Transport and thermodynamics in quantum junctions: A scattering approach

TL;DR

This paper introduces a scattering approach for analyzing transport and thermodynamics in strongly coupled quantum systems, providing new explicit formulas, validating existing methods, and applying the framework to driven quantum devices with multiple baths.

Contribution

The paper develops a comprehensive scattering formalism for quantum transport and thermodynamics in multi-bath systems, deriving explicit steady-state and power expressions without approximations.

Findings

Derived a general explicit steady-state density matrix for multi-bath systems.

Obtained a first-order expression for dissipated power in driven resonant levels.

Validated the approach's equivalence to Landauer-Buttiker formalism and extended entropy production formulas.

Abstract

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)]. To demonstrate the use of this formalism we analyze the operation a device in which the dot is driven cyclically between two leads under strong coupling conditions. We also generalize the previously obtained expression for entropy production in such driven processes to the many-bath case.