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David Damanik, Andras Suto, Serguei Tcheremchantsev
Power-law Bounds on Transfer Matrices and Quantum Dynamics in One Dimension II.
ABSTRACT. We establish quantum dynamical lower bounds for a number of
discrete one-dimensional Schr\"odinger operators. These dynamical
bounds are derived from power-law upper bounds on the norms of
transfer matrices. We develop further the approach from part I and
study many examples. Particular focus is put on models with
finitely or at most countably many exceptional energies for which
one can prove power-law bounds on transfer matrices. The models
discussed in this paper include substitution models, Sturmian
models, a hierarchical model, the prime model, and a class of
moderately sparse potentials.