Effective noise theory for the Nonlinear Schrödinger Equation with disorder

Abstract

For the Nonlinear Shrödinger Equation with disorder it was found numerically that in some regime of the parameters Anderson localization is destroyed and subdiffusion takes place for a long time interval. It was argued that the nonlinear term acts as random noise. In the present work the properties of this effective noise are studied numerically. Some assumptions made in earlier work were verified, the dependence of various quantities on the localization length of the linear problem were computed. A scenario for the possible breakdown of the theory for a very long time is outlined.

17 pages, 10 figures

References in corpus (10)

• 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
• The Nonlinear Schroedinger Equation with a random potential: Results and Puzzles
• Superfluidity versus Anderson localization in a dilute Bose gas
• KAM tori in 1D random discrete nonlinear Schrödinger model?
• Anderson localization or nonlinear waves? A matter of probability
• Numerical study of one-dimensional and interacting Bose-Einstein condensates in a random potential

Cited by in corpus (19)

• Flat band states: disorder and nonlinearity
• Nonequilibrium chaos of disordered nonlinear waves
• Nonlinear lattice waves in heterogeneous media
• Characteristics of chaos evolution in one-dimensional disordered nonlinear lattices
• Kinetic theory of nonlinear diffusion in a weakly disordered nonlinear Schrödinger chain in the regime of homogeneous chaos
• On the local nature and scaling of chaos in weakly nonlinear disordered chains
• Super-exponential diffusion in nonlinear non-Hermitian systems
• Do nonlinear waves in random media follow nonlinear diffusion equations?
• Nonlinear Lattice Waves in Random Potentials
• Effective protection of quantum coherence by non-Hermitian driving
• Enhancement of chaotic subdiffusion in disordered ladders with synthetic gauge fields
• Destruction of Anderson localization in quantum nonlinear Schrödinger lattices
• Subdiffusive Lévy flights in quantum nonlinear Schrödinger lattices with algebraic power nonlinearity
• Anderson attractors in active arrays
• Scaling of Chaos in Strongly Nonlinear Lattices
• Numerical integrators for continuous disordered nonlinear Schrödinger equation
• Chaotic behaviour of disordered nonlinear lattices
• Nonlinear dynamics and chaos in multidimensional disordered Hamiltonian systems
• Statistical Properties of the one dimensional Anderson model relevant for the Nonlinear Schrödinger Equation in a random potential