The HADES seminar on Tuesday, October 25th will be at 3:30 pm in Room 740.

Speaker: Lingfu Zhang

Abstract: I will talk about the Anderson model (i.e., the random Schordinger operator of Laplacian plus i.i.d. potential on the lattice). It is widely used to understand the conductivity of materials in condensed matter physics. An interesting phenomenon is Anderson localization, where eigenfunctions have exponential decay, and the spectrum of this random operator is pure-point (in some intervals). This phenomenon was first rigorously established in the 1980s, while one main remaining question is on the case of Bernoulli potential. A continuous space analog of this problem was proved in a seminal paper by Bourgain and Kenig, and the 2D lattice setting was proved by Ding and Smart. Following their framework, we prove 3D lattice Anderson-Bernoulli localization near the edges of the spectrum. Our main contribution is proving a 3D discrete unique continuation principle, using combinatorial and polynomial arguments. This is joint work with Linjun Li.