Non-equilibrium boundary driven quantum systems: models, methods and properties

TL;DR

This paper reviews recent advances in the modeling, methods, and phenomenology of boundary-driven open quantum systems, emphasizing transport properties, phase transitions, and disordered systems in one dimension.

Contribution

It provides a comprehensive overview of models, analytical and numerical methods, and transport phenomena in boundary-driven quantum systems, integrating recent progress across these areas.

Findings

Transport phenomena in disordered quantum chains analyzed

Emergence of rectification and negative differential conductance discussed

Role of phase transitions in non-equilibrium properties highlighted

Abstract

Recent years have seen tremendous progress in the theoretical understanding of quantum systems driven dissipatively by coupling them to different baths at their edges. This was possible because of the concurrent advances in the models used to represent these systems, the methods employed, and the analysis of the emerging phenomenology. Here we aim to give a comprehensive review of these three integrated research directions. We first provide an overarching view of the models of boundary-driven open quantum systems, both in the weak and strong coupling regimes. This is followed by a review of state-of-the-art analytical and numerical methods, both exact, perturbative and approximate. Finally, we discuss the transport properties of some paradigmatic one-dimensional chains, with an emphasis on disordered and quasiperiodic systems, the emergence of rectification and negative differential conductance, and the role of phase transitions, and we give an outlook on further research options.