Thermal out-of-time-order correlators, KMS relations, and spectral functions
Abstract We describe general features of thermal correlation functions in quantum systems, with specific focus on the fluctuation-dissipation type relations implied by the KMS condition. These end up relating correlation functions with different time ordering and thus should naturally be viewed in t...
Main Authors: | , , , , |
---|---|
Format: | Article |
Language: | English |
Published: |
SpringerOpen
2017-12-01
|
Series: | Journal of High Energy Physics |
Subjects: | |
Online Access: | http://link.springer.com/article/10.1007/JHEP12(2017)154 |
id |
doaj-8f18397f456f46d99e5b243eaa018ef9 |
---|---|
record_format |
Article |
spelling |
doaj-8f18397f456f46d99e5b243eaa018ef92020-11-24T21:05:42ZengSpringerOpenJournal of High Energy Physics1029-84792017-12-0120171215510.1007/JHEP12(2017)154Thermal out-of-time-order correlators, KMS relations, and spectral functionsFelix M. Haehl0R. Loganayagam1Prithvi Narayan2Amin A. Nizami3Mukund Rangamani4Department of Physics and Astronomy, University of British ColumbiaInternational Centre for Theoretical Sciences (ICTS-TIFR)International Centre for Theoretical Sciences (ICTS-TIFR)International Centre for Theoretical Sciences (ICTS-TIFR)Center for Quantum Mathematics and Physics (QMAP), Department of Physics, University of CaliforniaAbstract We describe general features of thermal correlation functions in quantum systems, with specific focus on the fluctuation-dissipation type relations implied by the KMS condition. These end up relating correlation functions with different time ordering and thus should naturally be viewed in the larger context of out-of-time-ordered (OTO) observables. In particular, eschewing the standard formulation of KMS relations where thermal periodicity is combined with time-reversal to stay within the purview of Schwinger-Keldysh functional integrals, we show that there is a natural way to phrase them directly in terms of OTO correlators. We use these observations to construct a natural causal basis for thermal n-point functions in terms of fully nested commutators. We provide several general results which can be inferred from cyclic orbits of permutations, and exemplify the abstract results using a quantum oscillator as an explicit example.http://link.springer.com/article/10.1007/JHEP12(2017)154Quantum Dissipative SystemsStochastic ProcessesAdS-CFT CorrespondenceThermal Field Theory |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Felix M. Haehl R. Loganayagam Prithvi Narayan Amin A. Nizami Mukund Rangamani |
spellingShingle |
Felix M. Haehl R. Loganayagam Prithvi Narayan Amin A. Nizami Mukund Rangamani Thermal out-of-time-order correlators, KMS relations, and spectral functions Journal of High Energy Physics Quantum Dissipative Systems Stochastic Processes AdS-CFT Correspondence Thermal Field Theory |
author_facet |
Felix M. Haehl R. Loganayagam Prithvi Narayan Amin A. Nizami Mukund Rangamani |
author_sort |
Felix M. Haehl |
title |
Thermal out-of-time-order correlators, KMS relations, and spectral functions |
title_short |
Thermal out-of-time-order correlators, KMS relations, and spectral functions |
title_full |
Thermal out-of-time-order correlators, KMS relations, and spectral functions |
title_fullStr |
Thermal out-of-time-order correlators, KMS relations, and spectral functions |
title_full_unstemmed |
Thermal out-of-time-order correlators, KMS relations, and spectral functions |
title_sort |
thermal out-of-time-order correlators, kms relations, and spectral functions |
publisher |
SpringerOpen |
series |
Journal of High Energy Physics |
issn |
1029-8479 |
publishDate |
2017-12-01 |
description |
Abstract We describe general features of thermal correlation functions in quantum systems, with specific focus on the fluctuation-dissipation type relations implied by the KMS condition. These end up relating correlation functions with different time ordering and thus should naturally be viewed in the larger context of out-of-time-ordered (OTO) observables. In particular, eschewing the standard formulation of KMS relations where thermal periodicity is combined with time-reversal to stay within the purview of Schwinger-Keldysh functional integrals, we show that there is a natural way to phrase them directly in terms of OTO correlators. We use these observations to construct a natural causal basis for thermal n-point functions in terms of fully nested commutators. We provide several general results which can be inferred from cyclic orbits of permutations, and exemplify the abstract results using a quantum oscillator as an explicit example. |
topic |
Quantum Dissipative Systems Stochastic Processes AdS-CFT Correspondence Thermal Field Theory |
url |
http://link.springer.com/article/10.1007/JHEP12(2017)154 |
work_keys_str_mv |
AT felixmhaehl thermaloutoftimeordercorrelatorskmsrelationsandspectralfunctions AT rloganayagam thermaloutoftimeordercorrelatorskmsrelationsandspectralfunctions AT prithvinarayan thermaloutoftimeordercorrelatorskmsrelationsandspectralfunctions AT aminanizami thermaloutoftimeordercorrelatorskmsrelationsandspectralfunctions AT mukundrangamani thermaloutoftimeordercorrelatorskmsrelationsandspectralfunctions |
_version_ |
1716767694486765568 |