Asymptotic localization of stationary states in the nonlinear Schrödinger equation

Shmuel Fishman; Alexander Iomin; Kirone Mallick

doi:10.1103/PhysRevE.78.066605

Asymptotic localization of stationary states in the nonlinear Schrödinger equation

Shmuel Fishman, Alexander Iomin, Kirone Mallick

Research output: Contribution to journal › Article › peer-review

Abstract

The mapping of the nonlinear Schrödinger 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 Schrödinger equation in a random potential are computed analytically, and resummation is used to obtain the corresponding growth rate for the nonlinear Schrödinger equation and the localization length of the stationary states.

Original language	English
Article number	066605
Journal	Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume	78
Issue number	6
DOIs	https://doi.org/10.1103/PhysRevE.78.066605
Publication status	Published - 1 Dec 2008
Externally published	Yes

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title = "Asymptotic localization of stationary states in the nonlinear Schr{\"o}dinger equation",

abstract = "The mapping of the nonlinear Schr{\"o}dinger 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 Schr{\"o}dinger equation in a random potential are computed analytically, and resummation is used to obtain the corresponding growth rate for the nonlinear Schr{\"o}dinger equation and the localization length of the stationary states.",

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AU - Iomin, Alexander

AU - Mallick, Kirone

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N2 - The mapping of the nonlinear Schrödinger 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 Schrödinger equation in a random potential are computed analytically, and resummation is used to obtain the corresponding growth rate for the nonlinear Schrödinger equation and the localization length of the stationary states.

AB - The mapping of the nonlinear Schrödinger 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 Schrödinger equation in a random potential are computed analytically, and resummation is used to obtain the corresponding growth rate for the nonlinear Schrödinger equation and the localization length of the stationary states.

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DO - 10.1103/PhysRevE.78.066605

M3 - Article

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VL - 78

JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

IS - 6

M1 - 066605

ER -

Asymptotic localization of stationary states in the nonlinear Schrödinger equation

Abstract

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