We propose a model of nonequilibrium quantum transport of particles and energy in a system connected to mesoscopic Fermi reservoirs (meso-reservoir). The meso-reservoirs 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 non-interacting spinless fermions. We show numerically the breakdown of the Onsager reciprocity relation due to the dissipative terms of the model.
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