Limit-Periodic Schrodinger Operators on Z^d: Uniform Localization

2012/07/25 by Damanik, David, Gan, Zheng · 1 citation
#81Q10 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Primary 47B36 #Secondary 47B80 #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1207.5881

Abstract

We exhibit d-dimensional limit-periodic Schrodinger operators that are uniformly localized in the strongest sense possible. That is, for each of these operators, there is a uniform exponential decay rate such that every element of the hull of the corresponding Schrodinger operator has a complete set of eigenvectors that decay exponentially off their centers of localization at least as fast as prescribed by the uniform decay rate. Consequently, these operators exhibit uniform dynamical localization.

Cited by

• Area Law for the entanglement entropy of free fermions in nonrandom ergodic field

Related

• Spectral Properties of Limit-Periodic Schrödinger Operators (PhD Thesis)
• Dynamical localization for polynomial long-range hopping random operators on ℤ^d
• Anderson Localization for Time Periodic Random Schrödinger operators
• Anderson localized states for the quasi-periodic nonlinear Schrödinger equation on \mathbb Z^d
• Localization for Lipschitz monotone quasi-periodic Schrödinger operators on ℤ^d via Rellich functions analysis