Asymptotic localization of stationary states in the nonlinear Schroedinger equation

Abstract

The mapping of the Nonlinear Schroedinger Equation with a random potential on the Fokker-Planck equation is used to calculate the localization length of its stationary states. The asymptotic growth rates of the moments of the wave function and its derivative for the linear Schroedinger Equation in a random potential are computed analytically and resummation is used to obtain the corresponding growth rate for the nonlinear Schroedinger equation and the localization length of the stationary states.

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Cited by in corpus (13)

• Direct observation of a localization transition in quasi-periodic photonic lattices
• The crossover from strong to weak chaos for nonlinear waves in disordered systems
• Weak chaos in the disordered nonlinear Schroedinger chain: destruction of Anderson localization by Arnold diffusion
• Perturbation theory for the Nonlinear Schroedinger Equation with a random potential
• Anderson localization of a weakly interacting one dimensional Bose gas
• Coherent propagation of waves in random media with weak nonlinearity
• One Parameter Scaling Theory for Stationary States of Disordered Nonlinear Systems
• Testing the universality of the many-body metal-insulator transition by time evolution of a disordered one-dimensional ultracold fermionic gas
• Lyapunov exponents in 1d disordered system with long-range memory
• Dynamics of wave packets for the nonlinear Schroedinger equation with a random potential
• From power law to Anderson localization in nonlinear Schrödinger equation with nonlinear randomness
• A self-consistent theory of localization in nonlinear random media
• Subdiffusion in classical and quantum nonlinear Schrödinger equations with disorder