{"title":"Higher order polynomial complex invariants for one-dimensional anharmonic potentials","authors":"S.B. Bhardwaj, Ram Mehar Singh, Vipin Kumar, Narender Kumar, Fakir Chand, Shalini Gupta","doi":"10.1016/S0034-4877(24)00011-9","DOIUrl":null,"url":null,"abstract":"<div><p>Exact quadratic in momenta complex invariants are investigated for both time independent and time dependent one-dimensional Hamiltonian systems possessing higher order nonlinearities within the framework of the rationalization method. The extended complex phase space approach is utilized to map a real system into complex space. Such invariants are expected to play a role in the analysis of complex trajectories and help to understand some new phenomena associated with complex potentials.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"93 1","pages":"Pages 71-86"},"PeriodicalIF":1.0000,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0034487724000119/pdfft?md5=7de74f018141c5f672b53eea0e7fe658&pid=1-s2.0-S0034487724000119-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Reports on Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0034487724000119","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}
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Abstract
Exact quadratic in momenta complex invariants are investigated for both time independent and time dependent one-dimensional Hamiltonian systems possessing higher order nonlinearities within the framework of the rationalization method. The extended complex phase space approach is utilized to map a real system into complex space. Such invariants are expected to play a role in the analysis of complex trajectories and help to understand some new phenomena associated with complex potentials.
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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