Title: Ballistic Transport for Limit-periodic Schr\"odinger Operators in One Dimension
Speaker: Giorgio Young (University of Michigan)
Speaker's URL: https://lsa.umich.edu/math/people/postdoc-faculty/gfyoung.html
Abstract: In this talk, we consider the transport properties of the class of limit-periodic continuum Schr\"odinger operators whose potentials are approximated exponentially quickly by a sequence of periodic functions. For such an operator $H$, and $X_H(t)$ the Heisenberg evolution of the position operator, we show the limit of $\frac{1}{t}X_H(t)\psi$ as $t\to\infty$ exists and is nonzero for $\psi\ne 0$ belonging to a dense subspace of initial states which are sufficiently regular and of suitably rapid decay. This is viewed as a particularly strong form of ballistic transport, and this is the first time it has been proven in a continuum almost periodic non-periodic setting. In particular, this statement implies that for the initial states considered, the second moment grows quadratically in time.
URL associated with Seminar: https://u.osu.edu/aots/