The Stability of the Non-Equilibrium Steady States

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 $\omega (k)=\cos k-\gamma$.

37pages,accepted for publication in Communications in Mathematical Physics

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