A Quantum Version of Spectral Decomposition Theorem of dynamical systems, quantum chaos hierarchy: Ergodic, mixing and exact
- Autores
- Gomez, Ignacio Sebastián; Castagnino, Mario Alberto G. J.
- Año de publicación
- 2015
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- In this paper we study Spectral Decomposition Theorem (Lasota and Mackey, 1985) and translate it to quantum language by means of the Wigner transform. We obtain a Quantum Version of Spectral Decomposition Theorem (QSDT) which enables us to achieve three distinct goals: First, to rank Quantum Ergodic Hierarchy levels (Castagnino and Lombardi, 2009, Gomez and Castagnino, 2014). Second, to analyze the classical limit in quantum ergodic systems and quantum mixing systems. And third, and maybe most important feature, to find a relevant and simple connection between the first three levels of Quantum Ergodic Hierarchy (ergodic, exact and mixing) and quantum spectrum. Finally, we illustrate the physical relevance of QSDT applying it to two examples: Microwave billiards (Stockmann, 1999, Stoffregen et al. 1995) and a phenomenological Gamow model type (Laura and Castagnino, 1998, Omnès, 1994).
Fil: Gomez, Ignacio Sebastián. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Instituto de Física de Rosario. Universidad Nacional de Rosario. Instituto de Física de Rosario; Argentina
Fil: Castagnino, Mario Alberto G. J.. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Instituto de Física de Rosario. Universidad Nacional de Rosario. Instituto de Física de Rosario; Argentina - Materia
-
Qsdt
Qeh
Ergodic
Mixing - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
- Repositorio
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/37667
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A Quantum Version of Spectral Decomposition Theorem of dynamical systems, quantum chaos hierarchy: Ergodic, mixing and exactGomez, Ignacio SebastiánCastagnino, Mario Alberto G. J.QsdtQehErgodicMixinghttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1In this paper we study Spectral Decomposition Theorem (Lasota and Mackey, 1985) and translate it to quantum language by means of the Wigner transform. We obtain a Quantum Version of Spectral Decomposition Theorem (QSDT) which enables us to achieve three distinct goals: First, to rank Quantum Ergodic Hierarchy levels (Castagnino and Lombardi, 2009, Gomez and Castagnino, 2014). Second, to analyze the classical limit in quantum ergodic systems and quantum mixing systems. And third, and maybe most important feature, to find a relevant and simple connection between the first three levels of Quantum Ergodic Hierarchy (ergodic, exact and mixing) and quantum spectrum. Finally, we illustrate the physical relevance of QSDT applying it to two examples: Microwave billiards (Stockmann, 1999, Stoffregen et al. 1995) and a phenomenological Gamow model type (Laura and Castagnino, 1998, Omnès, 1994).Fil: Gomez, Ignacio Sebastián. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Instituto de Física de Rosario. Universidad Nacional de Rosario. Instituto de Física de Rosario; ArgentinaFil: Castagnino, Mario Alberto G. J.. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Instituto de Física de Rosario. Universidad Nacional de Rosario. Instituto de Física de Rosario; ArgentinaPergamon-Elsevier Science Ltd2015-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/zipapplication/pdfhttp://hdl.handle.net/11336/37667Gomez, Ignacio Sebastián; Castagnino, Mario Alberto G. J.; A Quantum Version of Spectral Decomposition Theorem of dynamical systems, quantum chaos hierarchy: Ergodic, mixing and exact; Pergamon-Elsevier Science Ltd; Chaos, Solitons And Fractals; 70; 1; 1-2015; 99-1160960-0779CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.chaos.2014.11.002info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0960077914001866info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:48:07Zoai:ri.conicet.gov.ar:11336/37667instacron: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:34982025-09-03 09:48:08.011CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
dc.title.none.fl_str_mv |
A Quantum Version of Spectral Decomposition Theorem of dynamical systems, quantum chaos hierarchy: Ergodic, mixing and exact |
title |
A Quantum Version of Spectral Decomposition Theorem of dynamical systems, quantum chaos hierarchy: Ergodic, mixing and exact |
spellingShingle |
A Quantum Version of Spectral Decomposition Theorem of dynamical systems, quantum chaos hierarchy: Ergodic, mixing and exact Gomez, Ignacio Sebastián Qsdt Qeh Ergodic Mixing |
title_short |
A Quantum Version of Spectral Decomposition Theorem of dynamical systems, quantum chaos hierarchy: Ergodic, mixing and exact |
