The Green-Kubo Formula for the Spin-Fermion System

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The spin-fermion model describes a two level quantum system S (spin 1/2) coupled to finitely many free Fermi gas reservoirs R_j which are in thermal equilibrium at inverse temperatures beta_j. We consider non-equilibrium initial conditions where not all beta_j are the same. It is known that, at small coupling, the combined system S + R_1 + ... has a unique non-equilibrium steady state (NESS) characterized by strictly positive entropy production. In this paper we study linear response in this NESS and prove the Green-Kubo formula and the Onsager reciprocity relat ions for heat fluxes generated by temperature differentials.

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