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

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In this paper we translate the two higher levels of the Ergodic Hierarchy [11], the Kolmogorov level and the Bernoulli level, to quantum language. Moreover, this paper can be considered as the second part of [3]. As in [3], we consider the formalism where the states are positive functionals on the a...

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Detalles Bibliográficos
Autores principales: Gomez, I., Castagnino, M.
Formato: JOUR
Materias:
Bernoulli
EH
Ergodic
Kolmogorov
Mixing
QEH
Ergodics
Physics
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_03784371_v393_n_p112_Gomez
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_03784371_v393_n_p112_Gomez
record_format dspace
spelling todo:paper_03784371_v393_n_p112_Gomez2023-10-03T15:33:02Z Towards a definition of the Quantum Ergodic Hierarchy: Kolmogorov and Bernoulli systems Gomez, I. Castagnino, M. Bernoulli EH Ergodic Kolmogorov Mixing QEH Bernoulli EH Ergodics Kolmogorov QEH Mixing Physics In this paper we translate the two higher levels of the Ergodic Hierarchy [11], the Kolmogorov level and the Bernoulli level, to quantum language. Moreover, this paper can be considered as the second part of [3]. As in [3], we consider the formalism where the states are positive functionals on the algebra of observables and we use the properties of the Wigner transform [12]. We illustrate the physical relevance of the Quantum Ergodic Hierarchy with two emblematic examples of the literature: the Casati-Prosen model [13,14] and the kicked rotator [6-8]. © 2013 Elsevier B.V. All rights reserved. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_03784371_v393_n_p112_Gomez
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Bernoulli
EH
Ergodic
Kolmogorov
Mixing
QEH
Bernoulli
EH
Ergodics
Kolmogorov
QEH
Mixing
Physics
spellingShingle Bernoulli
EH
Ergodic
Kolmogorov
Mixing
QEH
Bernoulli
EH
Ergodics
Kolmogorov
QEH
Mixing
Physics
Gomez, I.
Castagnino, M.
Towards a definition of the Quantum Ergodic Hierarchy: Kolmogorov and Bernoulli systems
topic_facet Bernoulli
EH
Ergodic
Kolmogorov
Mixing
QEH
Bernoulli
EH
Ergodics
Kolmogorov
QEH
Mixing
Physics
description In this paper we translate the two higher levels of the Ergodic Hierarchy [11], the Kolmogorov level and the Bernoulli level, to quantum language. Moreover, this paper can be considered as the second part of [3]. As in [3], we consider the formalism where the states are positive functionals on the algebra of observables and we use the properties of the Wigner transform [12]. We illustrate the physical relevance of the Quantum Ergodic Hierarchy with two emblematic examples of the literature: the Casati-Prosen model [13,14] and the kicked rotator [6-8]. © 2013 Elsevier B.V. All rights reserved.
format JOUR
author Gomez, I.
Castagnino, M.
author_facet Gomez, I.
Castagnino, M.
author_sort Gomez, I.
title Towards a definition of the Quantum Ergodic Hierarchy: Kolmogorov and Bernoulli systems
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
url http://hdl.handle.net/20.500.12110/paper_03784371_v393_n_p112_Gomez
work_keys_str_mv AT gomezi towardsadefinitionofthequantumergodichierarchykolmogorovandbernoullisystems
AT castagninom towardsadefinitionofthequantumergodichierarchykolmogorovandbernoullisystems
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