Non-equilibrium steady state of sparse systems

TL;DR

This paper investigates the non-equilibrium steady states of sparse systems, revealing differences between stochastic and quantum cases, and introduces a toy model using a log-normal ensemble to analyze sparsity effects.

Contribution

It proposes a resistor-network framework for sparse systems' NESS and explores the quantum versus stochastic differences, extending fluctuation-dissipation concepts.

Findings

Quantum NESS can significantly differ from stochastic NESS.

Sparsity influences the saturation temperature in quantum systems.

A log-normal ensemble model effectively captures system sparsity effects.

Abstract

A resistor-network picture of transitions is appropriate for the study of energy absorption by weakly chaotic or weakly interacting driven systems. Such "sparse" systems reach a novel non-equilibrium steady state (NESS) once coupled to a bath. In the stochastic case there is an analogy to the physics of percolating glassy systems, and an extension of the fluctuation-dissipation phenomenology is proposed. In the mesoscopic case the quantum NESS might differ enormously from the stochastic NESS, with saturation temperature determined by the sparsity. A toy model where the sparsity of the system is modeled using a log-normal random ensemble is analyzed.