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 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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Correspondence to Felix M. Haehl.

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ArXiv ePrint: 1706.08956

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Haehl, F.M., Loganayagam, R., Narayan, P. et al. Thermal out-of-time-order correlators, KMS relations, and spectral functions. J. High Energ. Phys. 2017, 154 (2017). https://doi.org/10.1007/JHEP12(2017)154

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Keywords

  • Quantum Dissipative Systems
  • Stochastic Processes
  • AdS-CFT Correspondence
  • Thermal Field Theory