报告题目：量子计算中的高阶守恒型数值方法

主讲人：李祥贵教授 （北京信息科技大学）      

时间：2021年4月16日（周五）16:00 p.m.

形式：线上讲座      

主办单位：统计与数学学院

     摘要：In this talk, based on the operator-compensation method, a semi-discrete scheme, which is of any even order accuracy in space, with charge and energy conservation is proposed to solve the nonlinear Dirac equation (NLDE) . Then this semi-discrete scheme can be discretized in time by the second-order accuracy time-midpoint (or Crank-Nicolson) method or the time-splitting method, we therefore obtain two kinds of full discretized numerical methods. For the scheme derived the time-midpoint method, it can be proved to conserve charge and energy in the discrete level, but the other one, it can only be proved to satisfy the charge conservation. These properties of the schemes with any even order accuracy are proved theoretically by a rigorous way in this paper. Some numerical experiments for 1D and/or 2D NLDE are given to test the accuracy order and verify the stability and conservation laws for our schemes. In addition, the binary and ternary collisions for 1D NLDE and the dynamics of 2D NLDE are also discussed. This numerical method can also be extended to solve the nonlinear Schrödinger equation. Then extending the high-order operator-compensation methods can also be shown to keep mass and energy conservation. Some numerical results for BEC are given.

     主讲人简介：    

李祥贵，现任北京信息科技大学教授，北京高校数学教育发展研究中心常务副主任，中国计算数学分会委员。 曾任北京信息科技大学理学院院长、研工部部长兼研究生院副院长。2002年在北京应用物理与计算数学研究所获博士学位，主要从事计算数学研究，已在Numer Math, JCP等国内外高水平学术期刊发表论文数十篇。