Dynamical Upper Bounds for One-Dimensional Quasicrystals
David Damanik (Caltech)
TL;DR
This paper establishes quantum dynamical upper bounds for one-dimensional Schrödinger operators with Sturmian potentials, extending the understanding of quantum dynamics in quasicrystalline systems under various conditions.
Contribution
It introduces new dynamical bounds for Sturmian potentials using the Killip-Kiselev-Last method, applicable for large coupling, almost every rotation number, and all phases.
Findings
Proves quantum dynamical upper bounds for Sturmian potentials.
Results hold for large coupling constants.
Applicable to almost all rotation numbers and all phases.
Abstract
Following the Killip-Kiselev-Last method, we prove quantum dynamical upper bounds for discrete one-dimensional Schr\"odinger operators with Sturmian potentials. These bounds hold for sufficiently large coupling, almost every rotation number, and every phase.
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Taxonomy
TopicsQuasicrystal Structures and Properties · semigroups and automata theory · Geometric and Algebraic Topology