Localization in disordered, nonlinear dynamical systems
type: Item
instance of: scholarly article
title: Localization in disordered, nonlinear dynamical systems
zbMATH Open document ID: 0629.60105
DOI: 10.1007/BF01127712
author: C. Eugene Wayne
author: Jürg Fröhlich
author: Thomas Spencer
published in: Journal of Statistical Physics
publication date: 1986-01-01T00:00:00Z
review text: We study localization and wave trapping in disordered, nonlinear dynamical systems. For some models of classical, disordered anharmonic crystal lattices, we prove that, with large probability, there are quasiperiodic lattice vibrations of finite total energy which lie on some infinite-dimensional, compact invariant tori in phase space. Such vibrations remain localized, for all times, and there is no transport of energy through the lattice. Our general concepts and techniques extend to other systems, such as disordered, nonlinear Schrödinger equations, or randomly coupled rotors.
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 58J65
Mathematics Subject Classification ID: 81P20
Mathematics Subject Classification ID: 74H50
zbMATH DE Number: 4024478
zbMATH Keywords: disordered system
zbMATH Keywords: localization
zbMATH Keywords: quasiperiodic lattice vibrations
zbMATH Keywords: Schrödinger equations
zbMATH Keywords: randomly coupled rotors
MaRDI profile type: Publication
cites work: Coulomb system equivalent to the energy spectrum of the Calogero-Sutherland-Moser (CSM) model
cites work: Absence of diffusion in the Anderson tight binding model for large disorder or low energy
cites work: Constructive proof of localization in the Anderson tight binding model
cites work: Lagrangian submanifolds and Hamiltonian systems
cites work: AN EXPONENTIAL ESTIMATE OF THE TIME OF STABILITY OF NEARLY-INTEGRABLE HAMILTONIAN SYSTEMS
cites work: Q3657476
cites work: Structure of a quantized vortex in boson systems
cites work: Structure of Nuclear Matter
cites work: Nonlinear dynamics of the infinite classical Heisenberg model: existence proof and classical limit of the corresponding quantum time evolution
full work available at URL: https://doi.org/10.1007/bf01127712
OpenAlex ID: W1990521080
description: scientific article; zbMATH DE number 4024478