Eigenvalue Spacings and Dynamical Upper Bounds for Discrete One-Dimensional Schroedinger Operators

TL;DR

This paper establishes dynamical upper bounds for 1D discrete Schrödinger operators based on eigenvalue spacing properties, and applies these results to analyze the Fibonacci Hamiltonian.

Contribution

It introduces a novel approach linking eigenvalue spacings to dynamical bounds and demonstrates its effectiveness on the Fibonacci Hamiltonian.

Findings

Dynamical upper bounds are derived from eigenvalue spacing properties.

The approach is successfully applied to the Fibonacci Hamiltonian.

Eigenvalue spacing properties can predict dynamical behavior in quantum systems.

Abstract

We prove dynamical upper bounds for discrete one-dimensional Schroedinger operators in terms of various spacing properties of the eigenvalues of finite volume approximations. We demonstrate the applicability of our approach by a study of the Fibonacci Hamiltonian.