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

David Damanik (1) , Andras Süto (2) , Serguei Tcheremchantsev (3)

1 Department of Mathematics 253-37
2 Research Institute for Solid State Physics
3 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans

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.

Mots clés: Schrödinger operators; Quantum dynamics

Domaines: Systèmes dynamiques [math.DS]

David Damanik, Andras Süto, Serguei Tcheremchantsev. Power-law bounds on transfer matrices and quantum dynamics in one dimension–II. Journal of Functional Analysis, 2004, vol 216, pp.362-387. ⟨hal-00080284⟩