Statistics of wave interactions in nonlinear disordered systems

Abstract

We study the properties of mode-mode interactions for waves propagating in nonlinear disordered one-dimensional systems. We focus on i) the localization volume of a mode which defines the number of interacting partner modes, ii) the overlap integrals which determine the interaction strength, iii) the average spacing between eigenvalues of interacting modes, which sets a scale for the nonlinearity strength, and iv) resonance probabilities of interacting modes. Our results are discussed in the light of recent studies on spreading of wave packets in disordered nonlinear systems, and are related to the quantum many body problem in a random chain.

7 pages, 7 figures

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• Interactions destroy dynamical localization with strong and weak chaos
• Subdiffusion of nonlinear waves in quasiperiodic potentials
• Kinetic theory of nonlinear diffusion in a weakly disordered nonlinear Schrödinger chain in the regime of homogeneous chaos
• Two interacting particles in a random potential
• Wave interactions in localizing media - a coin with many faces
• Chaotic wave packet spreading in two-dimensional disordered nonlinear lattices
• Nonlinear Lattice Waves in Random Potentials
• Identifying localized and spreading chaos in nonlinear disordered lattices by the Generalized Alignment Index (GALI) method
• Floquet Anderson Localization of Two Interacting Discrete Time Quantum Walks
• Do nonlinear waves in random media follow nonlinear diffusion equations?
• Interaction-induced connectivity of disordered two-particle states
• Decohering localized waves
• Enhancement of chaotic subdiffusion in disordered ladders with synthetic gauge fields
• Anderson attractors in active arrays
• Anomalous localization enhancement in one-dimensional non-Hermitian disordered lattices
• Make Slow Fast -- how to speed up interacting disordered matter
• Nonlinear Topological Edge States: from Dynamic Delocalization to Thermalization
• Transport and localization properties of excitations in one-dimensional lattices with diagonal disordered mosaic modulations
• A general multi-wave quasi-resonance theory for lattice energy diffusion
• Nonlinear dynamics and chaos in multidimensional disordered Hamiltonian systems
• Equilibrium and Non-equilibrium Gross-Pitaevskii Lattice Dynamics: Interactions, Disorder, and Thermalization
• On the symplectic integration of the Klein Gordon lattice model
• Chaotic behaviour of disordered nonlinear lattices