Persistence of Anderson Localization in Schroedinger Operators With Decaying Random Potentials

Abstract

We show persistence of both Anderson and dynamical localization in Schroedinger operations with non-positive (attractive) random decaying potential. We consider an Anderson-type Schroedinger operator with a non-positive ergodic random potential, and multiply the random potential by a decaying envelope function. If the envelope function decays slower than absolute value of x (exp -2) at infinity, we prove that the operator has infinitely many eigen-values below zero. For envelopes decaying as absolute value of x (exp -alpha) at infinity, we determine the number of bound states below a given energy EPSILON < OMICRON, asymptotically as alpha darr OMICRON. To show that bound states located at the bottom of the spectrum are related to the phenomenon of Anderson localization in the corresponding related to the phenomenon of Anderson localization in the corresponding ergodic model, we prove: (a) these states are exponentially localized with a localization length that is uniform in the decay exponent alpha; (b) dynamical localization holds uniformly in alpha.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2006
Accession Number
ADA446215

Entities

People

  • Abel Klein
  • Alexander Figotin
  • Francois Germinet
  • Peter R. Müeller

Organizations

  • University of California, Irvine

Tags

Communities of Interest

  • C4I
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Air Force
  • Continuous Spectra
  • Diseases And Disorders
  • Eigenvalues
  • Eigenvectors
  • Electronic Mail
  • Hilbert Space
  • Inequalities
  • Information Operations
  • Intervals
  • Markov Processes
  • Mathematics
  • Probability
  • Random Variables
  • Spectra
  • Statistics
  • Stochastic Processes

Readers

  • Atmospheric Science / Meteorology, specifically Wind Wave Turbulence.
  • Mathematical Modeling and Probability Theory.
  • Sensor Fusion and Tracking Systems.