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arxiv: math-ph/0302029 · v1 · pith:EOG6E4ZZnew · submitted 2003-02-11 · 🧮 math-ph · math.MP

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

classification 🧮 math-ph math.MP
keywords boundsmodelsmatricespower-lawtransferdynamicalmanymodel
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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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