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 Schrödinger 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.
- Publication:
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arXiv e-prints
- Pub Date:
- February 2003
- DOI:
- 10.48550/arXiv.math-ph/0302029
- arXiv:
- arXiv:math-ph/0302029
- Bibcode:
- 2003math.ph...2029D
- Keywords:
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- Mathematical Physics
- E-Print:
- 20 pages