Michael Aizenman, Robert Sims, Simone Warzel
Published 2005-10-18Version 1
We summarize recent works on the stability under disorder of the absolutely continuous spectra of random operators on tree graphs. The cases covered include: Schr\"odinger operators with random potential, quantum graph operators for trees with randomized edge lengths, and radial quasi-periodic operators perturbed by random potentials.
Comments: The article covers talks given at UAB Int. Conf. on Diff. Eq. and Math. Phys., Birmingham, March 2005 (RS and SW), and at AMS Snowbird Conference, Utah, June 2005 (MA)
Journal: Quantum Graphs and Their Applications, (Proceedings AMS-IMA-SIAM Joint Res. Conf., Snowbird 2005). G. Berkolaiko, R.Carlson, S.A. Fulling, and P. Kuchment (eds.). AMS Contemporary Mathematics Series, vol. 415 (AMS, 2006).
Multiscale Analysis and Localization of Random Operators
Persistence under Weak Disorder of AC Spectra of Quasi-Periodic Schroedinger operators on Trees Graphs
Constructive Fractional-Moment Criteria for Localization in Random Operators
