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中央财经大学统计与数学学院双周学术报告会(四)
来源:  点击次数: 次 发布时间:2017-10-20   编辑:统计数学学院

时间:20171025星期1400-1600

地点:学院南路校区,主教405

报告一题目:Recent Progress in Numerical Methods for Many-Body Wigner Quantum Dynamics  

报告人北京大学数学科学学院、邵嗣烘副教授

邵嗣烘先后于2003 年和2009 年毕业于北京大学数学科学院并分别获得理学学士和博士学位。2009 2 月至2010 8 月在香港科技大学的The Joint KAUST-HKUST Micro/Nanofluidics Laboratory从事博士后工作。在美国的北卡罗莱那大学夏洛特分校普林斯顿大学、西班牙的塞维利亚大学以及香港中文大学等知名高校开展访问交流工作当前主要在量子化学和量子物理中的算法、非线性图谱理论及应用、微分方程数值解等领域开展可计算建模、数学分析和算法设计等研究工作。曾获中国计算数学学会优秀青年论文一等奖(2005),北京大学学术类创新奖(2005,2006,2008),北京大学优秀博士学位论文三等奖(2011)以及宝洁教师奖(2015)等。已在领域内主流国际学术期刊上发表20 余篇学术论文。  

摘要:The Wigner function has provided an equivalent and convenient way to render quantum mechanics in phase space. It allows one to express macroscopically measurable quantities, such as currents and heat fluxes, in statistical forms as usually does in classical statistical mechanics, thereby facilitating its applications in nanoelectronics, quantum optics and etc. Distinct from the Schrödinger equation, the most appealing feature of the Wigner equation, which governs the dynamics of the Wigner function, is that it shares many analogies to the classical mechanism and simply reduces to the classical counterpart when the reduced Planck constant vanishes. Despite the theoretical advantages, numerical resolutions for the Wigner equation is notoriously difficult and remains one of the most challenging problems in computational physics, mainly because of the high dimensionality and nonlocal pseudo-differential operator. On one hand, the commonly used finite difference methods fail to capture the highly oscillatory structure accurately. On the other hand, all existing stochastic algorithms, including the affinity-based Wigner Monte Carlo and signed particle Wigner Monte Carlo methods, have been confined to at most 4D phase space. Few results have been reported for higher dimensional simulations. My group has made substantial progress in both aspects. (1) We completed the design and implementation of a highly accurate numerical scheme for the Wigner quantum dynamics in 4D phase space. Our algorithm combines an efficient conservative semi-Lagrangian scheme in the temporal-spatial space with an accurate spectral element method in the momentum space. With it, the Wigner function for a one-dimensional Helium-like system was clearly shown for the first time. (2) We explored the inherent relation between the Wigner equation and a stochastic branching random walk model. With an auxiliary function, we can cast the Wigner equation into a renewal-type integral equation and prove that its solution is equivalent to the first moment of a stochastic branching random walk. In order to realize an efficient, reliable and integrated particle-based scheme to capture complicated quantum features in phase space, we utilized the probabilistic interpretation of the Wigner equation, efficient Monte Carlo strategies and non-parameter density estimation techniques. It should be noted that all proposed numerical schemes fully exploit the mathematical structure of the Wigner equation. Our target is an efficient simulator for analyzing some fundamental issues in many-body quantum mechanics, such as the nuclear quantum effect and dynamical correlation. These results are collected in the following contributions.

 

报告二题目:Testing Symmetry for Multiplicative  Distortion Measurement Errors Data

报告人:中央财经大学统计与数学学院、盖玉洁副教授

摘要:In this paper, we study  how to estimate and test the symmetry of a continuous variable under the multiplicative  distortion measurement errors setting. The unobservable  variable is distorted in a multiplicative fashion by  an  observed confounding variable. Firstly,  two direct plug-in estimation   procedures   are proposed, and  the empirical likelihood based confidence intervals are constructed to test the symmetry of the  unobserved variable. Next,  we propose four test statistics for testing whether an  unobserved variable is   symmetric or not. The asymptotic properties of the proposed estimators and test statistics are investigated. Monte Carlo simulation  experiments are conducted to examine the performance of the proposed estimators and test statistics. These methods are applied to analyze a real dataset  for an illustration.

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