Glimmers of a Quantum KAM Theorem: Insights from Quantum Quenches in One-Dimensional Bose Gases
Real-time dynamics in a quantum many-body system are inherently complicated and hence difficult to predict. There are, however, a special set of systems where these dynamics are theoretically tractable: integrable models. Such models possess nontrivial conserved quantities beyond energy and momentum...
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American Physical Society
2015-12-01
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Series: | Physical Review X |
Online Access: | http://doi.org/10.1103/PhysRevX.5.041043 |
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doaj-deda3a955aad4e29bc2168712f6e95a32020-11-24T23:22:45ZengAmerican Physical SocietyPhysical Review X2160-33082015-12-015404104310.1103/PhysRevX.5.041043Glimmers of a Quantum KAM Theorem: Insights from Quantum Quenches in One-Dimensional Bose GasesG. P. BrandinoJ.-S. CauxR. M. KonikReal-time dynamics in a quantum many-body system are inherently complicated and hence difficult to predict. There are, however, a special set of systems where these dynamics are theoretically tractable: integrable models. Such models possess nontrivial conserved quantities beyond energy and momentum. These quantities are believed to control dynamics and thermalization in low-dimensional atomic gases as well as in quantum spin chains. But what happens when the special symmetries leading to the existence of the extra conserved quantities are broken? Is there any memory of the quantities if the breaking is weak? Here, in the presence of weak integrability breaking, we show that it is possible to construct residual quasiconserved quantities, thus providing a quantum analog to the KAM theorem and its attendant Nekhoreshev estimates. We demonstrate this construction explicitly in the context of quantum quenches in one-dimensional Bose gases and argue that these quasiconserved quantities can be probed experimentally.http://doi.org/10.1103/PhysRevX.5.041043 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
G. P. Brandino J.-S. Caux R. M. Konik |
spellingShingle |
G. P. Brandino J.-S. Caux R. M. Konik Glimmers of a Quantum KAM Theorem: Insights from Quantum Quenches in One-Dimensional Bose Gases Physical Review X |
author_facet |
G. P. Brandino J.-S. Caux R. M. Konik |
author_sort |
G. P. Brandino |
title |
Glimmers of a Quantum KAM Theorem: Insights from Quantum Quenches in One-Dimensional Bose Gases |
title_short |
Glimmers of a Quantum KAM Theorem: Insights from Quantum Quenches in One-Dimensional Bose Gases |
title_full |
Glimmers of a Quantum KAM Theorem: Insights from Quantum Quenches in One-Dimensional Bose Gases |
title_fullStr |
Glimmers of a Quantum KAM Theorem: Insights from Quantum Quenches in One-Dimensional Bose Gases |
title_full_unstemmed |
Glimmers of a Quantum KAM Theorem: Insights from Quantum Quenches in One-Dimensional Bose Gases |
title_sort |
glimmers of a quantum kam theorem: insights from quantum quenches in one-dimensional bose gases |
publisher |
American Physical Society |
series |
Physical Review X |
issn |
2160-3308 |
publishDate |
2015-12-01 |
description |
Real-time dynamics in a quantum many-body system are inherently complicated and hence difficult to predict. There are, however, a special set of systems where these dynamics are theoretically tractable: integrable models. Such models possess nontrivial conserved quantities beyond energy and momentum. These quantities are believed to control dynamics and thermalization in low-dimensional atomic gases as well as in quantum spin chains. But what happens when the special symmetries leading to the existence of the extra conserved quantities are broken? Is there any memory of the quantities if the breaking is weak? Here, in the presence of weak integrability breaking, we show that it is possible to construct residual quasiconserved quantities, thus providing a quantum analog to the KAM theorem and its attendant Nekhoreshev estimates. We demonstrate this construction explicitly in the context of quantum quenches in one-dimensional Bose gases and argue that these quasiconserved quantities can be probed experimentally. |
url |
http://doi.org/10.1103/PhysRevX.5.041043 |
work_keys_str_mv |
AT gpbrandino glimmersofaquantumkamtheoreminsightsfromquantumquenchesinonedimensionalbosegases AT jscaux glimmersofaquantumkamtheoreminsightsfromquantumquenchesinonedimensionalbosegases AT rmkonik glimmersofaquantumkamtheoreminsightsfromquantumquenchesinonedimensionalbosegases |
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