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

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.

References in corpus (2)

• Power-Law Bounds on Transfer Matrices and Quantum Dynamics in One Dimension
• Upper bounds on wavepacket spreading for random Jacobi matrices

Cited by in corpus (8)

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• The Fibonacci Hamiltonian
• Absolutely Continuous Convolutions of Singular Measures and an Application to the Square Fibonacci Hamiltonian
• Quantitative continuity of singular continuous spectral measures and arithmetic criteria for quasiperiodic Schrödinger operators
• Quantum quasiballistic dynamics and thick point spectrum
• Conductance and absolutely continuous spectrum of 1D samples
• Hydrogen atom bound states whose spectral measures have positive upper fractal dimensions
• Almost Ballistic Transport for the Weakly Coupled Fibonacci Hamiltonian