain Diophantine frequencies, and that this implies certain regularity of the integrated density of states in energy for Jacobi operators. In this paper, we establish the pointwise modulus of continuity in both cocycle and frequency and obtain analogous regularity of the integrated
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An integrable four-component Camassa–Holm-type system J. Math. Phys. (IF 1.3) Pub Date : 2024-03-27 Chendi Zhu, Jing Kang
In this paper, we propose a new four-component Camassa–Holm-type system. The Lax pair and infinitely many conservation laws of this system are constructed. Bi-Hamiltonian structures and N-peakon solutions of some prototypical equations in this system are considered. In particular, the “W/M”-shape peakon solutions are obtained.
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Direct and inverse resonance problems for the massless Dirac operator on the half line J. Math. Phys. (IF 1.3) Pub Date : 2024-03-26 Xiao-Chuan Xu, Ting-Ting Zuo
For the direct problem, we give the asymptotic distribution of the resonances in the complex plane. For the inverse problem, we prove several uniqueness theorems of recovering the potential on the whole interval from partial resonances and the information of the potential on a subinterval.
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A counterexample to a conjecture of M. Ismail J. Math. Phys. (IF 1.3) Pub Date : 2024-03-25 K. Castillo, D. Mbouna
In an earlier work [K. Castillo et al., J. Math. Anal. Appl. 514, 126358 (2022)], we give positive answer to the first, and apparently more easy, part of a conjecture of M. Ismail concerning the characterization of the continuous q-Jacobi polynomials, Al-Salam-Chihara polynomials or special or limiting cases of them. In this note we present an example that disproves the second part of such a conjecture
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On a class of Kirchhoff type logarithmic Schrödinger equations involving the critical or supercritical Sobolev exponent J. Math. Phys. (IF 1.3) Pub Date : 2024-03-22 Haining Fan, Yongbin Wang, Lin Zhao
In this paper, we study a class of Kirchhoff type logarithmic Schrödinger equations involving the critical or supercritical Sobolev exponent. Such problems cannot be studied by applying variational methods in a standard way, because the nonlinearities do not satisfy the Ambrosetti-Rabinowitz condition and change sign. Moreover, the appearance of the logarithmic term makes the associated energy functional
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BMS-supertranslation charges at the critical sets of null infinity J. Math. Phys. (IF 1.3) Pub Date : 2024-03-21 Mariem Magdy Ali Mohamed, Kartik Prabhu, Juan A. Valiente Kroon
For asymptotically flat spacetimes, a conjecture by Strominger states that asymptotic BMS-supertranslations and their associated charges at past null infinity I− can be related to those at future null infinity I+ via an antipodal map at spatial infinity i0. We analyze the validity of this conjecture using Friedrich’s formulation of spatial infinity, which gives rise to a regular initial value problem
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Thermal time as an unsharp observable J. Math. Phys. (IF 1.3) Pub Date : 2024-03-20 Jan van Neerven, Pierre Portal
We show that the Connes–Rovelli thermal time associated with the quantum harmonic oscillator can be described as an (unsharp) observable, that is, as a positive operator valued measure. We furthermore present extensions of this result to the free massless relativistic particle in one dimension and to a hypothetical physical system whose equilibrium state is given by the noncommutative integral.
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A new division algebra representation of E7 from E8 J. Math. Phys. (IF 1.3) Pub Date : 2024-03-20 Tevian Dray, Corinne A. Manogue, Robert A. Wilson
We decompose the Lie algebra e8(−24) into representations of e7(−25)⊕sl(2,R) using our recent description of e8 in terms of (generalized) 3 × 3 matrices over pairs of division algebras. Freudenthal’s description of both e7 and its minimal representation are therefore realized explicitly within e8, with the action given by the (generalized) matrix commutator in e8, and with a natural parameterization
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A new division algebra representation of E8 J. Math. Phys. (IF 1.3) Pub Date : 2024-03-20 Tevian Dray, Corinne A. Manogue, Robert A. Wilson
We construct the well-known decomposition of the Lie algebra e8 into representations of e6⊕su(3) using explicit matrix representations over pairs of division algebras. The minimal representation of e6, namely the Albert algebra, is thus realized explicitly within e8, with the action given by the matrix commutator in e8, and with a natural parameterization using division algebras. Each resulting copy
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Painlevé analysis, Prelle–Singer approach, symmetries and integrability of damped Hénon–Heiles system J. Math. Phys. (IF 1.3) Pub Date : 2024-03-19 C. Uma Maheswari, N. Muthuchamy, V. K. Chandrasekar, R. Sahadevan, M. Lakshmanan