title_full |
A Quantum Version of Spectral Decomposition Theorem of dynamical systems, quantum chaos hierarchy: Ergodic, mixing and exact |
title_fullStr |
A Quantum Version of Spectral Decomposition Theorem of dynamical systems, quantum chaos hierarchy: Ergodic, mixing and exact |
title_full_unstemmed |
A Quantum Version of Spectral Decomposition Theorem of dynamical systems, quantum chaos hierarchy: Ergodic, mixing and exact |
title_sort |
A Quantum Version of Spectral Decomposition Theorem of dynamical systems, quantum chaos hierarchy: Ergodic, mixing and exact |
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 |
Qsdt Qeh Ergodic Mixing |
topic |
Qsdt Qeh Ergodic Mixing |
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 study Spectral Decomposition Theorem (Lasota and Mackey, 1985) and translate it to quantum language by means of the Wigner transform. We obtain a Quantum Version of Spectral Decomposition Theorem (QSDT) which enables us to achieve three distinct goals: First, to rank Quantum Ergodic Hierarchy levels (Castagnino and Lombardi, 2009, Gomez and Castagnino, 2014). Second, to analyze the classical limit in quantum ergodic systems and quantum mixing systems. And third, and maybe most important feature, to find a relevant and simple connection between the first three levels of Quantum Ergodic Hierarchy (ergodic, exact and mixing) and quantum spectrum. Finally, we illustrate the physical relevance of QSDT applying it to two examples: Microwave billiards (Stockmann, 1999, Stoffregen et al. 1995) and a phenomenological Gamow model type (Laura and Castagnino, 1998, Omnès, 1994). Fil: Gomez, Ignacio Sebastián. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Instituto de Física de Rosario. Universidad Nacional de Rosario. Instituto de Física de Rosario; Argentina Fil: Castagnino, Mario Alberto G. J.. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Instituto de Física de Rosario. Universidad Nacional de Rosario. Instituto de Física de Rosario; Argentina |
description |
In this paper we study Spectral Decomposition Theorem (Lasota and Mackey, 1985) and translate it to quantum language by means of the Wigner transform. We obtain a Quantum Version of Spectral Decomposition Theorem (QSDT) which enables us to achieve three distinct goals: First, to rank Quantum Ergodic Hierarchy levels (Castagnino and Lombardi, 2009, Gomez and Castagnino, 2014). Second, to analyze the classical limit in quantum ergodic systems and quantum mixing systems. And third, and maybe most important feature, to find a relevant and simple connection between the first three levels of Quantum Ergodic Hierarchy (ergodic, exact and mixing) and quantum spectrum. Finally, we illustrate the physical relevance of QSDT applying it to two examples: Microwave billiards (Stockmann, 1999, Stoffregen et al. 1995) and a phenomenological Gamow model type (Laura and Castagnino, 1998, Omnès, 1994). |
publishDate |
2015 |
dc.date.none.fl_str_mv |
2015-01 |
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/11336/37667 Gomez, Ignacio Sebastián; Castagnino, Mario Alberto G. J.; A Quantum Version of Spectral Decomposition Theorem of dynamical systems, quantum chaos hierarchy: Ergodic, mixing and exact; Pergamon-Elsevier Science Ltd; Chaos, Solitons And Fractals; 70; 1; 1-2015; 99-116 0960-0779 CONICET Digital CONICET |
url |
http://hdl.handle.net/11336/37667 |
identifier_str_mv |
Gomez, Ignacio Sebastián; Castagnino, Mario Alberto G. J.; A Quantum Version of Spectral Decomposition Theorem of dynamical systems, quantum chaos hierarchy: Ergodic, mixing and exact; Pergamon-Elsevier Science Ltd; Chaos, Solitons And Fractals; 70; 1; 1-2015; 99-116 0960-0779 CONICET Digital CONICET |
dc.language.none.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.chaos.2014.11.002 info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0960077914001866 |
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/zip application/pdf |
dc.publisher.none.fl_str_mv |
Pergamon-Elsevier Science Ltd |
publisher.none.fl_str_mv |
Pergamon-Elsevier Science Ltd |
dc.source.none.fl_str_mv |
reponame:CONICET Digital (CONICET) instname:Consejo Nacional de Investigaciones Científicas y Técnicas |
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CONICET Digital (CONICET) |
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CONICET Digital (CONICET) |
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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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1842268904603254784 |
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13.13397 |