{"title":"量子耗散系统稳定性分析的简单试验台","authors":"Thierry Goudon, Simona Rota Nodari","doi":"10.1007/s00023-024-01458-7","DOIUrl":null,"url":null,"abstract":"<p>We study a two-state quantum system with a nonlinearity intended to describe interactions with a complex environment, arising through a nonlocal coupling term. We study the stability of particular solutions, obtained as constrained extrema of the energy functional of the system. The simplicity of the model allows us to justify a complete stability analysis. This is the opportunity to review in detail the techniques to investigate the stability issue. We also bring out the limitations of perturbative approaches based on simpler asymptotic models.</p>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"1 1","pages":""},"PeriodicalIF":1.4000,"publicationDate":"2024-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Simple Testbed for Stability Analysis of Quantum Dissipative Systems\",\"authors\":\"Thierry Goudon, Simona Rota Nodari\",\"doi\":\"10.1007/s00023-024-01458-7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We study a two-state quantum system with a nonlinearity intended to describe interactions with a complex environment, arising through a nonlocal coupling term. We study the stability of particular solutions, obtained as constrained extrema of the energy functional of the system. The simplicity of the model allows us to justify a complete stability analysis. This is the opportunity to review in detail the techniques to investigate the stability issue. We also bring out the limitations of perturbative approaches based on simpler asymptotic models.</p>\",\"PeriodicalId\":463,\"journal\":{\"name\":\"Annales Henri Poincaré\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":1.4000,\"publicationDate\":\"2024-06-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annales Henri Poincaré\",\"FirstCategoryId\":\"4\",\"ListUrlMain\":\"https://doi.org/10.1007/s00023-024-01458-7\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"PHYSICS, MATHEMATICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annales Henri Poincaré","FirstCategoryId":"4","ListUrlMain":"https://doi.org/10.1007/s00023-024-01458-7","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
A Simple Testbed for Stability Analysis of Quantum Dissipative Systems
We study a two-state quantum system with a nonlinearity intended to describe interactions with a complex environment, arising through a nonlocal coupling term. We study the stability of particular solutions, obtained as constrained extrema of the energy functional of the system. The simplicity of the model allows us to justify a complete stability analysis. This is the opportunity to review in detail the techniques to investigate the stability issue. We also bring out the limitations of perturbative approaches based on simpler asymptotic models.
期刊介绍：
The two journals Annales de l''Institut Henri Poincaré, physique théorique and Helvetica Physical Acta merged into a single new journal under the name Annales Henri Poincaré - A Journal of Theoretical and Mathematical Physics edited jointly by the Institut Henri Poincaré and by the Swiss Physical Society.
The goal of the journal is to serve the international scientific community in theoretical and mathematical physics by collecting and publishing original research papers meeting the highest professional standards in the field. The emphasis will be on analytical theoretical and mathematical physics in a broad sense.
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