We consider a modified damped version of Hénon–Heiles system and investigate its integrability. By extending the Painlevé analysis of ordinary differential equations we find that the modified Hénon–Heiles system possesses the Painlevé property for three distinct parametric restrictions. For each of the identified cases, we construct two independent integrals of motion using the well known Prelle–Singer
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Hamiltonian Monodromy via spectral Lax pairs J. Math. Phys. (IF 1.3) Pub Date : 2024-03-19 G. J. Gutierrez Guillen, D. Sugny, P. Mardešić
Hamiltonian Monodromy is the simplest topological obstruction to the existence of global action-angle coordinates in a completely integrable system. We show that this property can be studied in a neighborhood of a focus-focus singularity by a spectral Lax pair approach. From the Lax pair, we derive a Riemann surface which allows us to compute in a straightforward way the corresponding Monodromy matrix
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Analytic structure of the associated Legendre functions of the second kind J. Math. Phys. (IF 1.3) Pub Date : 2024-03-18 Tianye Liu, Daniel A. Norman, Philip D. Mannheim
We consider the complex ν plane structure of the associated Legendre functions of the second kind Qν−1/2−K(coshρ). We find that for any noninteger value of K the Qν−1/2−K(coshρ) have an infinite number of poles in the complex ν plane, but for any negative integer K there are no poles at all. For K = 0 or any positive integer K there is only a finite number of poles, with there only being one single
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On topological obstructions to the existence of non-periodic Wannier bases J. Math. Phys. (IF 1.3) Pub Date : 2024-03-18 Yu. Kordyukov, V. Manuilov
Recently, Ludewig and Thiang introduced a notion of a uniformly localized Wannier basis with localization centers in an arbitrary uniformly discrete subset D in a complete Riemannian manifold X. They show that, under certain geometric conditions on X, the class of the orthogonal projection onto the span of such a Wannier basis in the K-theory of the Roe algebra C*(X) is trivial. In this paper, we clarify
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Cosmic strings arising in a self-dual Abelian Higgs model J. Math. Phys. (IF 1.3) Pub Date : 2024-03-15 Lei Cao, Shouxin Chen
In this note we construct self-dual cosmic strings from an Abelian Higgs model in two-dimension with a polynomial formation of the potential energy density. By integrating the Einstein equations, we obtain an equivalent form to the sources, which is a nonlinear elliptic equation with singularities and complicated exponential terms. We prove the existence of a solution governing strings in the broken
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Exact solutions of Burgers equation with moving boundary J. Math. Phys. (IF 1.3) Pub Date : 2024-03-13 Eugenia N. Petropoulou, Mohammad Ferdows, Efstratios E. Tzirtzilakis
In this paper, new symmetry reductions and similarity solutions for Burgers equation with moving boundary are obtained by means of Lie’s method of infinitesimal transformation groups, for a linearly moving boundary as well as a parabolically moving boundary. By using discrete symmetries, new analytical solutions for the problem under consideration are presented, for two cases of the moving boundary:
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Convergence rates for the stationary and non-stationary Navier–Stokes equations over non-Lipschitz boundaries J. Math. Phys. (IF 1.3) Pub Date : 2024-03-11 Yiping Zhang
In this paper, we consider the convergence rates for the 2D stationary and non-stationary Navier–Stokes Equations over highly oscillating periodic bumpy John domains with C2 regularity in some neighborhood of the boundary point (0,0). For the stationary case, using the variational equation satisfied by the solution and the correctors for the bumpy John domains obtained by Higaki and Zhuge [Arch. Ration
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Summation formulas generated by Hilbert space eigenproblem J. Math. Phys. (IF 1.3) Pub Date : 2024-03-11 Petar Mali, Sonja Gombar, Slobodan Radošević, Milica Rutonjski, Milan Pantić, Milica Pavkov-Hrvojević
We demonstrate that certain classes of Schlömilch-like infinite series and series that include generalized hypergeometric functions can be calculated in closed form starting from a simple quantum model of a particle trapped inside an infinite potential well and using principles of quantum mechanics. We provide a general framework based on the Hilbert space eigenproblem that can be applied to different
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Local spectral optimisation for Robin problems with negative boundary parameter on quadrilaterals J. Math. Phys. (IF 1.3) Pub Date : 2024-03-11 James Larsen-Scott, Julie Clutterbuck
We investigate the Robin eigenvalue problem for the Laplacian with negative boundary parameter on quadrilateral domains of fixed area. In this paper, we prove that the square is a local maximiser of the first eigenvalue with respect to the Hausdorff metric. We also provide asymptotic results relating to the optimality of the square for extreme values of the Robin parameter.
