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- W2078386091 abstract "We analyze the weak-coupling limit of the random Schrodinger equation with low frequency initial data and a slowly decorrelating random potential. For the probing signal with a sufficiently long wavelength, we prove a homogenization result, that is, the properly compensated wave field admits a deterministic limit in the very low frequency regime. The limit is anomalous in the sense that the solution behaves as $exp(-Dt^{s})$ with $s>1$ rather than the usual~$exp(-Dt)$ homogenized behavior when the random potential is rapidly decorrelating. Unlike in rapidly decorrelating potentials, as we decrease the wavelength of the probing signal, stochasticity appears in the asymptotic limit -- there exists a critical scale depending on the random potential which separates the deterministic and stochastic regimes." @default.
- W2078386091 created "2016-06-24" @default.
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- W2078386091 date "2015-08-06" @default.
- W2078386091 modified "2023-09-26" @default.
- W2078386091 title "The random Schrodinger equation: slowly decorrelating time-dependent potentials" @default.
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- W2078386091 doi "https://doi.org/10.48550/arxiv.1508.01550" @default.
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