Student Harmonic Analysis and PDE Seminar (HADES): Eigenvalues for Schrödinger operators with random, highly oscillatory potentials.

Seminar | February 28 | 3:40-5 p.m. | 740 Evans Hall

 Alexis Drouot, UCB

 Department of Mathematics

We study eigenvalues of 3D Schrödinger operators modified by a stochastic term $V_N$, oscillating at typical frequency $N \gg 1$. Such operators are a rough model for the propagation of waves inside a disordered medium. Using a perturbation argument, we show that eigenvalues converge almost surely as $N \rightarrow \infty$. The rate of convergence is investigated: we identify two regimes, deterministic and stochastic, depending on high-frequency interference and on the typical amplitude of the low-frequencies of $V_N$ -- created by large deviations effects.