Closed hierarchies and non-equilibirum steady states of driven systems

TL;DR

This paper introduces a class of non-equilibrium quantum systems with a hierarchy of equations that can be efficiently simulated, revealing insights into current generation and energy distribution under weak driving conditions.

Contribution

It develops a tractable framework for analyzing driven quantum systems with hierarchical correlations, including explicit solutions for long-term energy distributions.

Findings

Hierarchy of equations closes for specific measurements

Efficient simulation of long-time dynamics

Explicit formula for energy distribution in weak driving limit

Abstract

We present a class of tractable non-equilibrium dynamical quantum systems which includes combinations of injection, detection and extraction of particles interspersed by unitary evolution. We show how such operations generate a hierarchy of equations tying lower correlation functions with higher order ones. The hierarchy closes for particular choices of measurements and leads to a rich class of evolutions whose long time behavior can be simulated efficiently. In particular, we use the method to describe the dynamics of current generation through a generalized quantum exclusion process, and exhibit an explicit formula for the long time energy distribution in the limit of weak driving.