Non-Equilibrium Steady States of the XY Chain

Abstract

We study the non-equilibrium statistical mechanics of the two-sided XY chain. We start from an initial state in which the left and right part of the lattice ℤL = {x ∈ ℤ|x < - M}, ℤR = {x ∈ ℤ|x > M}, are at inverse temperatures βL and βR. Using a simple scattering theoretic analysis, we construct the unique non-equilibrium steady state (NESS). This state depends on βL and βR, but not on the choice of the decoupling parameter M. We prove that in the non-equilibrium case, β L ≠ βR, this state has strictly positive entropy production.