Entanglement of classical and quantum short-range dynamics in mean-field systems

The relationship between classical and quantum mechanics is usually understood via the limit ħ→0. This is the underlying idea behind the quantization of classical objects. The apparent incompatibility of general relativity with quantum mechanics and quantum field theory has challenged for many decad...

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Authors: Bru, J. B., de Siqueira Pedra, W.
Format: article
Status:Published version
Publication Date:2021
Country:España
Institution:Basque Center for Applied Mathematics (BCAM)
Repository:BIRD. BCAM's Institutional Repository Data
OAI Identifier:oai:bird.bcamath.org:20.500.11824/1438
Online Access:http://hdl.handle.net/20.500.11824/1438
Access Level:Open access
Keyword:BCS
Classical dynamics
Entanglement
Mean-field
Quantum dynamics
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spelling Entanglement of classical and quantum short-range dynamics in mean-field systemsBru, J. B.de Siqueira Pedra, W.BCSClassical dynamicsEntanglementMean-fieldQuantum dynamicsThe relationship between classical and quantum mechanics is usually understood via the limit ħ→0. This is the underlying idea behind the quantization of classical objects. The apparent incompatibility of general relativity with quantum mechanics and quantum field theory has challenged for many decades this basic idea. We recently showed (Bru and de Siqueira Pedra, 0000; Bru and de Siqueira Pedra, 2021 [46,47]) the emergence of classical dynamics for very general quantum lattice systems with mean-field interactions, without (complete) suppression of its quantum features, in the infinite volume limit. This leads to a theoretical framework in which the classical and quantum worlds are entangled. Such an entanglement is noteworthy and is a consequence of the highly non-local character of mean-field interactions. Therefore, this phenomenon should not be restricted to systems with mean-field interactions only, but should also appear in presence of interactions that are sufficiently long-range, yielding effective, classical background fields, in the spirit of the Higgs mechanism of quantum field theory. In order to present the result in a less abstract way than in its original version, here we apply it to a concrete, physically relevant, example and discuss, by this means, various important aspects of our general approach. The model we consider is not exactly solvable and the particular results obtained are new.CNPq (309723/2020-5), FAPESP (2017/22340- 9), as well as by the Basque Government through the grant IT641-13 and by the Spanish Ministry of Science, Innovation and Universities: MTM2017-82160-C2-2-P.info202220222021info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttp://hdl.handle.net/20.500.11824/1438reponame:BIRD. BCAM's Institutional Repository Datainstname:Basque Center for Applied Mathematics (BCAM)Inglésinfo:eu-repo/grantAgreement/MINECO//SEV-2017-0718info:eu-repo/grantAgreement/Gobierno Vasco/BERC/BERC.2018-2021Reconocimiento-NoComercial-CompartirIgual 3.0 Españahttp://creativecommons.org/licenses/by-nc-sa/3.0/es/info:eu-repo/semantics/openAccessoai:bird.bcamath.org:20.500.11824/14382026-06-19T12:47:47Z
dc.title.none.fl_str_mv Entanglement of classical and quantum short-range dynamics in mean-field systems
title Entanglement of classical and quantum short-range dynamics in mean-field systems
spellingShingle Entanglement of classical and quantum short-range dynamics in mean-field systems
Bru, J. B.
BCS
Classical dynamics
Entanglement
Mean-field
Quantum dynamics
title_short Entanglement of classical and quantum short-range dynamics in mean-field systems
title_full Entanglement of classical and quantum short-range dynamics in mean-field systems
title_fullStr Entanglement of classical and quantum short-range dynamics in mean-field systems
title_full_unstemmed Entanglement of classical and quantum short-range dynamics in mean-field systems
title_sort Entanglement of classical and quantum short-range dynamics in mean-field systems
dc.creator.none.fl_str_mv Bru, J. B.
de Siqueira Pedra, W.
author Bru, J. B.
author_facet Bru, J. B.
de Siqueira Pedra, W.
author_role author
author2 de Siqueira Pedra, W.
author2_role author
dc.subject.none.fl_str_mv BCS
Classical dynamics
Entanglement
Mean-field
Quantum dynamics
topic BCS
Classical dynamics
Entanglement
Mean-field
Quantum dynamics
description The relationship between classical and quantum mechanics is usually understood via the limit ħ→0. This is the underlying idea behind the quantization of classical objects. The apparent incompatibility of general relativity with quantum mechanics and quantum field theory has challenged for many decades this basic idea. We recently showed (Bru and de Siqueira Pedra, 0000; Bru and de Siqueira Pedra, 2021 [46,47]) the emergence of classical dynamics for very general quantum lattice systems with mean-field interactions, without (complete) suppression of its quantum features, in the infinite volume limit. This leads to a theoretical framework in which the classical and quantum worlds are entangled. Such an entanglement is noteworthy and is a consequence of the highly non-local character of mean-field interactions. Therefore, this phenomenon should not be restricted to systems with mean-field interactions only, but should also appear in presence of interactions that are sufficiently long-range, yielding effective, classical background fields, in the spirit of the Higgs mechanism of quantum field theory. In order to present the result in a less abstract way than in its original version, here we apply it to a concrete, physically relevant, example and discuss, by this means, various important aspects of our general approach. The model we consider is not exactly solvable and the particular results obtained are new.
publishDate 2021
dc.date.none.fl_str_mv 2021
2022
2022
info
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/20.500.11824/1438
url http://hdl.handle.net/20.500.11824/1438
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv info:eu-repo/grantAgreement/MINECO//SEV-2017-0718
info:eu-repo/grantAgreement/Gobierno Vasco/BERC/BERC.2018-2021
dc.rights.none.fl_str_mv Reconocimiento-NoComercial-CompartirIgual 3.0 España
http://creativecommons.org/licenses/by-nc-sa/3.0/es/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Reconocimiento-NoComercial-CompartirIgual 3.0 España
http://creativecommons.org/licenses/by-nc-sa/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:BIRD. BCAM's Institutional Repository Data
instname:Basque Center for Applied Mathematics (BCAM)
instname_str Basque Center for Applied Mathematics (BCAM)
reponame_str BIRD. BCAM's Institutional Repository Data
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