Rate of Convergence Towards Hartree Dynamics

被引：64

作者：

Chen, Li ^{[3
]}

Lee, Ji Oon ^{[2
]}

Schlein, Benjamin ^{[1
]}

机构：

[1] Univ Bonn, Inst Appl Math, D-53115 Bonn, Germany

[2] Korea Adv Inst Sci & Technol, Dept Math Sci, Taejon 305701, South Korea

[3] Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China

来源：

JOURNAL OF STATISTICAL PHYSICS | 2011年 / 144卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Many body quantum dynamics; Hartree equation; Mean field limit; CLASSICAL FIELD LIMIT; SCATTERING THEORY; QUANTUM DYNAMICS;

D O I：

10.1007/s10955-011-0283-y

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We consider a system of N bosons interacting through a two-body potential with, possibly, Coulomb-type singularities. We show that the difference between the many-body Schrodinger evolution in the mean-field regime and the effective nonlinear Hartree dynamics is at most of the order 1/N, for any fixed time. The N-dependence of the bound is optimal.

引用

页码：872 / 903

页数：32

共 18 条

[1]

Bardos C., 2000, Methods Appl. Anal., V7, P275

[2] Rate of convergence in nonlinear Hartree dynamics with factorized initial data [J].

Chen, Li ;

Lee, Ji Oon .

JOURNAL OF MATHEMATICAL PHYSICS, 2011, 52 (05)

[3] Mean field dynamics of boson stars [J].

Elgart, Alexander ;

Schlein, Benjamin .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2007, 60 (04) :500-545

[4]

Erdo, 2001, Adv. Theor. Math. Phys., V5, P1169

[5]

ERDOS L, J AM MATH S IN PRESS

[6]

ERDOS L, ANN MATH IN PRESS

[7] Derivation of the cubic non-linear Schrodinger equation from quantum dynamics of many-body systems [J].

Erdos, Laszlo ;

Schlein, Benjamin ;

Yau, Horng-Tzer .

INVENTIONES MATHEMATICAE, 2007, 167 (03) :515-614

[8] Quantum Dynamics with Mean Field Interactions: a New Approach [J].

Erdos, Laszlo ;

Schlein, Benjamin .

JOURNAL OF STATISTICAL PHYSICS, 2009, 134 (5-6) :859-870

[9] CLASSICAL FIELD LIMIT OF SCATTERING THEORY FOR NONRELATIVISTIC MANY-BOSON SYSTEMS .1. [J].

GINIBRE, J ;

VELO, G .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1979, 66 (01) :37-76

[10]

GINIBRE J, 1979, COMMUN MATH PHYS, V68, P45, DOI 10.1007/BF01562541

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