Nonlinear waves in disordered chains: probing the limits of chaos and spreading

Abstract

We probe the limits of nonlinear wave spreading in disordered chains which are known to localize linear waves. We particularly extend recent studies on the regimes of strong and weak chaos during subdiffusive spreading of wave packets [EPL {\bf 91}, 30001 (2010)] and consider strong disorder, which favors Anderson localization. We probe the limit of infinite disorder strength and study Fröhlich-Spencer-Wayne models. We find that the assumption of chaotic wave packet dynamics and its impact on spreading is in accord with all studied cases. Spreading appears to be asymptotic, without any observable slowing down. We also consider chains with spatially inhomogeneous nonlinearity which give further support to our findings and conclusions.

11 pages, 7 figures

References in corpus (24)

• Anderson localization of a non-interacting Bose-Einstein condensate
• Direct observation of Anderson localization of matter-waves in a controlled disorder
• Anderson localization and nonlinearity in one dimensional disordered photonic lattices
• Destruction of Anderson localization by a weak nonlinearity
• Universal spreading of wavepackets in disordered nonlinear systems
• High order symplectic integrators for perturbed Hamiltonian systems
• Absence of Wavepacket Diffusion in Disordered Nonlinear Systems
• Delocalization of wave packets in disordered nonlinear chains
• The crossover from strong to weak chaos for nonlinear waves in disordered systems
• Weak chaos in the disordered nonlinear Schroedinger chain: destruction of Anderson localization by Arnold diffusion
• Numerical integration of variational equations
• Spreading of wave packets in disordered systems with tunable nonlinearity
• Spreading of waves in nonlinear disordered media
• Spreading for the generalized nonlinear Schroedinger equation with disorder
• KAM tori in 1D random discrete nonlinear Schrödinger model?
• Statistics of wave interactions in nonlinear disordered systems
• The long-term stability of extrasolar system HD 37124. Numerical study of resonance effects
• Perturbation theory for the Nonlinear Schroedinger Equation with a random potential
• Scaling of energy spreading in strongly nonlinear disordered lattices
• Anderson Localization in a String of Microwave Cavities
• Wave chaos in the non-equilibrium dynamics of the Gross-Pitaevskii equation
• Scaling Properties of Weak Chaos in Nonlinear Disordered Lattices
• Probing Localization in Absorbing Systems via Loschmidt Echos
• Anomalous Thermostat and Intraband Discrete Breathers

Cited by in corpus (39)

• The Nonlinear Schroedinger Equation with a random potential: Results and Puzzles
• Weakly nonergodic dynamics in the Gross--Pitaevskii lattice
• Nonequilibrium chaos of disordered nonlinear waves
• Anderson localization or nonlinear waves? A matter of probability
• Nonlinear lattice waves in heterogeneous media
• Characteristics of chaos evolution in one-dimensional disordered nonlinear lattices
• Interactions destroy dynamical localization with strong and weak chaos
• Subdiffusion of nonlinear waves in quasiperiodic potentials
• Energy transport in one-dimensional disordered granular solids
• Kinetic theory of nonlinear diffusion in a weakly disordered nonlinear Schrödinger chain in the regime of homogeneous chaos
• Non-Reciprocal Geometric Wave Diode by Engineering Asymmetric Shapes of Nonlinear Materials
• Quantum chaotic subdiffusion in random potentials
• High order three part split symplectic integrators: Efficient techniques for the long time simulation of the disordered discrete nonlinear Schroedinger equation
• Chaotic wave packet spreading in two-dimensional disordered nonlinear lattices
• On the local nature and scaling of chaos in weakly nonlinear disordered chains
• Destruction of Anderson localization by nonlinearity in kicked rotator at different effective dimensions
• Computational efficiency of symplectic integration schemes: Application to multidimensional disordered Klein-Gordon lattices
• Complex Statistics and Diffusion in Nonlinear Disordered Particle Chains
• Nonlinear Lattice Waves in Random Potentials
• Dissipative solitons in forced cyclic and symmetric structures
• Identifying localized and spreading chaos in nonlinear disordered lattices by the Generalized Alignment Index (GALI) method
• Do nonlinear waves in random media follow nonlinear diffusion equations?
• Transport, correlations, and chaos in a classical disordered anharmonic chain
• Long-time Anderson Localization for the Nonlinear Schrodinger Equation Revisited
• Analyzing Chaos in Higher Order Disordered Quartic-Sextic Klein-Gordon Lattices Using $q$-Statistics
• Decohering localized waves
• Polydispersed Granular Chains: From Long-lived Chaotic Anderson-like Localization to Energy Equipartition
• Quantum subdiffusion with two- and three-body interactions
• Chaoticity without thermalisation in disordered lattices
• Spreading, Nonergodicity, and Selftrapping: a puzzle of interacting disordered lattice waves
• Subdiffusion in wave packets with periodically kicked interactions
• Coupled symplectic maps as models for subdiffusive processes in disordered Hamiltonian lattices
• Simulating DNLS models
• High Order Three Part Split Symplectic Integration Schemes
• Computational efficiency of numerical integration methods for the tangent dynamics of many-body Hamiltonian systems in one and two spatial dimensions
• Nonlinear dynamics and chaos in multidimensional disordered Hamiltonian systems
• Chaotic behaviour of disordered nonlinear lattices
• Equilibrium and Non-equilibrium Gross-Pitaevskii Lattice Dynamics: Interactions, Disorder, and Thermalization
• Frequency map analysis of spatiotemporal chaos in the nonlinear disordered Klein-Gordon lattice