The Localization Length of Stationary States in the Nonlinear Schreodinger Equation

Abstract

For the nonlinear Schreodinger equation (NLSE), in presence of disorder, exponentially localized stationary states are found. In the present Letter it is demonstrated analytically that the localization length is typically independent of the strength of the nonlinearity and is identical to the one found for the corresponding linear equation. The analysis makes use of the correspondence between the stationary NLSE and the Langevin equation as well as of the resulting Fokker-Planck equation. The calculations are performed for the ``white noise'' random potential and an exact expression for the exponential growth of the eigenstates is obtained analytically. It is argued that the main conclusions are robust.

References in corpus (5)

• Anderson Localization of Expanding Bose-Einstein Condensates in Random Potentials
• Superfluidity versus Anderson localization in a dilute Bose gas
• Expansion of a Bose-Einstein Condensate in the Presence of Disorder
• Compactlike discrete breathers in systems with nonlinear and nonlocal dispersive terms
• Numerical study of one-dimensional and interacting Bose-Einstein condensates in a random potential

Cited by in corpus (15)

• Absence of Wavepacket Diffusion in Disordered Nonlinear Systems
• Weak chaos in the disordered nonlinear Schroedinger chain: destruction of Anderson localization by Arnold diffusion
• Dynamical Thermalization of Disordered Nonlinear Lattices
• Perturbation theory for the Nonlinear Schroedinger Equation with a random potential
• Matter-wave localization in a weakly perturbed optical lattice
• Asymptotic localization of stationary states in the nonlinear Schroedinger equation
• One Parameter Scaling Theory for Stationary States of Disordered Nonlinear Systems
• Nonlinear Lattice Waves in Random Potentials
• Lyapunov exponents in 1d disordered system with long-range memory
• Dynamics of wave packets for the nonlinear Schroedinger equation with a random potential
• A self-consistent theory of localization in nonlinear random media
• From power law to Anderson localization in nonlinear Schrödinger equation with nonlinear randomness
• Subdiffusion in classical and quantum nonlinear Schrödinger equations with disorder
• Soliton Propagation through a Disordered System: Statistics of the Transmission Delay
• Density, phase and coherence properties of a low dimensional Bose-Einstein systems moving in a disordered potential