Nonequlibrium particle and energy currents in quantum chains connected   to mesoscopic Fermi reservoirs
  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. 
S. Ajisaka, F. Barra, C. Mejia-Monasterio, and T. Prosen
cond-mat.mes-hall quant-ph