报告题目：Hamiltonian Systems with Singular Hamiltonians and Semiclassical Computations of Quantum Tunneling
报告时间：2020年5月27日 10:00-11:00
Singular Hamiltonian systems arise in modeling high frequency or quantum waves through interfaces or barriers, in which the potential functions become discontinuous and the underlying Hamiltonian systems have singular forces, preventing the initial value problems from being well-posed. We first introduce a notion of solutions, by building in wave transmission and reflection mechanism at the barriers, allowing one to go beyond the singular point and defines a well-posed initial value problem consistent with physical laws of refractions. This also naturally induces numerical methods that build in the interface condition into the numerical fluxes.
Such ideas have found applications from partial transmissions, reflections and even diffractions of high frequency waves, semi-classical computation of quantum tunneling through barriers, and surface hopping in which the particles can tunnel through different quantum states due to degeneracy in the eigen-structures of the potential energy surfaces. The methods allow particle simulations, with the computational cost of classical mechanics, to capture certain important quantum phenomena.
金石，现为上海交通大学自然科学研究院院长，数学学院讲席教授。先后获北京大学学士学位，美国亚利桑那大学博士学位，历任美国纽约大学库朗数学研究所博士后，美国佐治亚理工学院助理教授、副教授，美国威斯康星大学（麦迪逊）正教授，数学系系主任，Vilas杰出成就教授，上海交通大学数学系讲席教授、系主任。他同时担任上海应用数学中心联合主任，上海交通大学教育部科学工程计算重点实验室主任与人工智能数学基础中心主任。他曾获得冯康科学计算奖。他是美国数学会（AMS）首批会士，工业与应用数学学会(SIAM)会士，及2018年国际数学家大会邀请报告人。他的研究方向包括动理学理论，双曲型守恒律，高频波计算，量子动力学，不确定量化，粒子系统，计算流体力学等。
