Averaging Principle for Multiscale Stochastic Fractional Schrodinger Equation

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Averaging Principle for Multiscale Stochastic Fractional Schrodinger Equation

机译：多尺度随机分数施罗德格方程的平均原理

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This paper is devoted to an averaging principle for multiscale stochastic fractional Schrodinger 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 Schrodinger semigroup is not enough to establish averaging principle; in order to overcome this difficulty, we use the vanishing viscosity method.

机译：本文致力于多尺度随机分数施罗德格方程的平均原理。该平均原理可以验证分数量子力学中平均方法的有效性; 确定通过平均方法获得的近似的效用。与随机热方程不同，分数施罗德格半群的平滑效果不足以建立平均原理; 为了克服这种困难，我们使用消失的粘度法。

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《Annales Henri Poincare》 |2020年第5期|共39页
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正文语种 eng
中图分类理论物理学;
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60H15; 70K65; 70K70;

机译：60 e 15;70套装;70公斤;

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1. Averaging Principle for Multiscale Stochastic Fractional Schrodinger Equation [J] . Annales Henri Poincare . 2020,第5期

机译：多尺度随机分数施罗德格方程的平均原理
2. Averaging principle for multiscale stochastic reaction-diffusion-advection equations [J] . Gao Peng Mathematical Methods in the Applied Sciences . 2019,第4期

机译：多尺度随机反应 - 扩散 - 平流 - 平面方程的平均原理
3. An Averaging Principle for Mckean–Vlasov-Type Caputo Fractional Stochastic Differential Equations [J] . Weifeng Wang, Lei Yan, Junhao Hu, Journal of Mathematics . 2021,第a期

机译：McKean-Vlasov型Caputo分数随机微分方程的平均原理
4. Discrete Fractional Solutions of the Radial Equation of the Fractional Schrodinger Equation [C] . Resat Yilmazer, Okkes Ozturk International Conference of Numerical Analysis and Applied Mathematics . 2017

机译：分数施罗德格方程径向方程的离散分数解
5. On absolute continuity for stochastic partial differential equations and an averaging principle for a queueing network. [D] . Watkins, Andrea Cherese. 2010

机译：随机偏微分方程的绝对连续性和排队网络的平均原理。
6. Analytical Solutions for Multi-Time Scale Fractional Stochastic Differential Equations Driven by Fractional Brownian Motion and Their Applications [O] . Xiao-Li Ding, Juan J. Nieto 2018

机译：分数褐色运动及其应用驱动的多时间尺度分数随机微分方程的分析解
7. Stochastic averaging principle for differential equations with non-Lipschitz coefficients driven by fractional Brownian motion [O] . Wu Jiang-lun 2017

机译：分数布朗运动驱动的非Lipschitz系数微分方程的随机平均原理
8. Averaging Principle and Systems of Singularly Perturbed Stochastic DifferentialEquations [R] . Golec, J., Ladde, G. 1990

机译：奇异摄动随机微分方程的平均原理与系统

Averaging Principle for Multiscale Stochastic Fractional Schrodinger Equation

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