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Texas A&M University
Mathematics

Mathematical Physics and Harmonic Analysis Seminar

Date: April 22, 2022

Time: 1:50PM - 2:50PM

Location: BLOC 302

Speaker: Giorgio Young, Rice University

  

Title: Ballistic Transport for Limit-periodic Schrodinger Operators in One Dimension

Abstract: In this talk, we will discuss recent work examining 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.