Topics in nonequilibrium quantum statistical mechanics

Walter H. Aschbacher (1) , Vojkan Jaksic (2) , Yan Pautrat (3) , Claude-Alain Pillet (4, 5, 6)

1 Zentrum Mathematik M5
2 Department of Mathematics and Statistics [Montréal]
3 LM-Orsay - Laboratoire de Mathématiques d'Orsay
4 CPT - E5 Physique statistique et systèmes complexes
5 CPT - Centre de Physique Théorique - UMR 6207
6 CPT - Centre de Physique Théorique - UMR 7332

These notes are an expanded and revised version of the lectures given by the second and fourth autor in the summer school "Open Quantum System" held in Grenoble, June 16-July 4, 2003. They provide an introduction to recent developments in non-equilibrium statistical mechanics of open quantum systems, including a completely worked out (simple) example. We discuss non-equilibrium steady states (NESS) and their structural properties, entropy production, linear response theory and weak coupling limit. The emphasis is on Ruelle's scattering approach to the construction of NESS.

Mots clés: nonequilibrium statistical mechanics; NESS; steady-state; entropy production; Kubo formula; Onsager reciprocity relations; free Fermi gas; linear response theory

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

Walter H. Aschbacher, Vojkan Jaksic, Yan Pautrat, Claude-Alain Pillet. Topics in nonequilibrium quantum statistical mechanics. S. Attal, A. Joye, C.-A. Pillet. Open Quantum Systems III, Springer, pp.1-66, 2006, Lecture Notes in Mathematics 1882, ⟨10.1007/b128453⟩. ⟨hal-00005352⟩