- Series
- Time
- Thursday, February 23, 2023 - 12:00pm for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Omar Hurtado – Georgia Tech and University of California, Irvine – ohurtad1@uci.edu
- Organizer
- Michael Loss
The Anderson tight binding model describes an electron moving in a disordered material. Such models are, depending on various parameters of the system, either expected to or known to display a phenomenon known as Anderson localization, in which this disorder can "trap" electrons. Different versions of this phenomenon can be characterized spectrally or locally. We will review both the dominant methods and some of the foundational results in the study of these systems in arbitrary dimension, before shifting our focus to aspects of the one-dimensional theory.
Specifically, we will examine the transfer matrix method, which allows us to leverage the Furstenberg theory of random matrix products to understand the asymptotics of generalized eigenfunctions. From this, we will briefly sketch a proof of localization given originally in Jitomirskaya-Zhu (2019). Finally, we will discuss recent work of the speaker combining the argument in Jitomirskaya-Zhu with certain probabilistic results to prove localization for a broader class of models.