Long Time Anderson Localization for Nonlinear Random Schrödinger Equation
نویسندگان
چکیده
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 {qj(0)} ∈ l , δ > 0, ∃ j0 such that
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