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有界域上一维双极量子力学模型解的经典极限
孔海阅1, 黎野平2
1.上海师范大学;2.华东理工大学
摘要:
考虑一维双极等熵量子力学模型.首先,对方程进行一些变形,利用Poincarés不等式及函数收敛和弱收敛的一些性质,得到了稳态解的经典极限,即当普朗克常量ε趋于0时,量子力学模型方程的稳态解趋于经典力学模型方程的稳态解.然后,利用非稳态解已有的一些结论和Sobolev不等式,Schwartz不等式,Gronwall不等式及一些能量估计,得到了非稳态解的经典极限,即量子力学模型方程的光滑解趋于经典力学模型方程的光滑解.
关键词:  双极  量子力学模型  经典极限
DOI:
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基金项目:
The classical limit to a bipolar quantum hydrodynamic model of semiconductors in a bounded domain
KONG Haiyue1, LI Yeping2
1.College of Mathematics and Sciences,Shanghai Normal University;2.College of Mathematics,East China University of Science and Technology
Abstract:
We consider a one-dimensional bipolar isentropic quantum hydrodynamical model from semiconductor devices.First,we discuss the classical limit of the stationary solution.Then we discuss the classical limit of the non-stationary initial boundary problem for a one-dimensional case in a bounded domain.We show that the solutions to the quantum hydrodynamic model of semiconductors approaches that to the hydrodynamic model of semiconductors as the scaled Planck constants ε tends to zero.
Key words:  bipolar  quantum hydrodynamic model  classical limit