Subdiffusion in the Nonlinear Schroedinger Equation with Disorder

Abstract

The nonlinear Schroedinger equation in the presence of disorder is considered. The dynamics of an initially localized wave packet is studied. A subdiffusive spreading of the wave packet is explained in the framework of a continuous time random walk. A probabilistic description of subdiffusion is suggested and a transport exponent of subdiffusion is obtained to be 2/5.

References in corpus (8)

• 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
• Delocalization of wave packets in disordered nonlinear chains
• Expansion of a Bose-Einstein Condensate in the Presence of Disorder
• Numerical study of one-dimensional and interacting Bose-Einstein condensates in a random potential
• Dynamics of wave packets for the nonlinear Schroedinger equation with a random potential

Cited by in corpus (16)

• Observation of subdiffusion of a disordered interacting system
• Weak chaos in the disordered nonlinear Schroedinger chain: destruction of Anderson localization by Arnold diffusion
• Nonlinear lattice waves in heterogeneous media
• Kinetic theory of nonlinear diffusion in a weakly disordered nonlinear Schrödinger chain in the regime of homogeneous chaos
• Chaotic wave packet spreading in two-dimensional disordered nonlinear lattices
• A topological approximation of the nonlinear Anderson model
• A mixed SOC-turbulence model for nonlocal transport and Levy-fractional Fokker-Planck equation
• Fractional Schrödinger equation in gravitational optics
• A self-consistent model of the plasma staircase and nonlinear Schrödinger equation with subquadratic power nonlinearity
• Control of anomalous diffusion of a Bose polaron
• Unidirectional transport of wave packets through tilted discrete breathers in nonlinear lattices with asymmetric defects
• Modeling the transport of interacting matter-waves in disorder by a non-linear diffusion equation
• Destruction of Anderson localization in quantum nonlinear Schrödinger lattices
• Subdiffusive Lévy flights in quantum nonlinear Schrödinger lattices with algebraic power nonlinearity
• A self-consistent theory of localization in nonlinear random media
• Subdiffusion in classical and quantum nonlinear Schrödinger equations with disorder