Thermal out-of-time-order correlators, KMS relations, and spectral functions

Haehl, Felix M.; Loganayagam, R.; Narayan, Prithvi; Nizami, Amin A.; Rangamani, Mukund

doi:10.1007/jhep12(2017)154

Title: Thermal out-of-time-order correlators, KMS relations, and spectral functions

Journal Article · Fri Dec 29 00:00:00 EST 2017 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/jhep12(2017)154· OSTI ID:1502422

Haehl, Felix M. ^[1]; Loganayagam, R. ^[2]; Narayan, Prithvi ^[2]; Nizami, Amin A. ^[2]; Rangamani, Mukund ^[3]

Univ. of British Columbia, Vancouver, BC (Canada). Dept. of Physics and Astronomy
International Centre for Theoretical Sciences (ICTS-TIFR), Bengahuru (India)
Univ. of California, Davis, CA (United States). Center for Quantum Mathematics and Physics (QMAP)

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.

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Research Organization:: Univ. of California, Davis, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: SC0009999

OSTI ID:: 1502422

Journal Information:: Journal of High Energy Physics (Online), Vol. 2017, Issue 12; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 25 works

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