Scaling Properties of Weak Chaos in Nonlinear Disordered Lattices

Abstract

The Discrete Nonlinear Schroedinger Equation with a random potential in one dimension is studied as a dynamical system. It is characterized by the length, the strength of the random potential and by the field density that determines the effect of nonlinearity. The probability of the system to be regular is established numerically and found to be a scaling function. This property is used to calculate the asymptotic properties of the system in regimes beyond our computational power.

4 pages, 5 figures

References in corpus (8)

• Anderson Transitions
• 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
• The crossover from strong to weak chaos for nonlinear waves in disordered systems
• KAM tori in 1D random discrete nonlinear Schrödinger model?
• Scaling of energy spreading in strongly nonlinear disordered lattices
• Spreading in Disordered Lattices with Different Nonlinearities

Cited by in corpus (30)

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• Strong and weak chaos in weakly nonintegrable many-body Hamiltonian systems
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• Energy Spreading in Strongly Nonlinear Disordered Lattices
• Nonlinear lattice waves in heterogeneous media
• Realization of Discrete Quantum Billiard in 2D Optical Lattices
• Kinetic theory of nonlinear diffusion in a weakly disordered nonlinear Schrödinger chain in the regime of homogeneous chaos
• Quantum chaotic subdiffusion in random potentials
• Effective noise theory for the Nonlinear Schrödinger Equation with disorder
• 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
• Scaling properties of energy spreading in nonlinear Hamiltonian two-dimensional lattices
• Super-exponential diffusion in nonlinear non-Hermitian systems
• Complex Statistics and Diffusion in Nonlinear Disordered Particle Chains
• Do nonlinear waves in random media follow nonlinear diffusion equations?
• Effective protection of quantum coherence by non-Hermitian driving
• Identifying localized and spreading chaos in nonlinear disordered lattices by the Generalized Alignment Index (GALI) method
• Analyzing Chaos in Higher Order Disordered Quartic-Sextic Klein-Gordon Lattices Using $q$-Statistics
• Quantum Gibbs distribution from dynamical thermalization in classical nonlinear lattices
• Quantum subdiffusion with two- and three-body interactions
• Kolmogorov turbulence, Anderson localization and KAM integrability
• Scaling of Chaos in Strongly Nonlinear Lattices
• Spreading of energy in the Ding-Dong Model
• Coupled symplectic maps as models for subdiffusive processes in disordered Hamiltonian lattices
• Spectral description of the dynamics of ultracold interacting bosons in disordered lattices
• Scaling of energy spreading in a disordered Ding-Dong lattice
• Simulating DNLS models
• Decoherence effects in the dynamics of interacting ultracold bosons in disordered lattices
• Nonlinear dynamics and chaos in multidimensional disordered Hamiltonian systems