{"title":"Gaussian quantum systems and Kahler geometrical structure","authors":"Mykola Yaremenko","doi":"10.19139/soic-2310-5070-1546","DOIUrl":null,"url":null,"abstract":"In this article, we study the phase-space distribution of the quantum state as a framework to describe the different properties of quantum systems in continuous-variable systems. The natural approach to quantum systems is given the Gaussian Wigner representation, to unify the description of bosonic and fermionic quantum states, we study the structure of the Kahler space geometry as the geometry generated by three forms under the agreement conditions depended on the nature of the state bosonic or fermionic. Multi-mode light is studied, and we established that the Fock space vacuum corresponds to a certain homogeneous Gaussian state.","PeriodicalId":53461,"journal":{"name":"Statistics, Optimization and Information Computing","volume":"8 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Statistics, Optimization and Information Computing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.19139/soic-2310-5070-1546","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0
Abstract
In this article, we study the phase-space distribution of the quantum state as a framework to describe the different properties of quantum systems in continuous-variable systems. The natural approach to quantum systems is given the Gaussian Wigner representation, to unify the description of bosonic and fermionic quantum states, we study the structure of the Kahler space geometry as the geometry generated by three forms under the agreement conditions depended on the nature of the state bosonic or fermionic. Multi-mode light is studied, and we established that the Fock space vacuum corresponds to a certain homogeneous Gaussian state.
期刊介绍：
Statistics, Optimization and Information Computing (SOIC) is an international refereed journal dedicated to the latest advancement of statistics, optimization and applications in information sciences. SOIC publishes original research/survey papers on theory, algorithms and applications which covering the range of the interface of statistics, optimization and information sciences. Topics of interest are (but not limited to): Statistical theory and applications [...] Optimization methods and applications[...] Information computing and machine intelligence[...]
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