Long-Time Anderson Localization for the Nonlinear Schrödinger Equation Revisited
نویسندگان
چکیده
In this paper, we confirm the conjecture of Wang and Zhang (J. Stat. Phys. 134 (5-6): 953--968, 2009) in a long time scale, i.e., displacement wavefront for $1D$ nonlinear random Schroedinger equation is logarithmic order $|t|$.
منابع مشابه
Long Time Anderson Localization for Nonlinear Random Schrödinger Equation
almost surely has pure point spectrum with exponentially localized eigenfunctions. In d ≥ 2, it is known [FS, vDK, AM] that for 0 < ǫ1 ≪ 1 almost surely the spectrum is pure point with exponentially localized eigenfunctions. This is called Anderson localization (A.L.) By the RAGE theorem [AG, E, R] (cf. also [CFKS]) pure point spectrum is equivalent to the following statement: ∀ initial datum {...
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ژورنال
عنوان ژورنال: Journal of Statistical Physics
سال: 2021
ISSN: ['0022-4715', '1572-9613']
DOI: https://doi.org/10.1007/s10955-020-02677-y