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標題Title: ON THE RIGOROUS DERIVATION OF THE 2D CUBIC NONLINEAR SCHRO ̈DINGER EQUATION FROM 3D QUANTUM MANY-BODY DYNAMICS
作者Authors: XUWEN CHEN AND JUSTIN HOLMER
上傳單位Department: 電子工程系
上傳時間Date: 2012-12-8
上傳者Author: 傅俊結
審核單位Department: 電子工程系
審核老師Teacher: 傅俊結
檔案類型Categories: 論文Thesis
關鍵詞Keyword: many-body dynamics,BBGKY,NLS
摘要Abstract: Abstract. We consider the 3D quantum many-body dynamics describing a dilute bose gas with strong confining in one direction. We study the corresponding BBGKY hierarchy which contains a diverging coefficient as the strength of the confining potential tends to ∞. We find that this diverging coefficient is counterbalanced by the limiting structure of the density matrices and establish the convergence of the BBGKY hierarchy. Moreover, we prove that the limit is fully described by a 2D cubic NLS and obtain the exact 3D to 2D coupling constant.

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