Dissertation/Thesis Abstract

Spectral Methods for Hamiltonian Systems and Their Applications
by Zhao, Lewei, Ph.D., Wayne State University, 2019, 81; 13883220
Abstract (Summary)

哈密顿系统是物理里一类很重要的守恒模型有着广泛的应用。本文用谱方法来解哈密顿系统长时间保它的能量守恒和辛结构。我们给出了一类非线性是多项式形式的哈密顿系统的保能量误差估计，并且使用Henon-Heiles系统进行了数值验证。本文介绍了三种有趣的应用：第一是多体问题；第二是外尔定律的逼近；第三是在量子光学系统中模拟耗散动力学。另外我们用非光滑哈密顿系统探讨了该方法的不足，这也是我们下一步的研究方向。

Indexing (document details)
Advisor: Zhang, Zhimin
Commitee: Chow, Paoliu, Li, Hengguang, Wang, Pei-Yong, Petrov, Alexey
School: Wayne State University
Department: Mathematics
School Location: United States -- Michigan
Source: DAI-B 81/3(E), Dissertation Abstracts International
Source Type: DISSERTATION
Subjects: Mathematics, Computational physics, Mechanics
Keywords: Energy error estimation, Hamiltonian systems, N-Body problems, Quantum cooling, Spectral methods, Weyl's law
Publication Number: 13883220
ISBN: 9781088381939
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