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- W2153189741 abstract "We study the behavior of solutions to a Schrödinger equation with large, rapidly oscillating, mean zero, random potential with Gaussian distribution. We show that in high dimension d > 𝔪, where 𝔪 is the order of the spatial pseudo-differential operator in the Schrödinger equation (with 𝔪 = 2 for the standard Laplace operator), the solution converges in the L 2 sense uniformly in time over finite intervals to the solution of a deterministic Schrödinger equation as the correlation length ε tends to 0. This generalizes to long times the convergence results obtained for short times and for the heat equation in [2]. The result is based on the decomposition of multiple scattering contributions introduced in [6]. In dimension d < 𝔪, the random solution converges to the solution of a stochastic partial differential equation; see [1, 13]." @default.
- W2153189741 created "2016-06-24" @default.
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- W2153189741 date "2013-12-29" @default.
- W2153189741 modified "2023-10-18" @default.
- W2153189741 title "HOMOGENIZATION OF THE SCHRÖDINGER EQUATION WITH LARGE, RANDOM POTENTIAL" @default.
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- W2153189741 doi "https://doi.org/10.1142/s0219493713500135" @default.
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