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Resolvent expansions of 3D magnetic Schrödinger operators and Pauli operators 三维磁性薛定谔算子和保利算子的重溶剂展开
IF 1.3 3区 物理与天体物理
Journal of Mathematical Physics Pub Date : 2024-07-22 DOI: 10.1063/5.0211421
Arne Jensen, Hynek Kovařík
{"title":"Resolvent expansions of 3D magnetic Schrödinger operators and Pauli operators","authors":"Arne Jensen, Hynek Kovařík","doi":"10.1063/5.0211421","DOIUrl":"https://doi.org/10.1063/5.0211421","url":null,"abstract":"We obtain asymptotic resolvent expansions at the threshold of the essential spectrum for magnetic Schrödinger and Pauli operators in dimension three. These operators are treated as perturbations of the Laplace operator in L2(R3) and L2(R3;C2), respectively. The main novelty of our approach is to show that the relative perturbations, which are first order differential operators, can be factorized in suitably chosen auxiliary spaces. This allows us to derive the desired asymptotic expansions of the resolvents around zero. We then calculate their leading and sub-leading terms explicitly. Analogous factorization schemes for more general perturbations, including e.g. finite rank perturbations, are discussed as well.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141770758","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Exact solutions to SIR epidemic models via integrable discretization 通过积分离散化获得 SIR 流行病模型的精确解
IF 1.3 3区 物理与天体物理
Journal of Mathematical Physics Pub Date : 2024-07-22 DOI: 10.1063/5.0152442
Atsushi Nobe
{"title":"Exact solutions to SIR epidemic models via integrable discretization","authors":"Atsushi Nobe","doi":"10.1063/5.0152442","DOIUrl":"https://doi.org/10.1063/5.0152442","url":null,"abstract":"An integrable discretization of the SIR model with vaccination is proposed. Through the discretization, the conserved quantities of the continuous model are inherited to the discrete model, since the discretization is based on the intersection structure of the non-algebraic invariant curve defined by the conserved quantities. Uniqueness of the forward/backward evolution of the discrete model is demonstrated in terms of the single-valuedness of the Lambert W function on the positive real axis. Furthermore, the exact solution to the continuous SIR model with vaccination is constructed via the integrable discretization. When applied to the original SIR model, the discretization procedure leads to two kinds of integrable discretization, and the exact solution to the continuous SIR model is also deduced. It is furthermore shown that the discrete SIR model geometrically linearizes the time evolution by using the non-autonomous parallel translation of the line intersecting the invariant curve.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141770897","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Transcendental properties of entropy-constrained sets II 熵约束集的超越性质 II
IF 1.3 3区 物理与天体物理
Journal of Mathematical Physics Pub Date : 2024-07-22 DOI: 10.1063/5.0182728
Vjosa Blakaj, Chokri Manai
{"title":"Transcendental properties of entropy-constrained sets II","authors":"Vjosa Blakaj, Chokri Manai","doi":"10.1063/5.0182728","DOIUrl":"https://doi.org/10.1063/5.0182728","url":null,"abstract":"In this work, we address the question of the impossibility of certain single-letter formulas by exploiting the semi-algebraic nature of various entropy-constrained sets. The focus lies on studying the properties of the level sets of relative entropy, mutual information, and Rényi entropies. We analyze the transcendental structure of the set of states in which one of the aforementioned entropy quantities is fixed. Our results rule out (semi)algebraic single-shot characterizations of these entropy measures with bounded ancilla for both the classical and quantum cases.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141770896","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Topology of dynamical systems on the Fermi surface and galvanomagnetic phenomena in normal metals 费米面上动力学系统的拓扑结构与普通金属中的电流磁现象
IF 1.3 3区 物理与天体物理
Journal of Mathematical Physics Pub Date : 2024-07-19 DOI: 10.1063/5.0151512
A. Ya. Maltsev, S. P. Novikov
