Video library: Dmitry Treschev, On a heavy quantum particle

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International conference «Real and Complex Dynamical Systems», dedicated to the to the 75th anniversary of Yu. S. Il'yashenko November 30, 2018 10:05, Moscow, Steklov Mathematical Institute (Gubkina, 8, 9th floor)

On a heavy quantum particle Dmitry Treschev Steklov Mathematical Institute of Russian Academy of Sciences
Abstract: We consider Schrödinger equation for a particle on a flat $n$-torus in a bounded potential, depending on time. Mass of the particle equals $1/\mu^2$, where $\mu$ is a small parameter. We show that the Sobolev $H^{\nu}$-norms of the wave function grow approximately as $t^{\nu}$ on the time interval $t \in [-t_,t_]$, where $t_$ is slightly less than $O(1/\mu)$. Language:* English