Notes on a non-thermal fluctuation-dissipation relation in quantum Brownian motion

TL;DR

This paper reviews how unitarity and stationarity in the Schwinger-Keldysh formalism lead to a generalized fluctuation-dissipation relation applicable beyond thermal equilibrium, including non-Gaussian corrections and applications to quantum Brownian motion.

Contribution

It introduces a quantum generalized fluctuation-dissipation relation derived from fundamental principles, extending its applicability beyond equilibrium conditions.

Findings

Derivation of a quantum gFDR from unitarity and stationarity

Inclusion of non-Gaussian loop corrections

Application to quantum Brownian motion scenarios

Abstract

We review how unitarity and stationarity in the Schwinger-Keldysh formalism naturally lead to a (quantum) generalized fluctuation-dissipation relation (gFDR) that works beyond thermal equilibrium. Non-Gaussian loop corrections are also presented. Additionally, we illustrate the application of this gFDR in various scenarios related to quantum Brownian motion and the generalized Langevin equation.