Steady-state nonequilibrium dynamical mean-field theory and the quantum Boltzman

TL;DR

This paper develops a formalism for steady-state nonequilibrium dynamical mean-field theory using real-time Kadanoff-Baym contour techniques, deriving a quantum Boltzmann equation that incorporates bandstructure effects.

Contribution

It introduces a real-time formalism for nonequilibrium DMFT and derives a quantum Boltzmann equation, connecting Kubo and nonequilibrium linear response approaches.

Findings

Derivation of the quantum Boltzmann equation within nonequilibrium DMFT.

Reduction to the Drude model in the relaxation time limit.

Demonstration of equivalence between Kubo and nonequilibrium linear response methods.

Abstract

We derive the formalism for steady state nonequilibrium dynamical mean-field theory in a real-time formalism along the Kadanoff-Baym contour. The resulting equations of motion are first transformed to Wigner coordinates (average and relative time), and then re-expressed in terms of differential operators. Finally, we perform a Fourier transform with respect to the relative time, and take the first-order limit in the electric field to produce the quantum Boltzmann equation for dynamical mean-field theory. We next discuss the structure of the equations and their solutions, describing how these equations reduce to the Drude result in the limit of a constant relaxation time. We also explicitly demonstrate the equivalence between the Kubo and nonequilibrium approaches to linear response. There are a number of interesting modifications of the conventional quantum Boltzmann equation that arise due to the underlying bandstructure of the lattice.