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Large time behavior for the Hall-MHD equations with horizontal dissipation J. Math. Phys. (IF 1.3) Pub Date : 2024-03-08 Haifeng Shang
This paper examines the large time behavior of solutions to the 3D Hall-magnetohydrodynamic equations with horizontal dissipation. As preparations we establish the global well-posedness of solutions and their global explicitly uniform upper bounds for Hk (k ≥ 1) to this system with initial data small in H2. Furthermore, if the initial data also belongs to homogeneous negative Besov spaces, we prove
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On the self-overlap in vector spin glasses J. Math. Phys. (IF 1.3) Pub Date : 2024-03-07 Hong-Bin Chen
We consider vector spin glass models with self-overlap correction. Since the limit of free energy is an infimum, we use arguments analogous to those for generic models to show the following: (1) the averaged self-overlap converges; (2) the self-overlap concentrates; (3) the infimum optimizes over paths whose right endpoints are the limit of self-overlap. Lastly, using these, we directly verify the
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Some uncertainty principles for the quaternion Heisenberg group J. Math. Phys. (IF 1.3) Pub Date : 2024-03-06 Adil Bouhrara, Samir Kabbaj
Hardy type theorem with the Heisenberg–Pauli–Weyl inequality and the logarithmic uncertainty principle for the quaternion Heisenberg group are established.
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On Doob h-transformations for finite-time quantum state reduction J. Math. Phys. (IF 1.3) Pub Date : 2024-03-06 Levent Ali Mengütürk
The paper develops a finite-time quantum state reduction framework via the use of Lévy random bridges (LRBs) that can be understood as Doob h-transformations on Lévy processes. Building upon the non-anticipative semimartingale representation of LRBs, we propose a family of energy-driven stochastic Schrödinger equations that go beyond the purely-continuous Brownian motion setup, and enter the scope
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Stability of the gapless pure point spectrum of self-adjoint operators J. Math. Phys. (IF 1.3) Pub Date : 2024-03-05 Paolo Facchi, Marilena Ligabò
We consider a self-adjoint operator T on a separable Hilbert space, with pure-point and simple spectrum with accumulations at finite points. Explicit conditions are stated on the eigenvalues of T and on the bounded perturbation V ensuring the global stability of the spectral nature of T + ɛV, ε∈R.
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Asymptotic distribution of nodal intersections for ARW against a surface J. Math. Phys. (IF 1.3) Pub Date : 2024-03-05 Riccardo W. Maffucci, Maurizia Rossi
We investigate Gaussian Laplacian eigenfunctions (Arithmetic Random Waves) on the three-dimensional standard flat torus, in particular the asymptotic distribution of the nodal intersection length against a fixed regular reference surface. Expectation and variance have been addressed by Maffucci [Ann. Henri Poincaré 20(11), 3651–3691 (2019)] who found that the expected length is proportional to the
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QFT with tensorial and local degrees of freedom: Phase structure from functional renormalization J. Math. Phys. (IF 1.3) Pub Date : 2024-03-04 Joseph Ben Geloun, Andreas G. A. Pithis, Johannes Thürigen
Field theories with combinatorial non-local interactions such as tensor invariants are interesting candidates for describing a phase transition from discrete quantum-gravitational to continuum geometry. In the so-called cyclic-melonic potential approximation of a tensorial field theory on the r-dimensional torus it was recently shown using functional renormalization group techniques that no such phase
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Effective splitting of invariant measures for a stochastic reaction diffusion equation with multiplicative noise J. Math. Phys. (IF 1.3) Pub Date : 2024-03-04 Ting Lei, Guanggan Chen
This work is concerned with the effective dynamics for the stochastic reaction diffusion equations with cubic nonlinearity driven by a multiplicative noise. By splitting the solution into the finite dimension kernel space and its complement space with some appropriate multi-scale, it derives the dominant solution and the effective invariant measure in the sense of the Wasserstein distance, which capture
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Regularity and uniqueness of global solutions for the 3D compressible micropolar fluids J. Math. Phys. (IF 1.3) Pub Date : 2024-03-01 Mingyu Zhang
This paper concerns the regularity and uniqueness of 3D compressible micropolar fluids in the whole space R3. We first establish some new Lp gradient estimates of the solutions for the system, then by virtue of the “div-rot” decomposition technique, the key estimates ‖∇u‖L3 and ‖∇w‖L3 are obtained. As a result, the existence and uniqueness of global solutions belonging to a new class of functions are
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Global existence of the strong solution to the climate dynamics model with topography effects and phase transformation of water vapor J. Math. Phys. (IF 1.3) Pub Date : 2024-03-01 Ruxu Lian, Jieqiong Ma, Qingcun Zeng
This study investigates a climate dynamics model that incorporates topographical effects and the phase transformation of water vapor. The system comprises the Navier–Stokes equations, the temperature equation, the specific humidity equation, and the water content equation, all adhering to principles of energy conservation. Applying energy estimation methods, the Helmholtz–Weyl decomposition theorem
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Reconstruction techniques for complex potentials J. Math. Phys. (IF 1.3) Pub Date : 2024-03-01 Vladislav V. Kravchenko
An approach for solving a variety of inverse coefficient problems for the Sturm–Liouville equation −y″ + q(x)y = ρ2y with a complex valued potential q(x) is presented. It is based on Neumann series of Bessel functions representations for solutions. With their aid the problem is reduced to a system of linear algebraic equations for the coefficients of the representations. The potential is recovered