题 目 ： Non-relativistic limit of the (nonlinear) Dirac equation and its numerical methods
时 间：2017年9月22日上午10:00-11:00
摘 要：Dirac equation, proposed by Paul Dirac in 1928, is a relativistic version of the Schroedinger equation for quantum mechanics. It describes the evolution of spin-1/2 massive particles, e.g. electrons. Due to its applications in graphene and 2D materials, Dirac equations has drawn considerable interests recently.
We consider the (nonlinear) Dirac equation in the non-relativistic limit regime, involving a small parameter inversely proportional to the speed of light. The (nonlinear) Dirac equation converges to the (nonlinear) Schroedinger equation in the non-relativistic limit. By a careful analysis, we obtain a semi-relativistic limit of the nonlinear Dirac equation, which enables a design of uniformly accurate multi-scale numerical method. The major difficulty of the problem is that the solution has a rapid oscillation in time depending on the small parameter.
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宣讲进行时丨吉林大学学习贯彻党...04-02
