## Mathematical Physics and Operator Algebras

•  Giorgio Young, University of Michigan
•  Ballistic Transport for Limit-periodic Schrödinger Operators in One Dimension
•  11/01/2022
•  11:00 AM - 12:00 PM
•  C304 Wells Hall
•  Jeffrey Hudson Schenker (schenke6@msu.edu)

Abstract: In this talk, I will discuss some results on 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.

## Contact

Department of Mathematics
Michigan State University