Dynamics of wave packets for the nonlinear Schroedinger equation with a random potential

Abstract

The dynamics of an initially localized Anderson mode is studied in the framework of the nonlinear Schroedinger equation in the presence of disorder. It is shown that the dynamics can be described in the framework of the Liouville operator. An analytical expression for a wave function of the initial time dynamics is found by a perturbation approach. As follows from a perturbative solution the initially localized wave function remains localized. At asymptotically large times the dynamics can be described qualitatively in the framework of a phenomenological probabilistic approach by means of a probability distribution function. It is shown that the probability distribution function may be governed by the fractional Fokker-Planck equation and corresponds to subdiffusion.

References in corpus (9)

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• Absence of Wavepacket Diffusion in Disordered Nonlinear Systems
• Delocalization of wave packets in disordered nonlinear chains
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Cited by in corpus (6)

• Weak chaos in the disordered nonlinear Schroedinger chain: destruction of Anderson localization by Arnold diffusion
• Nonlinear lattice waves in heterogeneous media
• Subdiffusion in the Nonlinear Schroedinger Equation with Disorder
• Kinetic theory of nonlinear diffusion in a weakly disordered nonlinear Schrödinger chain in the regime of homogeneous chaos
• A self-consistent theory of localization in nonlinear random media
• Subdiffusion in classical and quantum nonlinear Schrödinger equations with disorder