Mode-coupling theory and the fluctuation-dissipation theorem for nonlinear Langevin equations with multiplicative noise

TL;DR

This paper develops a mode-coupling theory for nonlinear Langevin equations with multiplicative noise, ensuring consistency with the fluctuation-dissipation theorem and discussing implications for real fluids and supercooled liquids.

Contribution

It introduces a field theoretic mode-coupling framework for nonlinear Langevin equations with multiplicative noise, addressing FDT consistency and extending to real fluids.

Findings

Derived equations are consistent with the fluctuation-dissipation theorem.

Standard idealized mode-coupling theory is not FDT consistent.

Discussed potential applications to supercooled fluids and aging regimes.

Abstract

In this letter, we develop a mode-coupling theory for a class of nonlinear Langevin equations with multiplicative noise using a field theoretic formalism. These equations are simplified models of realistic colloidal suspensions. We prove that the derived equations are consistent with the fluctuation-dissipation theorem. We also discuss the generalization of the result given here to real fluids, and the possible description of supercooled fluids in the aging regime. We demonstrate that the standard idealized mode-coupling theory is not consistent with the FDT in a strict field theoretic sense.