Homogenization results for Schrodinger operators with wildly varying potentials
Speaker: Alexis Drouot, Columbia U.
Location: Warren Weaver Hall 1302
Date: Thursday, October 26, 2017, 11 a.m.
I will study eigenvalues and resonances of Schrodinger operators with potential varying wildly at a small scale epsilon.
The variations are either deterministic or random. Using analytic Fredholm theory and estimates on oscillatory integrals, we will see that as epsilon goes to 0:
- In the deterministic case, resonances/eigenvalues admit a full expansion in powers of epsilon, whose first terms are best described by an effective potential;
- In the stochastic case, resonances/eigenvalues converge almost surely to those of the weak limit of the potential, with corrections satisfying a central limit theorem.