Thermal outoftimeorder correlators, KMS relations, and spectral functions
Abstract
We describe general features of thermal correlation functions in quantum systems, with specific focus on the fluctuationdissipation 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 outoftimeordered (OTO) observables. In particular, eschewing the standard formulation of KMS relations where thermal periodicity is combined with timereversal to stay within the purview of SchwingerKeldysh 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 npoint 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.
 Authors:

 Univ. of British Columbia, Vancouver, BC (Canada). Dept. of Physics and Astronomy
 International Centre for Theoretical Sciences (ICTSTIFR), Bengahuru (India)
 Univ. of California, Davis, CA (United States). Center for Quantum Mathematics and Physics (QMAP)
 Publication Date:
 Research Org.:
 Univ. of California, Davis, CA (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC)
 OSTI Identifier:
 1502422
 Grant/Contract Number:
 SC0009999
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 Journal of High Energy Physics (Online)
 Additional Journal Information:
 Journal Volume: 2017; Journal Issue: 12; Journal ID: ISSN 10298479
 Publisher:
 Springer Berlin
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Quantum Dissipative Systems; Stochastic Processes; AdSCFT Correspondence; Thermal Field Theory
Citation Formats
Haehl, Felix M., Loganayagam, R., Narayan, Prithvi, Nizami, Amin A., and Rangamani, Mukund. Thermal outoftimeorder correlators, KMS relations, and spectral functions. United States: N. p., 2017.
Web. doi:10.1007/jhep12(2017)154.
Haehl, Felix M., Loganayagam, R., Narayan, Prithvi, Nizami, Amin A., & Rangamani, Mukund. Thermal outoftimeorder correlators, KMS relations, and spectral functions. United States. doi:10.1007/jhep12(2017)154.
Haehl, Felix M., Loganayagam, R., Narayan, Prithvi, Nizami, Amin A., and Rangamani, Mukund. Fri .
"Thermal outoftimeorder correlators, KMS relations, and spectral functions". United States. doi:10.1007/jhep12(2017)154. https://www.osti.gov/servlets/purl/1502422.
@article{osti_1502422,
title = {Thermal outoftimeorder correlators, KMS relations, and spectral functions},
author = {Haehl, Felix M. and Loganayagam, R. and Narayan, Prithvi and Nizami, Amin A. and Rangamani, Mukund},
abstractNote = {We describe general features of thermal correlation functions in quantum systems, with specific focus on the fluctuationdissipation 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 outoftimeordered (OTO) observables. In particular, eschewing the standard formulation of KMS relations where thermal periodicity is combined with timereversal to stay within the purview of SchwingerKeldysh 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 npoint 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.},
doi = {10.1007/jhep12(2017)154},
journal = {Journal of High Energy Physics (Online)},
issn = {10298479},
number = 12,
volume = 2017,
place = {United States},
year = {2017},
month = {12}
}
Web of Science
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Works referenced in this record:
Equilibrium and nonequilibrium formalisms made unified
journal, February 1985
 Chou, Kuangchao; Su, Zhaobin; Hao, Bailin
 Physics Reports, Vol. 118, Issue 12
Threepoint functions at finite temperature
journal, February 1998
 Carrington, M. E.; Heinz, U.
 The European Physical Journal C, Vol. 1, Issue 3
Path integral approach to quantum Brownian motion
journal, September 1983
 Caldeira, A. O.; Leggett, A. J.
 Physica A: Statistical Mechanics and its Applications, Vol. 121, Issue 3
SchwingerKeldysh formalism. Part I: BRST symmetries and superspace
journal, June 2017
 Haehl, Felix M.; Loganayagam, R.; Rangamani, Mukund
 Journal of High Energy Physics, Vol. 2017, Issue 6
Retardedadvanced Npoint Green functions in thermal field theories
journal, December 1994
 Guerin, F.
 Nuclear Physics B, Vol. 432, Issue 12
Chaos and complexity by design
journal, April 2017
 Roberts, Daniel A.; Yoshida, Beni
 Journal of High Energy Physics, Vol. 2017, Issue 4
A bound on chaos
journal, August 2016
 Maldacena, Juan; Shenker, Stephen H.; Stanford, Douglas
 Journal of High Energy Physics, Vol. 2016, Issue 8
Chaos in quantum channels
journal, February 2016
 Hosur, Pavan; Qi, XiaoLiang; Roberts, Daniel A.
