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Numerical simulation and theoretical analysis of the quantum transport equation


报告人:卢眺 副教授(北京大学应用物理与技术研究中心&北京大学数学学院)
时间:2015年11月3日(周二)15:00-16:00
地 点:工学院1号楼210会议室
主持人:唐少强 教授

报告简介:

The (semi-) classical Boltzmann/Vlasov equation has become a popular tool in many fields such as semiconductor device simulation and plasma transportation. As the density of the carriers becomes extremely high or the the size of semiconductor devices becomes extremely small, the quantum effects such as, quantum tunneling, will be non-ignorable. As a quantum counterpart of the classical transport equation (the Boltzmann/Vlasov equation), the Wigner transport equation has been attract many researchers. For example, Frensley used it to successfully reproduce the negative differential resistance of resonant tunneling diodes in 1987. In this talk, I will introduce our recent results in numerical simulation and theoretical analysis on the Wigner equation. We have proposed adaptive conservative cell average spectral element methods and globally hyperbolic moment methods for the Wigner equation. However, the numerical convergence and the well-posedness of the stationary Wigner equation with inflow boundary conditions (boundary value problem, BVP) is still an open problem. We have obtained two results on the continuous BVP. First, we proved the solution is symmetric if the potential is symmetric even if the inflow data are non-symmetric (Li et al., SIAM J. Appl. Math., Vol. 74(3), 885-897, 2014). Second, we proposed a semi-discrete version of the Wigner equation and proved that the constructed numerical solution by using the Shannon-Whittaker interpolation formula converges to the solution of the continuous BVP as the velocity mesh size goes to zero.


报告人介绍:

卢朓老师1999年和2004年在北京大学数学科学学院分别取得学士和博士学位,后赴美国北卡莱罗纳大学夏洛特分校从事博士后研究工作,现为北京大学数学科学学院副教授,北京市计算数学学会常务理事。他的研究领域包括1.用间断有限元方法求解色散媒质中的Maxwell方程;2.纳米双栅金属氧化物场效应晶体管的数值模拟;3.用密度泛函理论中的密度矩阵最小化方法求电子结构的基态能量;4.经典和量子输运方程的数值方法。

版权所有: 北京大学应用物理与技术研究中心

地址: 中国 北京 北京大学工学院1号楼402室 邮编:100871 电话:010-62753944 Email:zhoulixin@pku.edu.cn