Duality in quantum transport models

TL;DR

This paper extends the classical duality approach to quantum transport models, enabling simplification and equilibrium mapping, exemplified by the quantum symmetric exclusion process, through dynamical symmetries.

Contribution

It introduces a duality method for quantum systems with thermal baths, simplifying models and linking them to equilibrium processes, which was not previously established.

Findings

Mapped quantum models to simpler forms with fewer particles

Showed that quantum processes can be related to equilibrium baths

Demonstrated the approach on the quantum symmetric exclusion process

Abstract

We develop the `duality approach', that has been extensively studied for classical models of transport, for quantum systems in contact with a thermal `Lindbladian' bath. The method provides (a) a mapping of the original model to a simpler one, containing only a few particles and (b) shows that any dynamic process of this kind with generic baths may be mapped onto one with equilibrium baths. We exemplify this through the study of a particular model: the quantum symmetric exclusion process introduced in [D. Bernard, T. Jin, Phys. Rev. Lett. 123, 080601 (2019)]. As in the classical case, the whole construction becomes intelligible by considering the dynamical symmetries of the problem.