 Journal of High Energy Physics, Vol. 2016, Issue 2
n point functions at finite temperature
journal, October 1998
 Hou, Defu; Wang, Enke; Heinz, Ulrich
 Journal of Physics G: Nuclear and Particle Physics, Vol. 24, Issue 10
Chaos, complexity, and random matrices
journal, November 2017
 Cotler, Jordan; HunterJones, Nicholas; Liu, Junyu
 Journal of High Energy Physics, Vol. 2017, Issue 11
Theory of ManyParticle Systems. I
journal, September 1959
 Martin, Paul C.; Schwinger, Julian
 Physical Review, Vol. 115, Issue 6
Black holes and the butterfly effect
journal, March 2014
 Shenker, Stephen H.; Stanford, Douglas
 Journal of High Energy Physics, Vol. 2014, Issue 3
Jarzynskilike equality for the outoftimeordered correlator
journal, January 2017
 Yunger Halpern, Nicole
 Physical Review A, Vol. 95, Issue 1
Nonequilibrium Equality for Free Energy Differences
journal, April 1997
 Jarzynski, C.
 Physical Review Letters, Vol. 78, Issue 14
Thermodynamic equilibrium as a symmetry of the SchwingerKeldysh action
journal, October 2015
 Sieberer, L. M.; Chiocchetta, A.; Gambassi, A.
 Physical Review B, Vol. 92, Issue 13
Spectral representation of threepoint functions at finite temperature
journal, December 1990
 Evans, T. S.
 Physics Letters B, Vol. 252, Issue 1
A comparison of the realtime and the imaginarytime formalisms of finitetemperature field theory for 2, 3 and 4point Green functions
journal, July 1992
 Aurenche, P.; Becherrawy, T.
 Nuclear Physics B, Vol. 379, Issue 12
Npoint finite temperature expectation values at real times
journal, April 1992
 Evans, T. S.
 Nuclear Physics B, Vol. 374, Issue 2
Equilibrium freeenergy differences from nonequilibrium measurements: A masterequation approach
journal, November 1997
 Jarzynski, C.
 Physical Review E, Vol. 56, Issue 5
Bulk locality from modular flow
journal, July 2017
 Faulkner, Thomas; Lewkowycz, Aitor
 Journal of High Energy Physics, Vol. 2017, Issue 7
KuboMartinSchwinger conditions for 4point Green functions at finite temperature
journal, August 2000
 Carrington, M. E.; Defu, Hou; Sowiak, J. C.
 Physical Review D, Vol. 62, Issue 6
Threepoint functions at finite temperature
journal, October 1990
 Evans, T. S.
 Physics Letters B, Vol. 249, Issue 2
The theory of a general quantum system interacting with a linear dissipative system
journal, October 1963
 Feynman, R. P.; Vernon, F. L.
 Annals of Physics, Vol. 24
Index summation in real time statistical field theory
journal, March 2007
 Carrington, M. E.; Fugleberg, T.; Irvine, D. S.
 The European Physical Journal C, Vol. 50, Issue 3
StatisticalMechanical Theory of Irreversible Processes. I. General Theory and Simple Applications to Magnetic and Conduction Problems
journal, June 1957
 Kubo, Ryogo
 Journal of the Physical Society of Japan, Vol. 12, Issue 6
On the equilibrium states in quantum statistical mechanics
journal, June 1967
 Haag, R.; Hugenholtz, N. M.; Winnink, M.
 Communications in Mathematical Physics, Vol. 5, Issue 3
Generalized fluctuationdissipation theorem for nonlinear response functions
journal, July 2002
 Wang, Enke; Heinz, Ulrich
 Physical Review D, Vol. 66, Issue 2
Relative entropy equals bulk relative entropy
journal, June 2016
 Jafferis, Daniel L.; Lewkowycz, Aitor; Maldacena, Juan
 Journal of High Energy Physics, Vol. 2016, Issue 6
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