Nonequilibrium density matrix description of steady state quantum transport

TL;DR

This paper develops an analytical method to derive the explicit steady-state density matrix for quantum transport systems connected to reservoirs, applicable to electronic and phononic transport with quadratic Hamiltonians, especially in weak coupling regimes.

Contribution

It provides a detailed analytical procedure for obtaining the nonequilibrium steady-state density matrix in quantum transport systems with quadratic Hamiltonians, including weak coupling cases.

Findings

Explicit steady-state density matrix expressions for electronic and phonon transport.

Application to various transport setups demonstrating the method's versatility.

Enhanced understanding of quantum transport in weak system-reservoir coupling regimes.

Abstract

With this work we investigate the stationary nonequilibrium density matrix of current carrying nonequilibrium steady states of in-between quantum systems that are connected to reservoirs. We describe the analytical procedure to obtain the explicit result for the reduced density matrix of quantum transport when the system, the connecting reservoirs and, as well, the system-reservoir interactions are described by quadratic Hamiltonians. Our procedure is detailed for both, electronic transport described by the tight-binding Hamiltonian and for phonon transport described by harmonic Hamiltonians. For the special case of weak system-reservoir couplings, a more detailed description of the steady-state density matrix is obtained. Several paradigm transport setups for inter-electrode electron transport and low-dimensional phonon heat flux are elucidated.