Transport and thermodynamics in quantum junctions: A scattering approach

Alexander Semenov, Abraham Nitzan

Published 2019-12-08Version 1

We present a scattering approach for the study of the transport and thermodynamics of quantum systems strongly coupled to their thermal environment(s). This formalism recovers the standard non-equilibrium Green's function expressions for quantum transport and reproduces recently obtained results for the quantum thermodynamic of slowly driven systems. Using this approach, new results have been obtained. First, we derived of a general explicit expression for non-equilibrium steady state density matrix of a system compromised of multiple infinite baths coupled through a general interaction. Then, we obtained a general expression for the dissipated power for the driven non-interacting resonant level to first order in the driving speeds, where both the dot energy level and its couplings are changing, without invoking the wide band approximation. In addition, we also showed that the symmetric splitting of system bath interaction, employed for the case of a system coupled to one bath to determine the effective system Hamiltonian [Phys. Rev. B 93, 115318 (2016)] is valid for the multiple baths case as well. Finally, we demonstrated an equivalence of our method to the Landauer-Buttiker formalism and its extension to slowly driven systems developed by von Oppen and co-workers [Phys. Rev. Lett. 120, 107701 (2018)]. Our development makes it possible to consider full engine cycles for non-equilibrium quantum thermodynamics of strongly coupled systems.