半经典极限意义下一维WPFP系统的性质

Some properties of one-dimensional WPFP system under the semi-classical limit

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摘要研究了一类耦合了Poisson方程的非线性量子半导体模型(Wigner-Poisson-Fokker-Planck系统),在半经典极限(0)情况下,证明了一维WPFP系统的质量守恒率、电量呈指数衰减.同时在Husimi变换下导出了电子动能与Husimi动能、电子惯性动量与Husimi惯性动量的关系,最后利用广义Gronwall不等式分别得到了Husimi动能与Husimi惯性动量的估计. The paper studies the Wigner-Poisson-Fokker-Planck（WPFP） system which describes a quantum model of semiconductor device, in presence of a self-consistent potential. The analysis of properties of WPFP equation in one dimension is carried out with the application of aWigner function approach and the semiclassieal limit. The conservation of mass and the decay rate of quantity of electric charge are established. The relationship of electron kinetic energy and Husimi kinetic energy is given. Moreover, some estimates are established.

作者李彬沈洁琼

机构地区四川大学锦城学院数学教研室

出处《西南民族大学学报（自然科学版）》 CAS 2013年第2期186-191,共6页 Journal of Southwest Minzu University(Natural Science Edition)

关键词 Wigner-Poisson-Fokker-Planck Wigner函数法半经典极限 Husimi变换广义Gronwall不等式 Wigner-Poisson-Fokker-Planck Wigner function approach semiclassical limit Husimi transform generalized Gronwall inequality.

分类号 O175 [理学—基础数学]

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西南民族大学学报（自然科学版）

2013年第2期

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半经典极限意义下一维WPFP系统的性质

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