Spreading of waves in nonlinear disordered media

Abstract

We analyze mechanisms and regimes of wave packet spreading in nonlinear disordered media. We predict that wave packets can spread in two regimes of strong and weak chaos. We discuss resonance probabilities, nonlinear diffusion equations, and predict a dynamical crossover from strong to weak chaos. The crossover is controlled by the ratio of nonlinear frequency shifts and the average eigenvalue spacing of eigenstates of the linear equations within one localization volume. We consider generalized models in higher lattice dimensions and obtain critical values for the nonlinearity power, the dimension, and norm density, which influence possible dynamical outcomes in a qualitative way.

24 pages, 3 figures. arXiv admin note: text overlap with arXiv:0901.4418

References in corpus (6)

• Direct observation of Anderson localization of matter-waves in a controlled disorder
• Destruction of Anderson localization by a weak nonlinearity
• Universal spreading of wavepackets in disordered nonlinear systems
• Anderson Localization of Expanding Bose-Einstein Condensates in Random Potentials
• Absence of Wavepacket Diffusion in Disordered Nonlinear Systems
• Delocalization induced by nonlinearity in systems with disorder

Cited by in corpus (44)

• Weak chaos in the disordered nonlinear Schroedinger chain: destruction of Anderson localization by Arnold diffusion
• The Nonlinear Schroedinger Equation with a random potential: Results and Puzzles
• Spreading of wave packets in disordered systems with tunable nonlinearity
• Nonequilibrium chaos of disordered nonlinear waves
• Nonlinear waves in disordered chains: probing the limits of chaos and spreading
• Strong and weak chaos in weakly nonintegrable many-body Hamiltonian systems
• Anderson localization or nonlinear waves? A matter of probability
• Energy Spreading in Strongly Nonlinear Disordered Lattices
• Statistics of wave interactions in nonlinear disordered systems
• Nonlinear lattice waves in heterogeneous media
• Characteristics of chaos evolution in one-dimensional disordered nonlinear lattices
• Quantum diffusion with disorder, noise and interaction
• 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
• Wave interactions in localizing media - a coin with many faces
• Chaotic wave packet spreading in two-dimensional disordered nonlinear lattices
• Computational efficiency of symplectic integration schemes: Application to multidimensional disordered Klein-Gordon lattices
• Transport of quantum excitations coupled to spatially extended nonlinear many-body systems
• Complex Statistics and Diffusion in Nonlinear Disordered Particle Chains
• Extreme events in two dimensional disordered nonlinear lattices
• Identifying localized and spreading chaos in nonlinear disordered lattices by the Generalized Alignment Index (GALI) method
• Nonlinear Lattice Waves in Random Potentials
• Do nonlinear waves in random media follow nonlinear diffusion equations?
• Transport, correlations, and chaos in a classical disordered anharmonic chain
• Analyzing Chaos in Higher Order Disordered Quartic-Sextic Klein-Gordon Lattices Using $q$-Statistics
• Polydispersed Granular Chains: From Long-lived Chaotic Anderson-like Localization to Energy Equipartition
• Decohering localized waves
• Enhancement of chaotic subdiffusion in disordered ladders with synthetic gauge fields
• Spreading, Nonergodicity, and Selftrapping: a puzzle of interacting disordered lattice waves
• Chaoticity without thermalisation in disordered lattices
• Thermal conductivity of nonlinear waves in disordered chains
• A self-consistent theory of localization in nonlinear random media
• Make Slow Fast -- how to speed up interacting disordered matter
• Spreading of energy in the Ding-Dong Model
• Coupled symplectic maps as models for subdiffusive processes in disordered Hamiltonian lattices
• Logarithmic expansion of many-body wave packets in random potentials
• Landau instability and mobility edges of the interacting one-dimensional Bose gas in weak random potentials
• Large-deviations approach to thermalization: the case of harmonic chains with conservative noise
• Extreme Events in Nonlinear Lattices
• Frequency map analysis of spatiotemporal chaos in the nonlinear disordered Klein-Gordon lattice
• Chaotic behaviour of disordered nonlinear lattices
• Nonlinear dynamics and chaos in multidimensional disordered Hamiltonian systems