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

J. K. Freericks·V. M. Turkowski
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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.

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J. K. Freericks, V. M. Turkowski. 2005-11-02. Steady-state nonequilibrium dynamical mean-field theory and the quantum Boltzman. https://doi.org/10.1088/1742-6596%2F35%2F1%2F004

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