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- W2963890147 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) 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.
- W2963890147 created "2019-07-30" @default.
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- W2963890147 date "2017-01-01" @default.
- W2963890147 modified "2023-09-24" @default.
- W2963890147 title "The random Schrödinger equation: Slowly decorrelating time-dependent potentials" @default.
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- W2963890147 doi "https://doi.org/10.4310/cms.2017.v15.n2.a4" @default.
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