Non-equilibrium steady states of the XY chain

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, Z(L)={x is an element of Z \ x < -M}, Z(R)={x is an element of Z vertical bar x > M}, are at inverse temperatures beta(L) and beta(R). Using a simple scattering theoretic analysis, we construct the unique non-equilibrium steady state (NESS). This state depends on beta(L) and beta(R), but not on the choice of the decoupling parameter M. We prove that in the non-equilibrium case, beta(L)not equalbeta(R), this state has strictly positive entropy production.