Central limit theorem for locally interacting Fermi gas

Vojkan Jaksic (1) , Yan Pautrat (2) , Claude-Alain Pillet (3, 4, 5)

1 Department of Mathematics and Statistics [Montréal]
2 LM-Orsay - Laboratoire de Mathématiques d'Orsay
3 CPT - E5 Physique statistique et systèmes complexes
4 CPT - Centre de Physique Théorique - UMR 6207
5 CPT - Centre de Physique Théorique - UMR 7332

We consider a locally interacting Fermi gas in its natural non-equilibrium steady state and prove the Quantum Central Limit Theorem (QCLT) for a large class of observables. A special case of our results concerns finitely many free Fermi gas reservoirs coupled by local interactions. The QCLT for flux observables, together with the Green-Kubo formulas and the Onsager reciprocity relations previously established (mp_arc:07-1), complete the proof of the Fluctuation-Dissipation Theorem and the development of linear response theory for this class of models.

Mots clés: quantum nonequilibrium statistical mechanics; fluctuations; nonequilibrium steady states; NESS; open system; linear response theory; fluctuation-dissipation

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]

Vojkan Jaksic, Yan Pautrat, Claude-Alain Pillet. Central limit theorem for locally interacting Fermi gas. Communications in Mathematical Physics, 2009, 285, pp.175-217. ⟨hal-00183637⟩