Quantum Many-Body Fluctuations Around Nonlinear Schrödinger Dynamics

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• 作者：Chiara Boccato ; Serena Cenatiempo ; Benjamin Schlein
• 刊名：Annales Henri Poincaré
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：18
• 期：1
• 页码：113-191
• 全文大小：
• 刊物类别：Physics and Astronomy
• 刊物主题：Theoretical, Mathematical and Computational Physics; Dynamical Systems and Ergodic Theory; Quantum Physics; Mathematical Methods in Physics; Classical and Quantum Gravitation, Relativity Theory; Eleme
• 出版者：Springer International Publishing
• ISSN：1424-0661
• 卷排序：18

文摘

We consider the many-body quantum dynamics of systems of bosons interacting through a two-body potential \({N^{3\beta-1} V (N^\beta x)}\), scaling with the number of particles N. For \({0 < \beta < 1}\), we obtain a norm-approximation of the evolution of an appropriate class of data on the Fock space. To this end, we need to correct the evolution of the condensate described by the one-particle nonlinear Schrödinger equation by means of a fluctuation dynamics, governed by a quadratic generator.