Spectral Representation of Thermal OTO Correlators

Abstract

We study the spectral representation of finite temperature, out of time ordered (OTO) correlators on the multi-time-fold generalised Schwinger-Keldysh contour. We write the contour-ordered correlators as a sum over time-order permutations acting on a funda- mental array of Wightman correlators. We decompose this Wightman array in a basis of column vectors, which provide a natural generalisation of the familiar retarded-advanced basis in the finite temperature Schwinger-Keldysh formalism. The coefficients of this de- composition take the form of generalised spectral functions, which are Fourier transforms of nested and double commutators. Our construction extends a variety of classical results on spectral functions in the SK formalism at finite temperature to the OTO case.

19 pages+appendices, references added

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• Holographic open quantum systems: Toy models and analytic properties of thermal correlators
• The Cosmological OTOC: Formulating new cosmological micro-canonical correlation functions for random chaotic fluctuations in Out-of-Equilibrium Quantum Statistical Field Theory
• Out of Time Ordered Quantum Dissipation
• Thermal three-point functions from holographic Schwinger-Keldysh contours
• Holographic KMS relations at finite density
• Open effective theory of scalar field in rotating plasma
• The Cosmological OTOC: A New Proposal for Quantifying Auto-Correlated Random Non-Chaotic Primordial Fluctuations
• A Bound on Thermal Relativistic Correlators at Large Spacelike Momenta
• Out of time ordered effective dynamics of a quartic oscillator
• Holographic thermal correlators: A tale of Fuchsian ODEs and integration contours
• A study of non-linear Langevin dynamics under non-Gaussian noise with quartic cumulant
• Cosmological Geometric Phase From Pure Quantum States: A study without/with having Bell's inequality violation
• Schwinger-Keldysh path integral formalism for a Quenched Quantum Inverted Oscillator