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.

References in corpus (2)

• Eigenfunctions, transfer matrices, and absolutely continuous spectrum of one-dimensional Schrodinger operators
• Independent electrons model for open quantum systems: Landauer-Buettiker formula and strict positivity of the entropy production

Cited by in corpus (4)

• Ballistic Transport for Limit-Periodic Jacobi Matrices with Applications to Quantum Many-Body Problems
• Two-dimensional Dirac operators with general $\delta$-shell interactions supported on a straight line
• Bound states in semi-Dirac semi-metals
• Asymptotic property of current for a conduction model of Fermi particles on finite lattice