The Green-Kubo formula for the spin-fermion system

Vojkan Jaksic (1) , Yoshiko Ogata (2, 3, 4) , Claude-Alain Pillet (5, 2, 4, 6)

1 Department of Mathematics and Statistics [Montréal]
2 CPT - Centre de Physique Théorique - UMR 6207
3 Department of Mathematical Sciences
4 CPT - Centre de Physique Théorique - UMR 7332
5 FRUMAM - Fédération de Recherche des Unités de MAthématiques de Marseille
6 CPT - E5 Physique statistique et systèmes complexes

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.

Mots clés: open systems; spin-fermion; Onsager reciprocity relations; nonequilibrium statistical mechanics; steady state; NESS; Kubo formula; linear response

Domaines: Physique mathématique [math-ph]

Vojkan Jaksic, Yoshiko Ogata, Claude-Alain Pillet. The Green-Kubo formula for the spin-fermion system. Communications in Mathematical Physics, 2006, 268 (2), pp.369-401. ⟨10.1007/s00220-006-0095-0⟩. ⟨hal-00009010v2⟩