Multiscale Computational Methods for Semiclassical Schrodinger Equations

半经典薛定谔方程的多尺度计算方法

• 批准号: 1114546
• 负责人: Shi Jin
• 金额: $ 35.26万
• 依托单位: University of Wisconsin-Madison
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-07-01 至 2015-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1114546&HistoricalAwards=false
• 关键词: Multiscale; Computational; Methods; Semiclassical; Schrodinger

The proposer proposes to develop efficient numerical methodsfor several problems in quantum dynamics. Specifically, the followingthree topics are selected: Semiclassical methods for quantumscattering, surface hopping, and Bloch-decomposition based computationalmethods for quantum dynamics in periodic lattice. These are challengingcomputational issues that involve high frequency waves andquantum-classical coupling. Mathematical and computationalmethods can play important roles to enhance our understanding as wellas our ability to simulate these problems.These problems arise in solid state physics, semiconductor devicemodeling, Bose-Eistein Condensations (BEC), solar energy, andfunctional materials such as graphane, thus the developed computationalmethods will have a wide range of applications, some of which ofsignificant national interests. Some of the research results willprovide excellent additions for future graduate courses in appliedmathematics and scientific computing, thus will help toimprove the graduate curriculum in applied mathematics in order tobetter train future graduate students in modern applied mathematics.

提出者建议发展有效的数值方法来解决量子动力学中的几个问题。具体地说，我们选择了以下三个主题：量子散射的半经典方法，表面跳跃和周期晶格中基于布洛赫分解的量子动力学计算方法。这些都是具有挑战性的计算问题，涉及高频波和量子经典耦合。数学和计算方法在提高我们对这些问题的理解和模拟能力方面发挥着重要作用。这些问题出现在固态物理、半导体器件建模、玻色-爱因斯坦凝聚（BEC）、太阳能和功能材料如石墨烷中，因此发展起来的计算方法将有广泛的应用，其中一些具有重大的国家利益。部分研究成果将为今后的应用数学和科学计算研究生课程提供很好的补充，从而有助于完善应用数学研究生课程体系，更好地培养未来的现代应用数学研究生。