Global Well-Posedness of the NLS System for Infinitely Many Fermions

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• 作者：Thomas Chen ; Younghun Hong ; Nataša Pavlović
• 刊名：Archive for Rational Mechanics and Analysis
• 出版年：2017
• 出版时间：April 2017
• 年：2017
• 卷：224
• 期：1
• 页码：91-123
• 全文大小：
• 刊物类别：Physics and Astronomy
• 刊物主题：Classical Mechanics; Physics, general; Theoretical, Mathematical and Computational Physics; Complex Systems; Fluid- and Aerodynamics;
• 出版者：Springer Berlin Heidelberg
• ISSN：1432-0673
• 卷排序：224

文摘

In this paper, we study the mean field quantum fluctuation dynamics for a system of infinitely many fermions with delta pair interactions in the vicinity of an equilibrium solution (the Fermi sea) at zero temperature, in dimensions d = 2, 3, and prove global well-posedness of the corresponding Cauchy problem. Our work extends some of the recent important results obtained by Lewin and Sabin in [33,34], who addressed this problem for more regular pair interactions.