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arXiv:1212.6369 · Physica Scripta

Current in coherent quantum systems connected to mesoscopic Fermi reservoirs

Shigeru Ajisaka, Felipe Barra, Carlos Mejía-Monasterio, Tomaž Prosen

Published Oct 19, 2012• 7 citations
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Abstract

We study particle current in a recently proposed model for coherent quantum transport. In this model a system connected to mesoscopic Fermi reservoirs (meso-reservoir) is driven out of equilibrium by the action of super reservoirs thermalized to prescribed temperatures and chemical potentials by a simple dissipative mechanism described by the Lindblad equation. We compare exact (numerical) results with theoretical expectations based on the Landauer formula

DOI
10.1088/0031-8949/86/05/058501

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We study particle current in a recently proposed model for coherent quantum transport. In this model a system connected to mesoscopic Fermi reservoirs (meso-reservoir) is driven out of equilibrium by the action of super reservoirs thermalized to prescribed temperatures and chemical potentials by a simple dissipative mechanism described by the Lindblad equation. We compare exact (numerical) results with theoretical expectations based on the Landauer formula
We study particle current and occupation distribution in a recently proposed model for coherent quantum transport. In this model a system connected to mesoscopic Fermi reservoirs (mesoreservoir) is driven out of equilibrium by the action of superreservoirs with prescribed temperatures and chemical potentials described by a simple dissipative mechanism with the Lindblad equation. We compare exact (numerical) results for the nonequilibrium steady-state particle current with theoretical expectations based on the Landauer formula and show that the model reproduces the behavior of coherent quantum systems in the expected parameter region. We also obtain the mesoreservoir occupation distribution in the nonequilibrium steady-state and compare them with the occupation distribution in the leads in usual description of coherent quantum transport.
We propose a model of nonequilibrium quantum transport of particles and energy in a system connected to mesoscopic Fermi reservoirs (mesoreservoir). The mesoreservoirs are in turn thermalized to prescribed temperatures and chemical potentials by a simple dissipative mechanism described by the Lindblad equation. As an example, we study transport in monoatomic and diatomic chains of noninteracting spinless fermions. We show numerically the breakdown of the Onsager reciprocity relation due to the dissipative terms of the model.
We present a generic, compact formula for the current flowing in interacting and noninteracting systems which are driven out of equilibrium by biased reservoirs described by Lindblad jump operators. We show that, in the limit of high temperature and chemical potential, our formula is equivalent to the well-known Meir-Wingreen formula, which describes the current flowing through a system connected to fermionic baths, therefore bridging the gap between the two formalisms. Our formulation gives a systematic way to address the transport properties of correlated systems strongly driven out of equilibrium. As an illustration, we provide explicit calculations of the current in three cases : (i) a single-site impurity, (ii) a free-fermionic chain, and (iii) a fermionic chain with loss and gain terms along the chain. In this last case, we find that the current across the system has the same behavior for loss or gain terms and depends on the loss/gain rate in a nonmonotonic way.
Using the formalism of Ford-Kac-Mazur we study nonequilibrium transport in fermionic systems connected to general particle and thermal reservoirs. Several exact results on electrical and thermal transport in one-dimensional disordered non-interacting fermionic wires are obtained. Landauer’s formula is shown to follow for a special choice of reservoirs. For general reservoirs the currents in the system depend on the spectral properties of the reservoirs and Landauer’s formula needs modification. Some experimental implications are discussed.