English

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

Mathematical Physics 2014-12-31 v1 math.MP

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.

Keywords

Cite

@article{arxiv.math-ph/0302029,
  title  = {Power-law bounds on transfer matrices and quantum dynamics in one dimension II},
  author = {David Damanik and Andras Suto and Serguei Tcheremchantsev},
  journal= {arXiv preprint arXiv:math-ph/0302029},
  year   = {2014}
}

Comments

20 pages

R2 v1 2026-07-22T16:22:33.504Z