Center for                           Nonlinear Analysis CNA Home People Seminars Publications Workshops and Conferences CNA Working Groups CNA Comments Form Summer Schools Summer Undergraduate Institute PIRE Cooperation Graduate Topics Courses SIAM Chapter Seminar Positions Contact CNA Seminar/Colloquium/Joint Pitt-CNA Colloquium Alexis Drouot Columbia University Title: Resonances for highly oscillatory and stochastic Schrodinger operators Abstract: We consider Schrodinger operators of the form $-\Delta+q(x)$, where the localized potential $q$ is the sum of a deterministic part $q_0$ and of a stochastic part $q_1$ varying randomly at scale $N^{-1}, N\gg 1$. The addition of $q_1$ to the potential $q_0$ corresponds to the introduction of a high disorder in the system. We show almost sure convergence of eigenvalues (resp. resonances) of $-\Delta+q(x)$ to eigenvalues (resp. resonances) of $-\Delta+q_0(x)$ as $N\to\infty$; and we study the form of higher order corrections. The result implies that with high probability, the local energy of waves scattered by $q$ decay exponentially.Date: Tuesday, October 31, 2017Time: 1:30 pmLocation: Wean Hall 7218Submitted by:  Ian Tice