{"title":"一维晶格φ4理论中的对称、混沌和温度","authors":"K. Aoki","doi":"10.12921/cmst.2017.0000055","DOIUrl":null,"url":null,"abstract":"The symmetries of the minimal $\\phi^4$ theory on the lattice, and trajectories which are chaotic, yet restricted to motions within subspaces due to symmetry reasons, are systematically analyzed. The chaotic dynamics of autonomous Hamiltonian systems are discussed, in relation to the thermodynamic laws. Possibilities of configurations with non-equal ideal gas temperatures in the steady state are investigated. The pairing of local (finite-time) Lyapunov exponents are analyzed, and their dependence on various factors, such as energy of the system, characteristics of the initial conditions are studied.","PeriodicalId":10561,"journal":{"name":"computational methods in science and technology","volume":"18 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2018-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Symmetry, Chaos and Temperature in the One-dimensional Lattice φ4 Theory\",\"authors\":\"K. Aoki\",\"doi\":\"10.12921/cmst.2017.0000055\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The symmetries of the minimal $\\\\phi^4$ theory on the lattice, and trajectories which are chaotic, yet restricted to motions within subspaces due to symmetry reasons, are systematically analyzed. The chaotic dynamics of autonomous Hamiltonian systems are discussed, in relation to the thermodynamic laws. Possibilities of configurations with non-equal ideal gas temperatures in the steady state are investigated. The pairing of local (finite-time) Lyapunov exponents are analyzed, and their dependence on various factors, such as energy of the system, characteristics of the initial conditions are studied.\",\"PeriodicalId\":10561,\"journal\":{\"name\":\"computational methods in science and technology\",\"volume\":\"18 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-01-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"computational methods in science and technology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.12921/cmst.2017.0000055\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"computational methods in science and technology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.12921/cmst.2017.0000055","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Symmetry, Chaos and Temperature in the One-dimensional Lattice φ4 Theory
The symmetries of the minimal $\phi^4$ theory on the lattice, and trajectories which are chaotic, yet restricted to motions within subspaces due to symmetry reasons, are systematically analyzed. The chaotic dynamics of autonomous Hamiltonian systems are discussed, in relation to the thermodynamic laws. Possibilities of configurations with non-equal ideal gas temperatures in the steady state are investigated. The pairing of local (finite-time) Lyapunov exponents are analyzed, and their dependence on various factors, such as energy of the system, characteristics of the initial conditions are studied.
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