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On the magnetic Schrödinger hyperbolic equation with randomized coefficients
ZAMM - Journal of Applied Mathematics and Mechanics ( IF 2.3 ) Pub Date : 2021-05-28 , DOI: 10.1002/zamm.202000127
Xiaojun Lu 1
Affiliation  

Magnetic Schrödinger type equations are important physical models in the study of quantum electrodynamics (QED). This manuscript focuses on the regularity behavior of the solution of the stochastic hyperbolic equation influenced by various types of exponentially oscillating coefficients on the principal Hamiltonian operator part. Techniques from harmonic analysis and stochastic analysis are applied to explore the upper bound of loss of regularity. Moreover, appropriate counter-examples with periodic coefficients are constructed to show the lower bound of loss of regularity by the application of instability arguments.

中文翻译:

关于具有随机系数的磁性薛定谔双曲方程

磁性薛定谔型方程是量子电动力学 (QED) 研究中的重要物理模型。本手稿重点研究随机双曲方程解的规律性行为,该方程受主哈密顿算子部分上各种指数振荡系数的影响。应用谐波分析和随机分析的技术来探索规律性损失的上限。此外,构建了具有周期性系数的适当反例,以通过应用不稳定性参数来显示规律性损失的下限。
更新日期:2021-05-28
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