Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2007-05-16
Phys.Rev.E76:056607,2007
Physics
Condensed Matter
Disordered Systems and Neural Networks
Scientific paper
10.1103/PhysRevE.76.056607
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.
Fishman Shmuel
Iomin Alexander
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