Krylov complexity and chaos in quantum mechanics

IF 5 1区物理与天体物理 Q1 PHYSICS, PARTICLES & FIELDS

Journal of High Energy Physics Pub Date : 2023-11-08 DOI:10.1007/jhep11(2023)040

Koji Hashimoto, Keiju Murata, Norihiro Tanahashi, Ryota Watanabe

引用次数: 11

Abstract

A bstract Recently, Krylov complexity was proposed as a measure of complexity and chaoticity of quantum systems. We consider the stadium billiard as a typical example of the quantum mechanical system obtained by quantizing a classically chaotic system, and numerically evaluate Krylov complexity for operators and states. Despite no exponential growth of the Krylov complexity, we find a clear correlation between variances of Lanczos coefficients and classical Lyapunov exponents, and also a correlation with the statistical distribution of adjacent spacings of the quantum energy levels. This shows that the variances of Lanczos coefficients can be a measure of quantum chaos. The universality of the result is supported by our similar analysis of Sinai billiards. Our work provides a firm bridge between Krylov complexity and classical/quantum chaos.

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量子力学中的克雷洛夫复杂性和混沌

最近，Krylov复杂度被提出作为量子系统复杂性和混沌性的度量。我们将体育场台球作为量子力学系统的一个典型例子，将一个经典混沌系统量子化，并对算子和状态的Krylov复杂度进行了数值计算。尽管Krylov复杂度没有指数增长，但我们发现Lanczos系数的方差与经典Lyapunov指数之间存在明显的相关性，并且与量子能级相邻间距的统计分布也存在相关性。这表明Lanczos系数的方差可以作为量子混沌的度量。我们对西奈台球的类似分析支持了结果的普适性。我们的工作为克雷洛夫复杂性和经典/量子混沌之间提供了一座坚实的桥梁。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of High Energy Physics PHYSICS, PARTICLES & FIELDS-

CiteScore

10.00

自引率

46.30%

发文量

2107

审稿时长

12 weeks

期刊介绍： The aim of the Journal of High Energy Physics (JHEP) is to ensure fast and efficient online publication tools to the scientific community, while keeping that community in charge of every aspect of the peer-review and publication process in order to ensure the highest quality standards in the journal. Consequently, the Advisory and Editorial Boards, composed of distinguished, active scientists in the field, jointly establish with the Scientific Director the journal''s scientific policy and ensure the scientific quality of accepted articles. JHEP presently encompasses the following areas of theoretical and experimental physics: Collider Physics Underground and Large Array Physics Quantum Field Theory Gauge Field Theories Symmetries String and Brane Theory General Relativity and Gravitation Supersymmetry Mathematical Methods of Physics Mostly Solvable Models Astroparticles Statistical Field Theories Mostly Weak Interactions Mostly Strong Interactions Quantum Field Theory (phenomenology) Strings and Branes Phenomenological Aspects of Supersymmetry Mostly Strong Interactions (phenomenology).