BIMSA >
YMSC-BIMSA Applied and Computational Mathematics Seminar
Convergence of the Planewave Approximations for Quantum Incommensurate Systems
Convergence of the Planewave Approximations for Quantum Incommensurate Systems
Organizer
Speaker
Huajie Chen
Time
Thursday, April 7, 2022 10:00 AM - 11:30 AM
Online
Tencent 836 6547 4971
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Abstract
We study the numerical approximations of the spectrum distribution of Schrodinger operators for incommensurate systems. We provide rigorous analysis to characterize the quantitative of interests, i.e. the density of states, and develop numerical methods to approximate them based on planewave discretizations. In particular, we (i) justify the thermodynamic limit of the density of states in the real space formulation; (ii) propose a planewave approximation for the problem with some novel energy cutoffs specified for incommensurate systems, and provide a convergence analysis and error estimates with respect to the cutoffs; (iii) design an efficient algorithm to evaluate the density of states by sampling the reciprocal space. We present numerical simulations of some typical incommensurate systems to support the reliability and efficiency of our numerical algorithms.
Speaker Intro
陈华杰，教授。2005年7月本科毕业于北京师范大学数学科学学院；2010年7月博士毕业于中国科学院数学与系统科学研究院计算数学与科学工程计算研究所；从2010年11月至2016年7月分别在德国柏林工业大学、德国慕尼黑工业大学、英国华威大学做博士后。一直从事量子化学计算中数学问题的研究，包括数学模型的建立和分析，数值算法的设计、分析和实现。