Next Talk

 Anderson Localization: From Spectral Theory to Quantum Dynamics 

Omar Hurtado 

June 2nd, 2025 (Monday) at 1pm - NSII 1201

Abstract

Anderson localization is a phenomenon first posited by physicist P. Anderson in Nobel prize winning work, where disorder in a material frustrates electronic transport, thus "localizing" wave functions (forcing them to remain more or less constrained to a small area forever even under the system's time evolution). Decades later, this phenomenon has been proven, empirically and theoretically, to a large degree. We recall the basics of spectral theory for Hilbert spaces, and basic quantum mechanical background before discussing the relationship between the spectral theory of a Hamiltonian and the associated dynamics in the context of Anderson localization. We will discuss the history of mathematically rigorous results concerning Anderson localization, and some of the key techniques. Time permitting, the speaker will discuss some of their own work in this field and key ideas therein.

About the Speaker

Omar Hurtado is a 6th year PhD student of Svetlana Jitomirskaya interested in the intersection of mathematical physics, spectral theory and probability.

何でもは知らないわよ。知ってることだけ。