Fluctuating Quantum Kinetic Theory

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.

17pp

References in corpus (3)

• Generalization of Luttinger's Theorem for Strongly Correlated Electron Systems
• Soft modes in Fermi liquids at arbitrary temperatures
• Rigidity and Superfast Signal Propagation in Fluids and Solids in Non-Equilibrium Steady States

Cited by in corpus (5)

• Soft modes in Fermi liquids at arbitrary temperatures
• Velocity-Dependent Forces and Non-Hydrodynamic Initial Conditions in Quantum and Classical Fluids
• Fluctuation-dissipation relation in a non-equilibrium quantum fluid
• A Fluctuation-Response Relation as a Probe of Long-Range Correlations in Non-Equilibrium Quantum and Classical Fluids
• Thermal Transport and Non-Mechanical Forces in Metals