On the Ballistic Transport for limit-periodic Jacobi Matrices

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 $\mathrm{\parallel }\mathcal{J}-{\mathcal{J}}_{q_n}\mathrm{\parallel }\sim e^{-\eta q_n}$, is sufficient. This improves on earlier results of Fillman arXiv:1603.01173