{"title":"Topology of dynamical systems on the Fermi surface and galvanomagnetic phenomena in normal metals","authors":"A. Ya. Maltsev, S. P. Novikov","doi":"10.1063/5.0151512","DOIUrl":"https://doi.org/10.1063/5.0151512","url":null,"abstract":"We discuss here the electron dynamics in crystals in rather strong magnetic fields. The most non-trivial part of this topic is the Novikov problem, namely, the problem of classifying non-closed trajectories for particles with an arbitrary dispersion relation in presence of a magnetic field. Here we will try to review both the classical results obtained in the study of this problem and the most recent results related to its most difficult part. At the same time, the study of electron dynamics on the Fermi surface can also be carried out in a more general setting, namely, as the study of the topology of the corresponding dynamical system and the physical phenomena associated with it. This approach is actually related to the Novikov problem, but includes the study of a wider range of issues, as well as a wider range of experimentally observed phenomena. Here we will try to describe a number of general principles relating changes in the topological pattern of trajectories on the Fermi surface to the observed phenomena in strong magnetic fields. We also note here that the study of the described effects can be quite informative for the experimental study of dispersion relations in conductors.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141742901","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Quantum continuity equations and quantum evolution systems for white noise operators 白噪声算子的量子连续性方程和量子演化系统
IF 1.3 3区 物理与天体物理
Journal of Mathematical Physics Pub Date : 2024-07-19 DOI: 10.1063/5.0176568
Un Cig Ji
{"title":"Quantum continuity equations and quantum evolution systems for white noise operators","authors":"Un Cig Ji","doi":"10.1063/5.0176568","DOIUrl":"https://doi.org/10.1063/5.0176568","url":null,"abstract":"Main purpose of this paper is to formulate canonical quantum continuity equations for white noise operators and to find their explicit unique solutions. By applying the continuity equations for white noise functionals and canonical topological isomorphisms between the spaces of white noise operators and the spaces of two-variable white noise functionals, we formulate canonical quantum continuity equations for white noise operators, and then we induce time dependent quantum evolution systems which are equivalent to the quantum continuity equations. Then we find explicit forms, in terms of the quantum analogues of generalized Fourier-Mehler transforms, of the unique solutions of the quantum continuity equations by solving the quantum evolution systems for white noise operators.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141743151","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Non-smoothness of the fundamental solutions for Schrödinger equations with super-quadratic and spherically symmetric potential 具有超二次方和球对称势的薛定谔方程基本解的非平稳性
IF 1.3 3区 物理与天体物理
Journal of Mathematical Physics Pub Date : 2024-07-19 DOI: 10.1063/5.0184443
Keiichi Kato, Wataru Nakahashi, Yukihide Tadano
{"title":"Non-smoothness of the fundamental solutions for Schrödinger equations with super-quadratic and spherically symmetric potential","authors":"Keiichi Kato, Wataru Nakahashi, Yukihide Tadano","doi":"10.1063/5.0184443","DOIUrl":"https://doi.org/10.1063/5.0184443","url":null,"abstract":"We study non-smoothness of the fundamental solution for the Schrödinger equation with a spherically symmetric and super-quadratic potential in the sense that V(x) ≥ C|x|2+ɛ at infinity with constants C > 0 and ɛ > 0. More precisely, we show the fundamental solution E(t, x, y) does not belong to C1 as a function of (t, x, y), which partially solves Yajima’s conjecture.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141742900","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Generalized solutions to the model of compressible viscous fluids coupled with the Poisson equation 与泊松方程耦合的可压缩粘性流体模型的广义解法
IF 1.3 3区 物理与天体物理
Journal of Mathematical Physics Pub Date : 2024-07-18 DOI: 10.1063/5.0190282
Zhong Tan, Hui Yang
{"title":"Generalized solutions to the model of compressible viscous fluids coupled with the Poisson equation","authors":"Zhong Tan, Hui Yang","doi":"10.1063/5.0190282","DOIUrl":"https://doi.org/10.1063/5.0190282","url":null,"abstract":"This paper deals with the model of compressible viscous and barotropic fluids coupled with the Poisson equation in a bounded domain Ω⊂R3 with C2+α (0 < α < 1) boundary ∂Ω. We prove the existence and weak-strong uniqueness of dissipative solutions when the adiabatic exponent γ > 1. We find that the Poisson term ρ∇Φ is not integrable when γ∈(1,32). We will make full use of the Poisson equation and energy inequality to overcome this difficulty. Finally, we obtain that ρ∇Φ leads to the decrease of Reynolds stress R and the increase of the energy dissipation defect E.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141743148","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Arithmetic version of Anderson localization for a class of C2 quasiperiodic Schrödinger operators 一类 C2 准周期薛定谔算子的算术版安德森定位法
