{"title":"CHAIN TRANSITIVITY AND SHADOWING PROPERTY IN QUANTUM DYNAMICAL SYSTEMS","authors":"Mona Khare, Ravi Singh Chauhan","doi":"10.1016/S0034-4877(24)00026-0","DOIUrl":null,"url":null,"abstract":"<div><p>In the present paper we investigate the notions of chain transitivity, ε-shadowing and expansiveness in the dynamics of quantum measure spaces (<em>P</em>, μ). Besides of several results proved for a chain transitive quantum dynamical system, it is shown that if a measure preserving morphism φ on (<em>P</em>, μ) is chain mixing, then φ<sup><em>n</em></sup> is chain transitive for each <em>n</em> ∊ ℕ. The present study also elucidates interrelationship between ε-shadowing and expansiveness of a quantum dynamical system (<em>P</em>, μ, φ) under suitable conditions. Examples are given to support the theory.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Reports on Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0034487724000260","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
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.
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.
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