Absence of ballistic motion and presence of almost-ballistic motion for unitary operators with pure point spectrum
Abstract
We adapt two results of Simon and collaborators to the setting of discrete-time unitary dynamics. We show that pure point spectrum precludes ballistic motion, and exhibit a family of examples showing that this is sharp within the class of extended Cantero--Moral-Vel\'azquez (CMV) matrices: that is, there exist extended CMV matrices exhibiting pure point spectrum together with quantum dynamics as close to ballistic motion as one desires.
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