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This analysis reveals an exponential decay rate for ballistic transport in limit-periodic matrices, suggesting new insights into their behavior.
Motivated by Open Problem 17 in Damanik-Fillman's manuscript , we study the decay rate of limit-periodic approximation such that ballistic transport persists in the limit-periodic setting. We show an exponential decay rate, roughly \|J-Jqₙ\|~ e-ηqₙ, is sufficient. This improves on earlier results of Fillman arXiv:1603.01173
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Han et al. (2025) studied this question.
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