Dynamical Contrast on Highly Correlated Anderson-type models

Abstract: We present examples of random Schödinger operators obtained in a similar fashion but exhibiting distinct transport properties. The models are constructed by connecting, in different ways, infinitely many copies of the one dimensional Anderson model. Spectral aspects of the models will also be presented. In particular, we obtain a physically motivated example of a random operator with purely absolutely continuous spectrum where the transient and recurrent components coexist. This can be interpreted as a sharp phase transition within the absolutely continuous spectrum. Time allowing, I will discuss some tools related to harmonic analysis, including a version of Boole's equality which, to the best of our knowledge, is new. Based on joint work with Rajinder Mavi and Jeffrey Schenker.

mathematical physics

Audience: researchers in the topic

TAMU: Mathematical Physics and Harmonic Analysis Seminar