The status of the quantum dissipation-fluctuation relation and Langevin equation

TL;DR

This paper critically examines the quantum fluctuation-dissipation relations, distinguishing between their weak and strong forms, and argues that the strong form involving Langevin equations has not been reliably established.

Contribution

It clarifies the conditions under which quantum fluctuation-dissipation theorems hold and questions the derivation of the Langevin equation-based strong form.

Findings

Weak form of the quantum fluctuation-dissipation theorem is generally valid.

Strong form involving Langevin equations lacks reliable derivation.

Highlights the need for careful validation of the Langevin approach in quantum systems.

Abstract

I examine the arguments which have been given for quantum fluctuation-dissipation theorems. I distinguish between a weak form of the theorem, which is true under rather general conditions, and a strong form which requires a Langevin equation for its statement. I argue that the latter has not been reliably derived.