Nonequilibrium density matrix description of steady state quantum transport

Details Nonequilibrium density matrix description of steady state quantum transport Nonequilibrium density matrix description of steady state quantum transport

2011-06-16

arxiv.org/abs/1106.3207v2

Phys. Rev. E 85, 011126 (2012)

Physics

Condensed Matter

Statistical Mechanics

24 pages, 2 figures, In press with Phys. Rev. E

Scientific paper

With this work we investigate the stationary nonequilibrium density matrix of current carrying nonequilibrium steady states of in-between quantum systems that are connected to reservoirs. We describe the analytical procedure to obtain the explicit result for the reduced density matrix of quantum transport when the system, the connecting reservoirs and, as well, the system-reservoir interactions are described by quadratic Hamiltonians. Our procedure is detailed for both, electronic transport described by the tight-binding Hamiltonian and for phonon transport described by harmonic Hamiltonians. For the special case of weak system-reservoir couplings, a more detailed description of the steady-state density matrix is obtained. Several paradigm transport setups for inter-electrode electron transport and low-dimensional phonon heat flux are elucidated.

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