A Central Limit Theorem in Many-Body Quantum Dynamics

被引：0
作者：
Gérard Ben Arous
Kay Kirkpatrick
Benjamin Schlein
机构：
[1] New York University,Courant Institute of Mathematics
[2] University of Illinois at Urbana-Champaign,Department of Mathematics
[3] Institute of Applied Mathematics,undefined
来源：
Communications in Mathematical Physics | 2013年 / 321卷
关键词：
Coherent State; Central Limit Theorem; Annihilation Operator; Kinetic Energy Operator; Hartree Equation;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We study the many body quantum evolution of bosonic systems in the mean field limit. The dynamics is known to be well approximated by the Hartree equation. So far, the available results have the form of a law of large numbers. In this paper we go one step further and we show that the fluctuations around the Hartree evolution satisfy a central limit theorem. Interestingly, the variance of the limiting Gaussian distribution is determined by a time-dependent Bogoliubov transformation describing the dynamics of initial coherent states in a Fock space representation of the system.
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页码：371 / 417
页数：46
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