V. Jaksic, Y. Ogata, C.-A. Pillet
The Green-Kubo formula for the spin-fermion system
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ABSTRACT.  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 relations for heat fluxes generated by temperature 
differentials.