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Localization for random Schroedinger operators with correlated potentials

Journal Article:

Abstract

We prove localization at high disorder or low energy for lattice Schroedinger operators with random potentials whose values at different lattice sites are correlated over large distances. The class of admissible random potentials for our multiscale analysis includes potentials with a stationary Gaussian distribution whose covariance function C(x,y) decays as vertical strokex-yvertical stroke{sup -{theta}}, where {theta}>0 can be arbitrarily small, and potentials whose probability distribution is a completely analytical Gibbs measure. The result for Gaussian potentials depends on a multivariable form of Nelson's best possible hypercontractive estimate. (orig.).
Authors:
Von Dreifus, H; [1]  Klein, A [2] 
  1. Princeton Univ., NJ (USA). Dept. of Physics
  2. California Univ., Irvine (USA). Dept. of Mathematics
Publication Date:
Aug 01, 1991
Product Type:
Journal Article
Reference Number:
DEN-91-006442; EDB-91-113653
Resource Relation:
Journal Name: Communications in Mathematical Physics; (Germany, F.R.); Journal Volume: 140:1
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; SCHROEDINGER EQUATION; RANDOMNESS; CORRELATION FUNCTIONS; CORRELATIONS; GAUSSIAN PROCESSES; HAMILTONIANS; INTERACTION RANGE; LOCALITY; POTENTIALS; PROBABILITY; STOCHASTIC PROCESSES; DIFFERENTIAL EQUATIONS; DISTANCE; EQUATIONS; FUNCTIONS; MATHEMATICAL OPERATORS; PARTIAL DIFFERENTIAL EQUATIONS; QUANTUM OPERATORS; WAVE EQUATIONS; 657002* - Theoretical & Mathematical Physics- Classical & Quantum Mechanics
OSTI ID:
5661728
Country of Origin:
Germany
Language:
English
Other Identifying Numbers:
Journal ID: ISSN 0010-3616; CODEN: CMPHA; Other: CNN: PHY-85-15288; DMS-89-05627
Submitting Site:
DEN
Size:
Pages: 133-147
Announcement Date:

Journal Article:

Citation Formats

Von Dreifus, H, and Klein, A. Localization for random Schroedinger operators with correlated potentials. Germany: N. p., 1991. Web. doi:10.1007/BF02099294.
Von Dreifus, H, & Klein, A. Localization for random Schroedinger operators with correlated potentials. Germany. doi:10.1007/BF02099294.
Von Dreifus, H, and Klein, A. 1991. "Localization for random Schroedinger operators with correlated potentials." Germany. doi:10.1007/BF02099294. https://www.osti.gov/servlets/purl/10.1007/BF02099294.
@misc{etde_5661728,
title = {Localization for random Schroedinger operators with correlated potentials}
author = {Von Dreifus, H, and Klein, A}
abstractNote = {We prove localization at high disorder or low energy for lattice Schroedinger operators with random potentials whose values at different lattice sites are correlated over large distances. The class of admissible random potentials for our multiscale analysis includes potentials with a stationary Gaussian distribution whose covariance function C(x,y) decays as vertical strokex-yvertical stroke{sup -{theta}}, where {theta}>0 can be arbitrarily small, and potentials whose probability distribution is a completely analytical Gibbs measure. The result for Gaussian potentials depends on a multivariable form of Nelson's best possible hypercontractive estimate. (orig.).}
doi = {10.1007/BF02099294}
journal = {Communications in Mathematical Physics; (Germany, F.R.)}
volume = {140:1}
journal type = {AC}
place = {Germany}
year = {1991}
month = {Aug}
}