Absence of ballistic motion and presence of almost-ballistic motion for unitary operators with pure point spectrum

Christopher Cedzich; Jake Fillman; Luis Velázquez

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arXiv · 2603.03114

Absence of ballistic motion and presence of almost-ballistic motion for unitary operators with pure point spectrum

Christopher Cedzich·Jake Fillman·Luis Velázquez

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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\'{a}zquez (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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BibTeX RIS

Christopher Cedzich, Jake Fillman, Luis Velázquez. 2026-03-03. Absence of ballistic motion and presence of almost-ballistic motion for unitary operators with pure point spectrum. https://arxiv.org/abs/2603.03114

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