{"title":"梳状非马尔可夫量子力学","authors":"Alexander Iomin","doi":"10.1063/5.0226335","DOIUrl":null,"url":null,"abstract":"<p><p>Quantum dynamics of a particle on a two-dimensional comb structure is considered. This dynamics of a Hamiltonian system with a topologically constrained geometry leads to the non-Markovian behavior. In the framework of a rigorous analytical consideration, it is shown how a fractional time derivative appears for the relevant description of this non-Markovian quantum mechanics in the framework of fractional time Schrödinger equations. Analytical solutions for the Green functions are obtained for both conservative and periodically driven in time Hamiltonian systems.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":null,"pages":null},"PeriodicalIF":2.7000,"publicationDate":"2024-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Non-Markovian quantum mechanics on comb.\",\"authors\":\"Alexander Iomin\",\"doi\":\"10.1063/5.0226335\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>Quantum dynamics of a particle on a two-dimensional comb structure is considered. This dynamics of a Hamiltonian system with a topologically constrained geometry leads to the non-Markovian behavior. In the framework of a rigorous analytical consideration, it is shown how a fractional time derivative appears for the relevant description of this non-Markovian quantum mechanics in the framework of fractional time Schrödinger equations. Analytical solutions for the Green functions are obtained for both conservative and periodically driven in time Hamiltonian systems.</p>\",\"PeriodicalId\":9974,\"journal\":{\"name\":\"Chaos\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.7000,\"publicationDate\":\"2024-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Chaos\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1063/5.0226335\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Chaos","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1063/5.0226335","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Quantum dynamics of a particle on a two-dimensional comb structure is considered. This dynamics of a Hamiltonian system with a topologically constrained geometry leads to the non-Markovian behavior. In the framework of a rigorous analytical consideration, it is shown how a fractional time derivative appears for the relevant description of this non-Markovian quantum mechanics in the framework of fractional time Schrödinger equations. Analytical solutions for the Green functions are obtained for both conservative and periodically driven in time Hamiltonian systems.
期刊介绍：
Chaos: An Interdisciplinary Journal of Nonlinear Science is a peer-reviewed journal devoted to increasing the understanding of nonlinear phenomena and describing the manifestations in a manner comprehensible to researchers from a broad spectrum of disciplines.
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