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arXiv · 1706.08956

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

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

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Felix M. Haehl, R. Loganayagam, Prithvi Narayan, Amin A. Nizami, Mukund Rangamani. 2017-06-27. Thermal out-of-time-order correlators, KMS relations, and spectral functions. https://doi.org/10.1007/jhep12(2017)154

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