Journal of High Energy Physics

, 2017:154 | Cite as

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

  • Felix M. HaehlEmail author
  • R. Loganayagam
  • Prithvi Narayan
  • Amin A. Nizami
  • Mukund Rangamani
Open Access
Regular Article - Theoretical Physics


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.


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


Open Access

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Copyright information

© The Author(s) 2017

Authors and Affiliations

  • Felix M. Haehl
    • 1
    Email author
  • R. Loganayagam
    • 2
  • Prithvi Narayan
    • 2
  • Amin A. Nizami
    • 2
  • Mukund Rangamani
    • 3
  1. 1.Department of Physics and AstronomyUniversity of British ColumbiaVancouverCanada
  2. 2.International Centre for Theoretical Sciences (ICTS-TIFR)BengaluruIndia
  3. 3.Center for Quantum Mathematics and Physics (QMAP), Department of PhysicsUniversity of CaliforniaDavisU.S.A.

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