Fokker-Planck equation for transport of wave packets in nonlinear disordered media

Abstract

Starting from first principles, we formulate a theory of wave packet propagation in a nonlinear, disordered medium of any dimension, through the derivation of a Fokker-Planck transport equation. Our theory is based on a diagrammatic expansion of the wave packet's density, and is supported by a heuristic picture that involves a Boltzmann equation with an effective, external potential. Our approach also confirms results obtained in previous work for two-dimensional, nonlinear disordered media.

15 pages, 3 figures

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Cited by in corpus (14)

• Nonlinear lattice waves in heterogeneous media
• Quantum diffusion with disorder, noise and interaction
• Thermalization of matter waves in speckle potentials
• Inelastic Multiple Scattering of Interacting Bosons in Weak Random Potentials
• Quantum boomerang effect for interacting particles
• Quench dynamics of a weakly interacting disordered Bose gas in momentum space
• Identifying localized and spreading chaos in nonlinear disordered lattices by the Generalized Alignment Index (GALI) method
• Do nonlinear waves in random media follow nonlinear diffusion equations?
• Effective theory for the propagation of a wave-packet in a disordered and nonlinear medium
• Microscopic scattering theory for interacting bosons in weak random potentials
• Modeling the transport of interacting matter-waves in disorder by a non-linear diffusion equation
• Kinetics of the disordered Bose gas with collisions
• A self-consistent theory of localization in nonlinear random media
• From inverse-cascade to sub-diffusive dynamic scaling in driven disordered Bose fluids