Application of the diffusion equation to prove scaling invariance on the transition from limited to unlimited diffusion

Detalhes bibliográficos
Autor(a) principal: Leonel, Edson D. [UNESP]
Data de Publicação: 2020
Outros Autores: Mayumi Kuwana, Célia [UNESP], Yoshida, Makoto [UNESP], Antonio De Oliveira, Juliano [UNESP]
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1209/0295-5075/131/10004
http://hdl.handle.net/11449/208002
Resumo: The scaling invariance for chaotic orbits near a transition from limited to unlimited diffusion in a dissipative standard mapping is explained via the analytical solution of the diffusion equation. It gives the probability of observing a particle with a specific action at a given time. We show the diffusion coefficient varies slowly with the time and is responsible for suppressing the unlimited diffusion. The momenta of the probability are determined and the behavior of the average squared action is obtained. The limits of small and large time recover the results known in the literature from the phenomenological approach and, as a bonus, a scaling for intermediate time is obtained as dependent on the initial action. The formalism presented is robust enough and can be applied in a variety of other systems including time-dependent billiards near a transition from limited to unlimited Fermi acceleration as we show at the end of the letter and in many other systems under the presence of dissipation as well as near a transition from integrability to non-integrability.
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spelling Application of the diffusion equation to prove scaling invariance on the transition from limited to unlimited diffusionThe scaling invariance for chaotic orbits near a transition from limited to unlimited diffusion in a dissipative standard mapping is explained via the analytical solution of the diffusion equation. It gives the probability of observing a particle with a specific action at a given time. We show the diffusion coefficient varies slowly with the time and is responsible for suppressing the unlimited diffusion. The momenta of the probability are determined and the behavior of the average squared action is obtained. The limits of small and large time recover the results known in the literature from the phenomenological approach and, as a bonus, a scaling for intermediate time is obtained as dependent on the initial action. The formalism presented is robust enough and can be applied in a variety of other systems including time-dependent billiards near a transition from limited to unlimited Fermi acceleration as we show at the end of the letter and in many other systems under the presence of dissipation as well as near a transition from integrability to non-integrability.Universidade Estadual Paulista (UNESP) Departamento de Física, Av. 24A, 1515, Bela VistaUniversidade Estadual Paulista (UNESP) Campus de S o Jo o da Boa Vista, Av. Profa. Isette Corr a Font o, 550Universidade Estadual Paulista (UNESP) Departamento de Física, Av. 24A, 1515, Bela VistaUniversidade Estadual Paulista (UNESP) Campus de S o Jo o da Boa Vista, Av. Profa. Isette Corr a Font o, 550Universidade Estadual Paulista (Unesp)Leonel, Edson D. [UNESP]Mayumi Kuwana, Célia [UNESP]Yoshida, Makoto [UNESP]Antonio De Oliveira, Juliano [UNESP]2021-06-25T11:04:41Z2021-06-25T11:04:41Z2020-07-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.1209/0295-5075/131/10004EPL, v. 131, n. 1, 2020.1286-48540295-5075http://hdl.handle.net/11449/20800210.1209/0295-5075/131/100042-s2.0-85091701098Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengEPLinfo:eu-repo/semantics/openAccess2021-10-23T18:47:15Zoai:repositorio.unesp.br:11449/208002Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462021-10-23T18:47:15Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Application of the diffusion equation to prove scaling invariance on the transition from limited to unlimited diffusion
title Application of the diffusion equation to prove scaling invariance on the transition from limited to unlimited diffusion
spellingShingle Application of the diffusion equation to prove scaling invariance on the transition from limited to unlimited diffusion
Leonel, Edson D. [UNESP]
title_short Application of the diffusion equation to prove scaling invariance on the transition from limited to unlimited diffusion
title_full Application of the diffusion equation to prove scaling invariance on the transition from limited to unlimited diffusion
title_fullStr Application of the diffusion equation to prove scaling invariance on the transition from limited to unlimited diffusion
title_full_unstemmed Application of the diffusion equation to prove scaling invariance on the transition from limited to unlimited diffusion
title_sort Application of the diffusion equation to prove scaling invariance on the transition from limited to unlimited diffusion
author Leonel, Edson D. [UNESP]
author_facet Leonel, Edson D. [UNESP]
Mayumi Kuwana, Célia [UNESP]
Yoshida, Makoto [UNESP]
Antonio De Oliveira, Juliano [UNESP]
author_role author
author2 Mayumi Kuwana, Célia [UNESP]
Yoshida, Makoto [UNESP]
Antonio De Oliveira, Juliano [UNESP]
author2_role author
author
author
dc.contributor.none.fl_str_mv Universidade Estadual Paulista (Unesp)
dc.contributor.author.fl_str_mv Leonel, Edson D. [UNESP]
Mayumi Kuwana, Célia [UNESP]
Yoshida, Makoto [UNESP]
Antonio De Oliveira, Juliano [UNESP]
description The scaling invariance for chaotic orbits near a transition from limited to unlimited diffusion in a dissipative standard mapping is explained via the analytical solution of the diffusion equation. It gives the probability of observing a particle with a specific action at a given time. We show the diffusion coefficient varies slowly with the time and is responsible for suppressing the unlimited diffusion. The momenta of the probability are determined and the behavior of the average squared action is obtained. The limits of small and large time recover the results known in the literature from the phenomenological approach and, as a bonus, a scaling for intermediate time is obtained as dependent on the initial action. The formalism presented is robust enough and can be applied in a variety of other systems including time-dependent billiards near a transition from limited to unlimited Fermi acceleration as we show at the end of the letter and in many other systems under the presence of dissipation as well as near a transition from integrability to non-integrability.
publishDate 2020
dc.date.none.fl_str_mv 2020-07-01
2021-06-25T11:04:41Z
2021-06-25T11:04:41Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://dx.doi.org/10.1209/0295-5075/131/10004
EPL, v. 131, n. 1, 2020.
1286-4854
0295-5075
http://hdl.handle.net/11449/208002
10.1209/0295-5075/131/10004
2-s2.0-85091701098
url http://dx.doi.org/10.1209/0295-5075/131/10004
http://hdl.handle.net/11449/208002
identifier_str_mv EPL, v. 131, n. 1, 2020.
1286-4854
0295-5075
10.1209/0295-5075/131/10004
2-s2.0-85091701098
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv EPL
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.source.none.fl_str_mv Scopus
reponame:Repositório Institucional da UNESP
instname:Universidade Estadual Paulista (UNESP)
instacron:UNESP
instname_str Universidade Estadual Paulista (UNESP)
instacron_str UNESP
institution UNESP
reponame_str Repositório Institucional da UNESP
collection Repositório Institucional da UNESP
repository.name.fl_str_mv Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)
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