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.