The non-equilibrium steady state of sparse systems with nontrivial topology

TL;DR

This paper investigates the steady state behavior of a sparse, multiply-connected system driven out of equilibrium, revealing a topological contribution to energy absorption and a unique crossover regime influenced by system sparsity.

Contribution

It introduces a model of a sparse, multiply-connected system with nontrivial topology under non-equilibrium conditions, highlighting a novel topological term in energy absorption and a new crossover regime.

Findings

Induced current controlled by driving strength.

Topological term in energy absorption rate.

Exponential suppression of current in intermediate regime.

Abstract

We study the steady state of a multiply-connected system that is driven out of equilibrium by a sparse perturbation. The prototype example is an $N$-site ring coupled to a thermal bath, driven by a stationary source that induces transitions with log-wide distributed rates. An induced current arises, which is controlled by the strength of the driving, and an associated topological term appears in the expression for the energy absorption rate. Due to the sparsity, the crossover from linear response to saturation is mediated by an intermediate regime, where the current is exponentially small in $\sqrt{N}$, which is related to the work of Sinai on "random walk in a random environment".