A Generalized Fluctuation-Dissipation Theorem for Nonlinear Response Functions

TL;DR

The paper develops a generalized fluctuation-dissipation theorem for nonlinear response within the Closed Time Path real-time formalism. It derives a complete, epsilon-free set of relations for n-point Green functions and amputated 1PI n-point vertex functions by combining tilde conjugation with the KMS condition, and verifies consistency with known results for n=2 and n=3 while providing explicit 4-point relations. These model-independent constraints facilitate spectral representations and transport-coefficient calculations in thermal field theory and have potential experimental relevance in nonlinear response scenarios.

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.