Journal of Statistical Physics

, Volume 112, Issue 5–6, pp 1153–1175 | Cite as

Non-Equilibrium Steady States of the XY Chain

  • Walter H. Aschbacher
  • Claude-Alain Pillet

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,
$$\mathbb{Z}_{\text{L}} = \{ x \in \mathbb{Z}|x < - M\} ,{\text{ }}\mathbb{Z}_{\text{R}} = \{ x \in \mathbb{Z}|x >M\} ,$$
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, βLβR, this state has strictly positive entropy production.
XY chain Jordan–Wigner transformation non-equilibrium steady state Bogoliubov automorphism scattering theory 

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Copyright information

© Plenum Publishing Corporation 2003

Authors and Affiliations

  • Walter H. Aschbacher
    • 1
    • 2
  • Claude-Alain Pillet
    • 1
    • 2
  1. 1.PHYMATUniversité de ToulonLa Garde CedexFrance
  2. 2.FRUMAM, CPT-CNRS Luminy, Case 907Marseille Cedex 9France

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