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Non-Equilibrium Steady States of the XY Chain

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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 β L and β R. Using a simple scattering theoretic analysis, we construct the unique non-equilibrium steady state (NESS). This state depends on β L and β R, but not on the choice of the decoupling parameter M. We prove that in the non-equilibrium case, β L≠β R, this state has strictly positive entropy production.

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Authors and Affiliations

  1. PHYMAT, Université de Toulon, B.P. 132, 83957, La Garde Cedex, France

    Walter H. Aschbacher & Claude-Alain Pillet

  2. FRUMAM, CPT-CNRS Luminy, Case 907, 13288, Marseille Cedex 9, France

    Walter H. Aschbacher & Claude-Alain Pillet

Authors
  1. Walter H. Aschbacher
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  2. Claude-Alain Pillet
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Aschbacher, W.H., Pillet, CA. Non-Equilibrium Steady States of the XY Chain. Journal of Statistical Physics 112, 1153–1175 (2003). https://doi.org/10.1023/A:1024619726273

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