Spectral statistics in noninteracting many-particle systems

It is widely accepted that the statistical properties of energy level spectra provide an essential characterization of quantum chaos. Indeed, the spectral fluctuations of many different systems like quantum billiards, atoms, or atomic nuclei have been studied. However, noninteracting many-body syste...

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Detalhes bibliográficos
Autores: Relaño Pérez, Armando, Muñoz Muñoz, Laura, Faleiro, E., Molina, R. A., Retamosa Granado, Joaquín
Formato: artículo
Fecha de publicación:2006
País:España
Recursos:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/51278
Acesso em linha:https://hdl.handle.net/20.500.14352/51278
Access Level:acceso abierto
Palavra-chave:536
Quantum Integrability
Level Spacings
Fluctuations
Ensembles
Termodinámica
2213 Termodinámica
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oai_identifier_str oai:docta.ucm.es:20.500.14352/51278
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spelling Spectral statistics in noninteracting many-particle systemsRelaño Pérez, ArmandoMuñoz Muñoz, LauraFaleiro, E.Molina, R. A.Retamosa Granado, Joaquín536Quantum IntegrabilityLevel SpacingsFluctuationsEnsemblesTermodinámica2213 TermodinámicaIt is widely accepted that the statistical properties of energy level spectra provide an essential characterization of quantum chaos. Indeed, the spectral fluctuations of many different systems like quantum billiards, atoms, or atomic nuclei have been studied. However, noninteracting many-body systems have received little attention, since it is assumed that they must exhibit Poisson-like fluctuations. Apart from a heuristic argument of Bloch, there are neither systematic numerical calculations nor a rigorous derivation of this fact. Here we present a rigorous study of the spectral fluctuations of noninteracting identical particles moving freely in a mean field emphasizing the evolution with the number of particles N as well as with the energy. Our results are conclusive. For N >= 2 the spectra of these systems exhibit Poisson fluctuations provided that we consider sufficiently high excitation energies. Nevertheless, when the mean field is chaotic there exists a critical energy scale L-c; beyond this scale, the fluctuations deviate from the Poisson statistics as a reminiscence of the statistical properties of the mean field.American Physical SocietyUniversidad Complutense de Madrid20062006-01-0120062006-01-01journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14352/51278reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/512782026-06-02T12:44:21Z
dc.title.none.fl_str_mv Spectral statistics in noninteracting many-particle systems
title Spectral statistics in noninteracting many-particle systems
spellingShingle Spectral statistics in noninteracting many-particle systems
Relaño Pérez, Armando
536
Quantum Integrability
Level Spacings
Fluctuations
Ensembles
Termodinámica
2213 Termodinámica
title_short Spectral statistics in noninteracting many-particle systems
title_full Spectral statistics in noninteracting many-particle systems
title_fullStr Spectral statistics in noninteracting many-particle systems
title_full_unstemmed Spectral statistics in noninteracting many-particle systems
title_sort Spectral statistics in noninteracting many-particle systems
dc.creator.none.fl_str_mv Relaño Pérez, Armando
Muñoz Muñoz, Laura
Faleiro, E.
Molina, R. A.
Retamosa Granado, Joaquín
author Relaño Pérez, Armando
author_facet Relaño Pérez, Armando
Muñoz Muñoz, Laura
Faleiro, E.
Molina, R. A.
Retamosa Granado, Joaquín
author_role author
author2 Muñoz Muñoz, Laura
Faleiro, E.
Molina, R. A.
Retamosa Granado, Joaquín
author2_role author
author
author
author
dc.contributor.none.fl_str_mv Universidad Complutense de Madrid
dc.subject.none.fl_str_mv 536
Quantum Integrability
Level Spacings
Fluctuations
Ensembles
Termodinámica
2213 Termodinámica
topic 536
Quantum Integrability
Level Spacings
Fluctuations
Ensembles
Termodinámica
2213 Termodinámica
description It is widely accepted that the statistical properties of energy level spectra provide an essential characterization of quantum chaos. Indeed, the spectral fluctuations of many different systems like quantum billiards, atoms, or atomic nuclei have been studied. However, noninteracting many-body systems have received little attention, since it is assumed that they must exhibit Poisson-like fluctuations. Apart from a heuristic argument of Bloch, there are neither systematic numerical calculations nor a rigorous derivation of this fact. Here we present a rigorous study of the spectral fluctuations of noninteracting identical particles moving freely in a mean field emphasizing the evolution with the number of particles N as well as with the energy. Our results are conclusive. For N >= 2 the spectra of these systems exhibit Poisson fluctuations provided that we consider sufficiently high excitation energies. Nevertheless, when the mean field is chaotic there exists a critical energy scale L-c; beyond this scale, the fluctuations deviate from the Poisson statistics as a reminiscence of the statistical properties of the mean field.
publishDate 2006
dc.date.none.fl_str_mv 2006
2006-01-01
2006
2006-01-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/20.500.14352/51278
url https://hdl.handle.net/20.500.14352/51278
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 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:Docta Complutense
instname:Universidad Complutense de Madrid (UCM)
instname_str Universidad Complutense de Madrid (UCM)
reponame_str Docta Complutense
collection Docta Complutense
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.300724

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