Non-equilibrium steady state and induced currents of a mesoscopically-glassy system: interplay of resistor-network theory and Sinai physics

TL;DR

This paper models the non-equilibrium steady state of a mesoscopic ring coupled to a thermal bath and driven by a hot source, revealing glassy dynamics and Sinai physics effects on induced currents.

Contribution

It provides an explicit solution for the NESS of a driven ring system with glassy time scales, connecting resistor-network theory and Sinai physics.

Findings

Sign of current fluctuates with driving intensity.

Distribution of current magnitude shows Sinai physics signatures.

Glassy dynamics influence the steady-state current behavior.

Abstract

We introduce an explicit solution for the non-equilibrium steady state (NESS) of a ring that is coupled to a thermal bath, and is driven by an external hot source with log-wide distribution of couplings. Having time scales that stretch over several decades is similar to glassy systems. Consequently there is a wide range of driving intensities where the NESS is like that of a random walker in a biased Brownian landscape. We investigate the resulting statistics of the induced current $I$. For a single ring we discuss how $sign(I)$ fluctuates as the intensity of the driving is increased, while for an ensemble of rings we highlight the fingerprints of Sinai physics on the $abs(I)$ distribution.