The Green-Kubo formula and the Onsager reciprocity relations in quantum statistical mechanics

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

We study linear response theory in the general framework of algebraic quantum statistical mechanics and prove the Green-Kubo formula and the Onsager reciprocity relations for heat fluxes generated by temperature differentials. Our derivation is axiomatic and the key assumptions concern ergodic properties of non-equilibrium steady states.

Mots clés: Onsager reciprocity relations; Kubo formula; linear response; nonequilibrium statistical mechanics; steady state; NESS

Domaines: Physique mathématique [math-ph]

Vojkan Jaksic, Yoshiko Ogata, Claude-Alain Pillet. The Green-Kubo formula and the Onsager reciprocity relations in quantum statistical mechanics. Communications in Mathematical Physics, 2006, 265 (3), pp.721-738. ⟨10.1007/s00220-006-0004-6⟩. ⟨hal-00005386⟩