A Central Limit Theorem in Many-Body Quantum Dynamics

被引：36

作者：

Ben Arous, Gerard ^{[1
]}

Kirkpatrick, Kay ^{[2
]}

Schlein, Benjamin ^{[3
]}

机构：

[1] NYU, Courant Inst Math, New York, NY 10012 USA

[2] Univ Illinois, Dept Math, Urbana, IL 61801 USA

[3] Inst Appl Math, D-53115 Bonn, Germany

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2013年 / 321卷 / 02期

基金：

美国国家科学基金会;

关键词：

NONLINEAR SCHRODINGER-EQUATION; GROSS-PITAEVSKII EQUATION; CLASSICAL FIELD LIMIT; SCATTERING THEORY; DERIVATION;

D O I：

10.1007/s00220-013-1722-1

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

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.

引用

页码：371 / 417

页数：47

共 32 条

[1]

[Anonymous], 2006, SCI TECH-BEL

[2] The effects of polymer molecular weight on filament thinning and drop breakup in microchannels [J].