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Title: Weak chaos in the disordered nonlinear Schroedinger chain: Destruction of Anderson localization by Arnold diffusion

Abstract

Research Highlights: > In a one-dimensional disordered chain of oscillators all normal modes are localized. > Nonlinearity leads to chaotic dynamics. > Chaos is concentrated on rare chaotic spots. > Chaotic spots drive energy exchange between oscillators. > Macroscopic transport coefficients are obtained. - Abstract: The subject of this study is the long-time equilibration dynamics of a strongly disordered one-dimensional chain of coupled weakly anharmonic classical oscillators. It is shown that chaos in this system has a very particular spatial structure: it can be viewed as a dilute gas of chaotic spots. Each chaotic spot corresponds to a stochastic pump which drives the Arnold diffusion of the oscillators surrounding it, thus leading to their relaxation and thermalization. The most important mechanism of equilibration at long distances is provided by random migration of the chaotic spots along the chain, which bears analogy with variable-range hopping of electrons in strongly disordered solids. The corresponding macroscopic transport equations are obtained.

Authors:
 [1]
  1. Laboratoire de Physique et Modelisation des Milieux Condenses, Universite de Grenoble 1 and CNRS, BP166, 38042 Grenoble (France)
Publication Date:
OSTI Identifier:
21583308
Resource Type:
Journal Article
Journal Name:
Annals of Physics (New York)
Additional Journal Information:
Journal Volume: 326; Journal Issue: 7; Other Information: DOI: 10.1016/j.aop.2011.02.004; PII: S0003-4916(11)00033-9; Copyright (c) 2011 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Journal ID: ISSN 0003-4916
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CHAOS THEORY; DIFFUSION; ELECTRONS; ENERGY TRANSFER; NONLINEAR PROBLEMS; ONE-DIMENSIONAL CALCULATIONS; OSCILLATORS; RANDOMNESS; RELAXATION; SCHROEDINGER EQUATION; SOLIDS; STOCHASTIC PROCESSES; THERMALIZATION; TRANSPORT THEORY; DIFFERENTIAL EQUATIONS; ELECTRONIC EQUIPMENT; ELEMENTARY PARTICLES; EQUATIONS; EQUIPMENT; FERMIONS; LEPTONS; MATHEMATICS; PARTIAL DIFFERENTIAL EQUATIONS; SLOWING-DOWN; WAVE EQUATIONS

Citation Formats

Basko, D.M., E-mail: denis.basko@grenoble.cnrs.fr. Weak chaos in the disordered nonlinear Schroedinger chain: Destruction of Anderson localization by Arnold diffusion. United States: N. p., 2011. Web. doi:10.1016/j.aop.2011.02.004.
Basko, D.M., E-mail: denis.basko@grenoble.cnrs.fr. Weak chaos in the disordered nonlinear Schroedinger chain: Destruction of Anderson localization by Arnold diffusion. United States. doi:10.1016/j.aop.2011.02.004.
Basko, D.M., E-mail: denis.basko@grenoble.cnrs.fr. Fri . "Weak chaos in the disordered nonlinear Schroedinger chain: Destruction of Anderson localization by Arnold diffusion". United States. doi:10.1016/j.aop.2011.02.004.
@article{osti_21583308,
title = {Weak chaos in the disordered nonlinear Schroedinger chain: Destruction of Anderson localization by Arnold diffusion},
author = {Basko, D.M., E-mail: denis.basko@grenoble.cnrs.fr},
abstractNote = {Research Highlights: > In a one-dimensional disordered chain of oscillators all normal modes are localized. > Nonlinearity leads to chaotic dynamics. > Chaos is concentrated on rare chaotic spots. > Chaotic spots drive energy exchange between oscillators. > Macroscopic transport coefficients are obtained. - Abstract: The subject of this study is the long-time equilibration dynamics of a strongly disordered one-dimensional chain of coupled weakly anharmonic classical oscillators. It is shown that chaos in this system has a very particular spatial structure: it can be viewed as a dilute gas of chaotic spots. Each chaotic spot corresponds to a stochastic pump which drives the Arnold diffusion of the oscillators surrounding it, thus leading to their relaxation and thermalization. The most important mechanism of equilibration at long distances is provided by random migration of the chaotic spots along the chain, which bears analogy with variable-range hopping of electrons in strongly disordered solids. The corresponding macroscopic transport equations are obtained.},
doi = {10.1016/j.aop.2011.02.004},
journal = {Annals of Physics (New York)},
issn = {0003-4916},
number = 7,
volume = 326,
place = {United States},
year = {2011},
month = {7}
}