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- W2922618268 abstract "In this work, we study the semi-classical limit of the Schrodinger equation with random inputs, and show that the semi-classical Schrodinger equation produces $O(varepsilon)$ oscillations in the random variable space. With the Gaussian wave packet transform, the original Schrodinger equation is mapped to an ODE system for the wave packet parameters coupled with a PDE for the quantity $w$ in rescaled variables. Further, we show that the $w$ equation does not produce $varepsilon$ dependent oscillations, and thus it is more amenable for numerical simulations. We propose multi-level sampling strategy in implementing the Gaussian wave packet transform, where in the most costly part, i.e. simulating the $w$ equation, it is sufficient to use $varepsilon$ independent samples. We also provide extensive numerical tests as well as meaningful numerical experiments to justify the properties of the numerical algorithm, and hopefully shed light on possible future directions." @default.
- W2922618268 created "2019-04-01" @default.
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- W2922618268 date "2019-03-15" @default.
- W2922618268 modified "2023-09-23" @default.
- W2922618268 title "Gaussian wave packet transform based numerical scheme for the semi-classical Schrodinger equation with random inputs" @default.
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- W2922618268 doi "https://doi.org/10.48550/arxiv.1903.08740" @default.
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