A Generalized Fluctuation-Dissipation Theorem for Nonlinear Response Functions

TL;DR

This paper derives a generalized Fluctuation-Dissipation Theorem for nonlinear response functions at finite temperature, extending known results and providing new relations among higher-order response and correlation functions.

Contribution

It introduces a comprehensive nonlinear FDT within the Closed Time Path formalism, applicable to n-point functions and includes explicit relations for 4-point functions.

Findings

Generalized FDT matches known results for n=2 and 3

New explicit relations for 4-point nonlinear response and correlation functions

Framework applicable to finite temperature quantum systems

Abstract

A nonlinear generalization of the Fluctuation-Dissipation Theorem (FDT) for the n-point Green functions and the amputated 1PI vertex functions at finite temperature is derived in the framework of the Closed Time Path formalism. We verify that this generalized FDT coincides with known results for n=2 and 3. New explicit relations among the 4-point nonlinear response and correlation (fluctuation) functions are presented.