{"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":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"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\":2,\"journal\":{\"name\":\"ACS Applied Bio Materials\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.6000,\"publicationDate\":\"2024-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACS Applied Bio Materials\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1063/5.0226335\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATERIALS SCIENCE, BIOMATERIALS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1063/5.0226335","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","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.
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