Fluctuating Quantum Kinetic Theory

TL;DR

This paper develops a quantum Langevin kinetic framework for fermions, deriving noise correlations, calculating structure factors, and formulating fluctuating hydrodynamics, advancing understanding of quantum fluids and disordered systems.

Contribution

It introduces a quantum Langevin kinetic equation for fermions, deriving noise correlations, and extends to fluctuating hydrodynamics and electron fluids with long-range interactions.

Findings

Equilibrium dynamic structure factor matches many-body results.

Derived fluctuating Navier-Stokes equations for quantum fluids.

Proved an H-theorem for nonlinear Landau kinetic equation.

Abstract

We consider a quantum Langevin kinetic equation for a system of fermions. We first derive the Langevin force noise correlation functions in Landau's Fermi-liquid kinetic theory from general considerations. We then use the resulting equation to calculate the equilibrium dynamic structure factor in the collisionless regime at low temperatures. The result is in agreement with the conventional many-body result. We then use the theory to derive both the fluctuating Navier-Stokes equations for a quantum fluid and the fluctuating hydrodynamic equations for fermions in the presence of quenched disorder. We also discuss the modifications needed for the fluctuating hydrodynamic equations to describe an electron fluid with long-ranged interactions, and we prove an H-theorem for the nonlinear Landau kinetic equation.