What is the absolutely continuous spectrum?

Abstract

We summarize (and comment on) the research program carried out in (CMP 319, 501 (2013)), (CMP 338, 347 (2015)), (CMP 344, 959 (2016), (LMP 106, 787 (2016)). This program is 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.