What is absolutely continuous spectrum?

Laurent Bruneau (1) , Vojkan Jaksic (2) , Yoram Last (3) , Claude-Alain Pillet (4, 5, 6)

1 AGM - UMR 8088 - Analyse, Géométrie et Modélisation
2 Department of Mathematics and Statistics [Montréal]
3 Einstein Institute of Mathematics
4 FRUMAM - Fédération de Recherche des Unités de MAthématiques de Marseille
5 CPT - Centre de Physique Théorique - UMR 7332
6 CPT - E8 Dynamique quantique et analyse spectrale

This note is an expanded version of the author's contribution to the Proceedings of the ICMP Santiago, 2015, and is based on a talk given by the second author at the same Congress. It concerns a research program devoted to the characterization of the absolutely continuous spectrum of a self-adjoint operator H in terms of the transport properties of a suitable class of open quantum systems canonically associated to H.

Mots clés: spectral theory; scattering theory; nonequilibrium statistical mechanics; quantum transport

Domaines: Physique mathématique [math-ph]; Mécanique statistique [cond-mat.stat-mech]

Laurent Bruneau, Vojkan Jaksic, Yoram Last, Claude-Alain Pillet. What is absolutely continuous spectrum?. 2016. ⟨hal-01269535⟩