Power-law bounds on transfer matrices and quantum dynamics in one dimension II

Details Power-law bounds on transfer matrices and quantum dynamics in one dimension II Power-law bounds on transfer matrices and quantum dynamics in one dimension II

2003-02-11

arxiv.org/abs/math-ph/0302029v1

Physics

Mathematical Physics

20 pages

Scientific paper

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.

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