IF 1.3 3区 物理与天体物理
Journal of Mathematical Physics Pub Date : 2024-07-18 DOI: 10.1063/5.0157371
Zhen Zhang, Xiong Li
{"title":"Arithmetic version of Anderson localization for a class of C2 quasiperiodic Schrödinger operators","authors":"Zhen Zhang, Xiong Li","doi":"10.1063/5.0157371","DOIUrl":"https://doi.org/10.1063/5.0157371","url":null,"abstract":"In this paper, we will prove that Anderson localization takes place for quasiperiodic Schrödinger operators with even C2 cos-type potentials, weak Liouvillean frequencies and Diophantine phases when the coupling is sufficiently large.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141742902","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Transitive nonlocal games 传递性非局部博弈
IF 1.3 3区 物理与天体物理
Journal of Mathematical Physics Pub Date : 2024-07-18 DOI: 10.1063/5.0199344
Prem Nigam Kar, Jitendra Prakash, David E. Roberson
{"title":"Transitive nonlocal games","authors":"Prem Nigam Kar, Jitendra Prakash, David E. Roberson","doi":"10.1063/5.0199344","DOIUrl":"https://doi.org/10.1063/5.0199344","url":null,"abstract":"We study a class of nonlocal games, called transitive games, for which the set of perfect strategies forms a semigroup. We establish several interesting correspondences of bisynchronous transitive games with the theory of compact quantum groups. In particular, we associate a quantum permutation group with each bisynchronous transitive game and vice versa. We prove that the existence of a C*-strategy, the existence of a quantum commuting strategy, and the existence of a classical strategy are all equivalent for bisynchronous transitive games. We then use some of these correspondences to establish necessary and sufficient conditions for some classes of correlations, that arise as perfect strategies of transitive games, to be nonlocal.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141742903","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Quantifying macrostructures in viscoelastic sub-diffusive flows 量化粘弹性亚扩散流中的宏观结构
IF 1.3 3区 物理与天体物理
Journal of Mathematical Physics Pub Date : 2024-07-17 DOI: 10.1063/5.0195666
T. Chauhan, K. Kalyanaraman, S. Sircar
{"title":"Quantifying macrostructures in viscoelastic sub-diffusive flows","authors":"T. Chauhan, K. Kalyanaraman, S. Sircar","doi":"10.1063/5.0195666","DOIUrl":"https://doi.org/10.1063/5.0195666","url":null,"abstract":"We present a theory to quantify the formation of spatiotemporal macrostructures (or the non-homogeneous regions of high viscosity at moderate to high fluid inertia) for viscoelastic sub-diffusive flows, by introducing a mathematically consistent decomposition of the polymer conformation tensor, into the so-called structure tensor. Our approach bypasses an inherent problem in the standard arithmetic decomposition, namely, the fluctuating conformation tensor fields may not be positive definite and hence, do not retain their physical meaning. Using well-established results in matrix analysis, the space of positive definite matrices is transformed into a Riemannian manifold by defining and constructing a geodesic via the inner product on its tangent space. This geodesic is utilized to define three scalar invariants of the structure tensor, which do not suffer from the caveats of the regular invariants (such as trace and determinant) of the polymer conformation tensor. First, we consider the problem of formulating perturbative expansions of the structure tensor using the geodesic, which is consistent with the Riemannian manifold geometry. A constraint on the maximum time, during which the evolution of the perturbative solution can be well approximated by linear theory along the Euclidean manifold, is found. A comparison between the linear and the nonlinear dynamics, identifies the role of nonlinearities in initiating the symmetry breaking of the flow variables about the centerline. Finally, fully nonlinear simulations of the viscoelastic sub-diffusive channel flows, underscore the advantage of using these invariants in effectively quantifying the macrostructures.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141743149","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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