Towards a definition of the Quantum Ergodic Hierarchy: Kolmogorov and Bernoulli systems

Autores
Gomez, Ignacio Sebastián; Castagnino, Mario Alberto G. J.
Año de publicación
2014
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper we translate the two higher levels of the Ergodic Hierarchy [1], the Kolmogorov level and the Bernoulli level, to quantum language. Moreover, this paper can be considered as the second part of [2]. As in paper [2], we consider the formalism where the states are positive functionals on the algebra of observables and we use the properties of the Wigner transform [3]. We illustrate the physical relevance of the Quantum Ergodic Hierarchy with two emblematic examples of the literature: the Casati-Prosen model [4], [5] and the kicked rotator [6], [7], [8].
Fil: Gomez, Ignacio Sebastián. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Rosario. Instituto de Física de Rosario (i); Argentina
Fil: Castagnino, Mario Alberto G. J.. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomía y Física del Espacio(i); Argentina
Materia
ERGODIC
MIXING
KOLMOGOROV
BERNOULLI
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/7503
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/7503
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Towards a definition of the Quantum Ergodic Hierarchy: Kolmogorov and Bernoulli systemsGomez, Ignacio SebastiánCastagnino, Mario Alberto G. J.ERGODICMIXINGKOLMOGOROVBERNOULLIhttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1In this paper we translate the two higher levels of the Ergodic Hierarchy [1], the Kolmogorov level and the Bernoulli level, to quantum language. Moreover, this paper can be considered as the second part of [2]. As in paper [2], we consider the formalism where the states are positive functionals on the algebra of observables and we use the properties of the Wigner transform [3]. We illustrate the physical relevance of the Quantum Ergodic Hierarchy with two emblematic examples of the literature: the Casati-Prosen model [4], [5] and the kicked rotator [6], [7], [8].Fil: Gomez, Ignacio Sebastián. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Rosario. Instituto de Física de Rosario (i); ArgentinaFil: Castagnino, Mario Alberto G. J.. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomía y Física del Espacio(i); ArgentinaElsevier2014-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/rarapplication/pdfhttp://hdl.handle.net/11336/7503Gomez, Ignacio Sebastián; Castagnino, Mario Alberto G. J.; Towards a definition of the Quantum Ergodic Hierarchy: Kolmogorov and Bernoulli systems; Elsevier; Physica A: Statistical Mechanics And Its Applications; 393; 1-2014; 112-1310378-4371enginfo:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0378437113008200info:eu-repo/semantics/altIdentifier/doi/10.1016/j.physa.2013.08.070info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-11-05T10:43:00Zoai:ri.conicet.gov.ar:11336/7503instacron: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:34982025-11-05 10:43:00.332CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Towards a definition of the Quantum Ergodic Hierarchy: Kolmogorov and Bernoulli systems
title Towards a definition of the Quantum Ergodic Hierarchy: Kolmogorov and Bernoulli systems
spellingShingle Towards a definition of the Quantum Ergodic Hierarchy: Kolmogorov and Bernoulli systems
Gomez, Ignacio Sebastián
ERGODIC
MIXING
KOLMOGOROV
BERNOULLI
title_short Towards a definition of the Quantum Ergodic Hierarchy: Kolmogorov and Bernoulli systems
title_full Towards a definition of the Quantum Ergodic Hierarchy: Kolmogorov and Bernoulli systems
title_fullStr Towards a definition of the Quantum Ergodic Hierarchy: Kolmogorov and Bernoulli systems
title_full_unstemmed Towards a definition of the Quantum Ergodic Hierarchy: Kolmogorov and Bernoulli systems
title_sort Towards a definition of the Quantum Ergodic Hierarchy: Kolmogorov and Bernoulli systems
dc.creator.none.fl_str_mv Gomez, Ignacio Sebastián
Castagnino, Mario Alberto G. J.
author Gomez, Ignacio Sebastián
author_facet Gomez, Ignacio Sebastián
Castagnino, Mario Alberto G. J.
author_role author
author2 Castagnino, Mario Alberto G. J.
author2_role author
dc.subject.none.fl_str_mv ERGODIC
MIXING
KOLMOGOROV
BERNOULLI
topic ERGODIC
MIXING
KOLMOGOROV
BERNOULLI
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In this paper we translate the two higher levels of the Ergodic Hierarchy [1], the Kolmogorov level and the Bernoulli level, to quantum language. Moreover, this paper can be considered as the second part of [2]. As in paper [2], we consider the formalism where the states are positive functionals on the algebra of observables and we use the properties of the Wigner transform [3]. We illustrate the physical relevance of the Quantum Ergodic Hierarchy with two emblematic examples of the literature: the Casati-Prosen model [4], [5] and the kicked rotator [6], [7], [8].
Fil: Gomez, Ignacio Sebastián. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Rosario. Instituto de Física de Rosario (i); Argentina
Fil: Castagnino, Mario Alberto G. J.. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomía y Física del Espacio(i); Argentina
description In this paper we translate the two higher levels of the Ergodic Hierarchy [1], the Kolmogorov level and the Bernoulli level, to quantum language. Moreover, this paper can be considered as the second part of [2]. As in paper [2], we consider the formalism where the states are positive functionals on the algebra of observables and we use the properties of the Wigner transform [3]. We illustrate the physical relevance of the Quantum Ergodic Hierarchy with two emblematic examples of the literature: the Casati-Prosen model [4], [5] and the kicked rotator [6], [7], [8].
publishDate 2014
dc.date.none.fl_str_mv 2014-01
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/11336/7503
Gomez, Ignacio Sebastián; Castagnino, Mario Alberto G. J.; Towards a definition of the Quantum Ergodic Hierarchy: Kolmogorov and Bernoulli systems; Elsevier; Physica A: Statistical Mechanics And Its Applications; 393; 1-2014; 112-131
0378-4371
url http://hdl.handle.net/11336/7503
identifier_str_mv Gomez, Ignacio Sebastián; Castagnino, Mario Alberto G. J.; Towards a definition of the Quantum Ergodic Hierarchy: Kolmogorov and Bernoulli systems; Elsevier; Physica A: Statistical Mechanics And Its Applications; 393; 1-2014; 112-131
0378-4371
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0378437113008200
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.physa.2013.08.070
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/rar
application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
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 13.084122

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