Thermal out-of-time-order correlators, KMS relations, and spectral functions
Thermal out-of-time-order correlators, KMS relations, and spectral functions
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.
hep-th, cond-mat.stat-mech, math-ph, math.MP, quant-ph
Haehl, Felix M.
eb0d74fd-0d8b-4b1b-8686-79d43c2a3a5f
Loganayagam, R.
18806477-1ac8-419a-9729-0e36440bd36a
Narayan, Prithvi
15b952ac-5fa3-42e8-8f17-59be747e47bf
Nizami, Amin A.
84ea4cf2-c4e9-481a-b55c-9a07c85cb851
Rangamani, Mukund
c6e93885-0b7e-4e8c-92e5-56227da78a81
29 December 2017
Haehl, Felix M.
eb0d74fd-0d8b-4b1b-8686-79d43c2a3a5f
Loganayagam, R.
18806477-1ac8-419a-9729-0e36440bd36a
Narayan, Prithvi
15b952ac-5fa3-42e8-8f17-59be747e47bf
Nizami, Amin A.
84ea4cf2-c4e9-481a-b55c-9a07c85cb851
Rangamani, Mukund
c6e93885-0b7e-4e8c-92e5-56227da78a81
Haehl, Felix M., Loganayagam, R., Narayan, Prithvi, Nizami, Amin A. and Rangamani, Mukund
(2017)
Thermal out-of-time-order correlators, KMS relations, and spectral functions.
J. High Energ. Phys., 2017 (12), [154].
(doi:10.1007/JHEP12(2017)154).
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.
More information
Accepted/In Press date: 18 December 2017
Published date: 29 December 2017
Additional Information:
36 pages + appendices. v2: minor changes + refs added. v3: minor changes, published version
Keywords:
hep-th, cond-mat.stat-mech, math-ph, math.MP, quant-ph
Identifiers
Local EPrints ID: 471238
URI: http://eprints.soton.ac.uk/id/eprint/471238
PURE UUID: caba416d-6df0-46b1-8028-7fd78cd7468f
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Date deposited: 01 Nov 2022 17:39
Last modified: 17 Mar 2024 04:14
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Contributors
Author:
Felix M. Haehl
Author:
R. Loganayagam
Author:
Prithvi Narayan
Author:
Amin A. Nizami
Author:
Mukund Rangamani
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