Langevin Interpretation of Kadanoff-Baym Equations

TL;DR

This paper interprets the Kadanoff-Baym equations as stochastic Langevin equations, providing an intuitive understanding of quantum thermalization by coupling a scalar field to a heat bath and analyzing noise and dissipation effects.

Contribution

It introduces a novel Langevin interpretation of the Kadanoff-Baym equations, linking quantum transport to stochastic processes and thermalization.

Findings

Kadanoff-Baym equations can be viewed as ensemble averages over Langevin equations.

The approach clarifies the role of noise and dissipation in thermalization.

The interpretation aligns with the fluctuation-dissipation theorem.

Abstract

We show that the nonperturbative quantum transport equations, the `Kadanoff-Baym equations', can be understood as the ensemble average over stochastic equations of Langevin type. For this we couple a free scalar boson quantum field to an environmental heat bath with some given temperature T. The inherent presence of noise and dissipation related by the fluctuation-dissipation-theorem guarantees that the modes or particles become thermally populated on average in the long-time limit. This interpretation leads to a more intuitive physical picture of the process of thermalization and of the interpretation of the Kadanoff-Baym equations.