Out of time ordered quantum dissipation
Abstract
We consider a quantum Brownian particle interacting with two harmonic baths, which is then perturbed by a cubic coupling linking the particle and the baths. This cubic coupling induces nonlinear dissipation and noise terms in the influence functional/master equation of the particle. Its effect on the OutofTimeOrdered Correlators (OTOCs) of the particle cannot be captured by the conventional FeynmanVernon formalism.We derive the generalised influence functional which correctly encodes the physics of OTO fluctuations, response, dissipation and decoherence. We examine an example where Markovian approximation is valid for the OTO dynamics.If the original cubic coupling has a definite timereversal parity, the leading order OTO influence functional is completely determined by the couplings in the usual master equation via OTO generalisation of OnsagerCasimir relations. New OTO fluctuationdissipation relations connect the nonGaussianity of the thermal noise to the thermal jitter in the damping constant of the Brownian particle.
 Publication:

Journal of High Energy Physics
 Pub Date:
 July 2019
 DOI:
 10.1007/JHEP07(2019)102
 arXiv:
 arXiv:1811.01513
 Bibcode:
 2019JHEP...07..102C
 Keywords:

 Quantum Dissipative Systems;
 Stochastic Processes;
 Effective Field Theories;
 Condensed Matter  Statistical Mechanics;
 High Energy Physics  Theory;
 Quantum Physics
 EPrint:
 46 pages+appendices, typos corrected, minor changes, references updated