Derivation of the cubic non-linear Schrodinger equation from quantum dynamics of many-body systems

• 成果类型: Article
• 署名作者: Erdos, Laszlo; Schlein, Benjamin; Yau, Horng-Tzer
• 署名单位: University of Munich; Harvard University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-006-0022-1
• 发表日期: 2007
• 页码: 515-614
• 关键词: field limit

摘要

We prove rigorously that the one-particle density matrix of three dimensional interacting Bose systems with a short-scale repulsive pair interaction converges to the solution of the cubic non-linear Schrodinger equation in a suitable scaling limit. The result is extended to k-particle density matrices for all positive integer k.