Quantum manifestations of classical nonlinear resonances

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 d...

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Autor principal: Wisniacki, Diego A.
Publicado: 2015
Materias:
Phase space methods
Resonance
Classical systems
In-phase
Localization properties
Nonlinear resonance
Quantum numbers
Splittings
Standard map
Quantum theory
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15393755_v92_n6_p_Wisniacki
http://hdl.handle.net/20.500.12110/paper_15393755_v92_n6_p_Wisniacki
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_15393755_v92_n6_p_Wisniacki
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spelling paper:paper_15393755_v92_n6_p_Wisniacki2023-06-08T16:21:04Z Quantum manifestations of classical nonlinear resonances Wisniacki, Diego A. Phase space methods Resonance Classical systems In-phase Localization properties Nonlinear resonance Quantum numbers Splittings Standard map Quantum theory 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. © 2015 American Physical Society. Fil:Wisniacki, D.A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2015 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15393755_v92_n6_p_Wisniacki http://hdl.handle.net/20.500.12110/paper_15393755_v92_n6_p_Wisniacki
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Phase space methods
Resonance
Classical systems
In-phase
Localization properties
Nonlinear resonance
Quantum numbers
Splittings
Standard map
Quantum theory
spellingShingle Phase space methods
Resonance
Classical systems
In-phase
Localization properties
Nonlinear resonance
Quantum numbers
Splittings
Standard map
Quantum theory
Wisniacki, Diego A.
Quantum manifestations of classical nonlinear resonances
topic_facet Phase space methods
Resonance
Classical systems
In-phase
Localization properties
Nonlinear resonance
Quantum numbers
Splittings
Standard map
Quantum theory
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. © 2015 American Physical Society.
author Wisniacki, Diego A.
author_facet Wisniacki, Diego A.
author_sort Wisniacki, Diego A.
title Quantum manifestations of classical nonlinear resonances
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
publishDate 2015
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15393755_v92_n6_p_Wisniacki
http://hdl.handle.net/20.500.12110/paper_15393755_v92_n6_p_Wisniacki
work_keys_str_mv AT wisniackidiegoa quantummanifestationsofclassicalnonlinearresonances
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