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Averaging Principle for Multiscale Stochastic Fractional Schrödinger Equation

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Abstract

This paper is devoted to an averaging principle for multiscale stochastic fractional Schrödinger equation. This averaging principle can validate the effectiveness of the averaging method in fractional quantum mechanics; it ascertains the utility of the approximation obtained by averaging method. Unlike the stochastic heat equation, the smoothing effect of fractional Schrödinger semigroup is not enough to establish averaging principle; in order to overcome this difficulty, we use the vanishing viscosity method.

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Acknowledgements

I would like to thank the referees and the editor for their careful comments and useful suggestions. I would like to thank the financial support of the China Scholarship Council (No. 201806625036) and the hospitality of CNRS and IMJ, Université Paris Diderot-Paris 7, during my visit from December 2018 to November 2019.

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Authors and Affiliations

  1. School of Mathematics and Statistics, and Center for Mathematics and Interdisciplinary Sciences, Northeast Normal University, Changchun, 130024, People’s Republic of China

    Peng Gao

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  1. Peng Gao
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Correspondence to Peng Gao.

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Communicated by Nader Masmoudi.

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Gao, P. Averaging Principle for Multiscale Stochastic Fractional Schrödinger Equation. Ann. Henri Poincaré 21, 1637–1675 (2020). https://doi.org/10.1007/s00023-020-00895-4

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