Quantum manifestations of classical nonlinear resonances

Autores
Wisniacki, Diego Ariel; Schlagheck, Peter
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
When an integrable classical system is perturbed, nonlinear resonances are born, grow, and eventually disappear due to chaos. In this paper the quantum manifestations of such a transition are studied in the standard map. We show that nonlinear resonances act as a perturbation that break eigenphase degeneracies for unperturbed states with quantum numbers that differ in a multiple of the order of the resonance. We show that the eigenphase splittings are well described by a semiclassical expression based on an integrable approximation of the Hamiltonian in the vicinity of the resonance. The morphology in phase space of these states is also studied. We show that the nonlinear resonance imprints a systematic influence in their localization properties
Fil: Wisniacki, Diego Ariel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina
Fil: Schlagheck, Peter. Universidad de Liege ; Bélgica
Materia
Quantum Chaos
Resonances
Mixed Systems
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/46645
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/46645
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repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Quantum manifestations of classical nonlinear resonancesWisniacki, Diego ArielSchlagheck, PeterQuantum ChaosResonancesMixed Systemshttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1When an integrable classical system is perturbed, nonlinear resonances are born, grow, and eventually disappear due to chaos. In this paper the quantum manifestations of such a transition are studied in the standard map. We show that nonlinear resonances act as a perturbation that break eigenphase degeneracies for unperturbed states with quantum numbers that differ in a multiple of the order of the resonance. We show that the eigenphase splittings are well described by a semiclassical expression based on an integrable approximation of the Hamiltonian in the vicinity of the resonance. The morphology in phase space of these states is also studied. We show that the nonlinear resonance imprints a systematic influence in their localization propertiesFil: Wisniacki, Diego Ariel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; ArgentinaFil: Schlagheck, Peter. Universidad de Liege ; BélgicaAmerican Physical Society2015-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/46645Wisniacki, Diego Ariel; Schlagheck, Peter; Quantum manifestations of classical nonlinear resonances; American Physical Society; Physical Review E: Statistical Physics, Plasmas, Fluids and Related Interdisciplinary Topics; 92; 6; 12-2015; 1-81063-651XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevE.92.062923info:eu-repo/semantics/altIdentifier/url/https://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.062923info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:11:33Zoai:ri.conicet.gov.ar:11336/46645instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 10:11:33.436CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Quantum manifestations of classical nonlinear resonances
title Quantum manifestations of classical nonlinear resonances
spellingShingle Quantum manifestations of classical nonlinear resonances
Wisniacki, Diego Ariel
Quantum Chaos
Resonances
Mixed Systems
title_short Quantum manifestations of classical nonlinear resonances
title_full Quantum manifestations of classical nonlinear resonances
title_fullStr Quantum manifestations of classical nonlinear resonances
title_full_unstemmed Quantum manifestations of classical nonlinear resonances
title_sort Quantum manifestations of classical nonlinear resonances
dc.creator.none.fl_str_mv Wisniacki, Diego Ariel
Schlagheck, Peter
author Wisniacki, Diego Ariel
author_facet Wisniacki, Diego Ariel
Schlagheck, Peter
author_role author
author2 Schlagheck, Peter
author2_role author
dc.subject.none.fl_str_mv Quantum Chaos
Resonances
Mixed Systems
topic Quantum Chaos
Resonances
Mixed Systems
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv When an integrable classical system is perturbed, nonlinear resonances are born, grow, and eventually disappear due to chaos. In this paper the quantum manifestations of such a transition are studied in the standard map. We show that nonlinear resonances act as a perturbation that break eigenphase degeneracies for unperturbed states with quantum numbers that differ in a multiple of the order of the resonance. We show that the eigenphase splittings are well described by a semiclassical expression based on an integrable approximation of the Hamiltonian in the vicinity of the resonance. The morphology in phase space of these states is also studied. We show that the nonlinear resonance imprints a systematic influence in their localization properties
Fil: Wisniacki, Diego Ariel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina
Fil: Schlagheck, Peter. Universidad de Liege ; Bélgica
description When an integrable classical system is perturbed, nonlinear resonances are born, grow, and eventually disappear due to chaos. In this paper the quantum manifestations of such a transition are studied in the standard map. We show that nonlinear resonances act as a perturbation that break eigenphase degeneracies for unperturbed states with quantum numbers that differ in a multiple of the order of the resonance. We show that the eigenphase splittings are well described by a semiclassical expression based on an integrable approximation of the Hamiltonian in the vicinity of the resonance. The morphology in phase space of these states is also studied. We show that the nonlinear resonance imprints a systematic influence in their localization properties
publishDate 2015
dc.date.none.fl_str_mv 2015-12
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/46645
Wisniacki, Diego Ariel; Schlagheck, Peter; Quantum manifestations of classical nonlinear resonances; American Physical Society; Physical Review E: Statistical Physics, Plasmas, Fluids and Related Interdisciplinary Topics; 92; 6; 12-2015; 1-8
1063-651X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/46645
identifier_str_mv Wisniacki, Diego Ariel; Schlagheck, Peter; Quantum manifestations of classical nonlinear resonances; American Physical Society; Physical Review E: Statistical Physics, Plasmas, Fluids and Related Interdisciplinary Topics; 92; 6; 12-2015; 1-8
1063-651X
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevE.92.062923
info:eu-repo/semantics/altIdentifier/url/https://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.062923
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv American Physical Society
publisher.none.fl_str_mv American Physical Society
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.070432

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