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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.Recording: http://mm.math.cmu.edu/recordings/cna/alexis_drouot_small.mp4Date: Tuesday, October 31, 2017Time: 1:30 pmLocation: Wean Hall 7218Submitted by: Ian Tice |