CHAIN TRANSITIVITY AND SHADOWING PROPERTY IN QUANTUM DYNAMICAL SYSTEMS

IF 1 4区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Reports on Mathematical Physics Pub Date : 2024-04-01 DOI:10.1016/S0034-4877(24)00026-0

Mona Khare, Ravi Singh Chauhan

引用次数: 0

Abstract

In the present paper we investigate the notions of chain transitivity, ε-shadowing and expansiveness in the dynamics of quantum measure spaces (P, μ). Besides of several results proved for a chain transitive quantum dynamical system, it is shown that if a measure preserving morphism φ on (P, μ) is chain mixing, then φⁿ is chain transitive for each n ∊ ℕ. The present study also elucidates interrelationship between ε-shadowing and expansiveness of a quantum dynamical system (P, μ, φ) under suitable conditions. Examples are given to support the theory.

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量子动力学系统中的链传递性和阴影特性

本文研究了量子度量空间（P，μ）动力学中的链传递性、ε阴影和广延性概念。除了证明了链传递性量子动力学系统的几个结果之外，还证明了如果（P, μ）上的度量保持态φ是链混合的，那么对于每个 n ∊ ℕ，φn 都是链传递性的。本研究还阐明了量子动力学系统（P, μ, φ）在适当条件下的ε阴影和扩张性之间的相互关系。举例说明了这一理论。

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

Reports on Mathematical Physics 物理-物理：数学物理

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： Reports on Mathematical Physics publish papers in theoretical physics which present a rigorous mathematical approach to problems of quantum and classical mechanics and field theories, relativity and gravitation, statistical physics, thermodynamics, mathematical foundations of physical theories, etc. Preferred are papers using modern methods of functional analysis, probability theory, differential geometry, algebra and mathematical logic. Papers without direct connection with physics will not be accepted. Manuscripts should be concise, but possibly complete in presentation and discussion, to be comprehensible not only for mathematicians, but also for mathematically oriented theoretical physicists. All papers should describe original work and be written in English.