The Stability of the Non-Equilibrium Steady States

TL;DR

This paper investigates the stability of non-equilibrium steady states in free lattice Fermion models, revealing their macroscopic instability far from equilibrium through spectral analysis and positive commutator methods.

Contribution

It introduces a novel spectral analysis approach using positive commutators to study the stability of NESS in lattice Fermion systems.

Findings

NESS is macroscopically unstable far from equilibrium

Constructs a positive commutator for the lattice Fermion system

Analyzes the dispersion relation (k)=cos k-

Abstract

We show that the non-equilibrium steady state (NESS) of the free lattice Fermion model far from equilibrium is macroscopically unstable. The problem is translated to that of the spectral analysis of {\it Liouville Operator}. We use the method of positive commutators to investigate it. We construct a positive commutator on the lattice Fermion system, whose dispersion relation is $\omega(k)=\cos k-\gamma$.