Dependence of the density of states on the probability distribution for discrete random Schrödinger operators, II

Speaker: 

Christoph Marx

Institution: 

Oberlin College

Time: 

Friday, April 20, 2018 - 1:00pm

Location: 

rh 340N

We prove the Hölder-continuity of the density of states measure (DOSm) and the integrated density of states (IDS) for discrete random Schrödinger operators with finite-range potentials with respect to the probability measure. In particular, our result implies that the DOSm and the IDS for smooth approximations of the Bernoulli distribution converge to the corresponding quantities for the Bernoulli-Anderson model. Other applications of the technique are given to the dependency of the DOSm and IDS on the disorder, and the continuity of the Lyapunov exponent in the weak-disorder regime for dimension one. The talk is based on joint work with Peter Hislop (Univ. of Kentucky) 

Concentration of Eigenfunctions: Sup-norms and Averages

Speaker: 

Jeffrey Galkowski

Institution: 

Stanford University

Time: 

Thursday, May 17, 2018 - 2:00pm

Host: 

Location: 

RH 340P

In this talk we relate concentration of Laplace eigenfunctions in position and momentum to sup-norms and submanifold averages. In particular, we present a unified picture for sup-norms and submanifold averages which characterizes the concentration of those eigenfunctions with maximal growth. We then exploit this characterization to derive geometric conditions under which maximal growth cannot occur. 

Exact bosonization in two spatial dimensions and a new class of lattice gauge theories

Speaker: 

Anton Kapustin

Institution: 

Caltech

Time: 

Sunday, December 10, 2017 - 5:00pm

Location: 

NS 1201

We describe a 2d analog of the Jordan-Wigner transformation which maps an arbitrary fermionic system on a 2d lattice to a lattice gauge theory while preserving the locality of the Hamiltonian. When the space is simply-connected, this bosonization map is an equivalence. We describe several examples of 2d bosonization, including free fermions on square and honeycomb lattices and the Hubbard model. We describe Euclidean actions for the corresponding lattice gauge theories and find that they contains Chern-Simons-like terms.

Spectral gaps for quasi-periodic Schrodinger operators with Liouville frequencies III

Speaker: 

Yunfeng Shi

Institution: 

Fudan University

Time: 

Thursday, December 14, 2017 - 2:00pm

Location: 

Rh 340P

We consider the spectral gaps of quasi-periodic Schrodinger operators with Liouville frequencies. By establishing quantitative reducibility of the associated Schrodinger cocycle,  we show that the size of the spectral gaps decays exponentially. This is a joint work with Wencai Liu. 

Dependence of the density of states on the probability distribution for discrete random Schrödinger operators

Speaker: 

Christoph Marx

Institution: 

Oberlin

Time: 

Thursday, February 15, 2018 - 2:00pm

Location: 

RH 340P

We prove the Hölder-continuity of the density of states measure (DOSm) and the integrated density of states (IDS) for discrete random Schrödinger operators with finite-range potentials with respect to the probability measure. In particular, our result implies that the DOSm and the IDS for smooth approximations of the Bernoulli distribution converge to the corresponding quantities for the Bernoulli-Anderson model. Other applications of the technique are given to the dependency of the DOSm and IDS on the disorder, and the continuity of the Lyapunov exponent in the weak-disorder regime for dimension one. The talk is based on joint work with Peter Hislop (Univ. of Kentucky) 

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