一维随机薛定谔算子的特征值波动

IF 1.2 3区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Journal of Mathematical Physics Pub Date : 2024-08-13 DOI:10.1063/5.0125197

Takuto Mashiko, Yuma Marui, Naoki Maruyama, Fumihiko Nakano

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引用次数: 0

摘要

作为 Breuer 等人的论文（Ann.Henri Poincare 22, 3763 (2021)）论文的扩展，我们研究了无穷远处具有随机衰减势的薛定谔算子特征值的线性统计量，其阶为 O(x-α) (α > 0)。我们首先证明了与 Breuer 等人，Ann.Henri Poincare 22, 3763 (2021)中关于f(H)迹的类似论述，其中f属于一类解析函数：存在一个临界指数αc，使得f(H)迹的波动在概率上收敛于α > αc，并满足α ≤ αc的中心极限定理声明，其中αc因f而异。

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Eigenvalue fluctuations of 1-dimensional random Schrödinger operators

As an extension to the paper by Breuer et al., Ann. Henri Poincare 22, 3763 (2021), we study the linear statistics for the eigenvalues of the Schrödinger operator with random decaying potential with order O(x−α) (α > 0) at infinity. We first prove similar statements as in Breuer et al., Ann. Henri Poincare 22, 3763 (2021) for the trace of f(H), where f belongs to a class of analytic functions: there exists a critical exponent αc such that the fluctuation of the trace of f(H) converges in probability for α > αc, and satisfies a central limit theorem statement for α ≤ αc, where αc differs depending on f. Furthermore we study the asymptotic behavior of its expectation value.

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来源期刊

Journal of Mathematical Physics 物理-物理：数学物理

CiteScore

2.20

自引率

15.40%

发文量

396

审稿时长

4.3 months

期刊介绍： Since 1960, the Journal of Mathematical Physics (JMP) has published some of the best papers from outstanding mathematicians and physicists. JMP was the first journal in the field of mathematical physics and publishes research that connects the application of mathematics to problems in physics, as well as illustrates the development of mathematical methods for such applications and for the formulation of physical theories. The Journal of Mathematical Physics (JMP) features content in all areas of mathematical physics. Specifically, the articles focus on areas of research that illustrate the application of mathematics to problems in physics, the development of mathematical methods for such applications, and for the formulation of physical theories. The mathematics featured in the articles are written so that theoretical physicists can understand them. JMP also publishes review articles on mathematical subjects relevant to physics as well as special issues that combine manuscripts on a topic of current interest to the mathematical physics community. JMP welcomes original research of the highest quality in all active areas of mathematical physics, including the following: Partial Differential Equations Representation Theory and Algebraic Methods Many Body and Condensed Matter Physics Quantum Mechanics - General and Nonrelativistic Quantum Information and Computation Relativistic Quantum Mechanics, Quantum Field Theory, Quantum Gravity, and String Theory General Relativity and Gravitation Dynamical Systems Classical Mechanics and Classical Fields Fluids Statistical Physics Methods of Mathematical Physics.