What is absolutely continuous spectrum?
  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. 
L. Bruneau, V. Jaksic, Y. Last, C.-A. Pillet
math-ph cond-mat.stat-mech math.MP quant-ph