Nonequilibrium density matrix for quantum transport: Hershfield approach as a McLennan-Zubarev form of the statistical operator

H. Ness

doi:10.1103/physreve.88.022121

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arXiv · 1305.4479

Nonequilibrium density matrix for quantum transport: Hershfield approach as a McLennan-Zubarev form of the statistical operator

H. Ness

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Abstract

In this paper, we formally demonstrate that the non-equilibrium density matrix developed by Hershfield for the steady state has the form of a McLennan-Zubarev non-equilibrium ensemble. The correction term in this pseudo equilibrium Gibbs-like ensemble is directly related to the entropy production in the quantum open system. The fact the both methods state that a non-equilibrium steady state can be mapped onto a pseudo-equilibrium, permits us to develop non-equilibrium quantities from formal expressions equivalent to the equilibrium case. We provide an example: the derivation of a non-equilibrium distribution function for the electron population in a scattering region in the context of quantum transport.

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H. Ness. 2013-08-06. Nonequilibrium density matrix for quantum transport: Hershfield approach as a McLennan-Zubarev form of the statistical operator. https://doi.org/10.1103/physreve.88.022121

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