{"title":"Construction of quadratic invariants for time-dependent systems in complex phase space using Struckmeier and Riedel approach","authors":"","doi":"10.1016/S0034-4877(24)00052-1","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we deal with the construction of quadratic invariants in a complex phase space under the transformation <em>z</em> = (<em>x</em> + <em>iy</em>) and\n<span><math><mrow><mover><mi>z</mi><mo>¯</mo></mover><mo>=</mo><mrow><mo>(</mo><mrow><mi>x</mi><mo>-</mo><mi>i</mi><mi>y</mi></mrow><mo>)</mo></mrow></mrow></math></span> for various time-dependent systems. For this purpose, Struckmeier and Riedel (SR) approach [<span><span>1</span></span>, <span><span>2</span></span>] is used. The constructed invariants include an unknown function <em>f</em><sub>2</sub>(<em>t</em>) that is a solution of a third-order differential equation and its coefficients can be determined by the trajectories of the particle. The invariants play an important role in the study of a dynamical system, to access the accuracy in numerical simulations and to investigate the classical and quantum integrability of a system.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Reports on Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0034487724000521","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}
引用次数: 0
Abstract
In this paper, we deal with the construction of quadratic invariants in a complex phase space under the transformation z = (x + iy) and
for various time-dependent systems. For this purpose, Struckmeier and Riedel (SR) approach [1, 2] is used. The constructed invariants include an unknown function f2(t) that is a solution of a third-order differential equation and its coefficients can be determined by the trajectories of the particle. The invariants play an important role in the study of a dynamical system, to access the accuracy in numerical simulations and to investigate the classical and quantum integrability of a system.
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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