Mean field dynamics of a quantum tracer particle interacting with a boson gas

被引：5

作者：

Chen, Thomas ^{[1
]}

Soffer, Avy ^{[2
,3
]}

机构：

[1] Univ Texas Austin, Dept Math, Austin, TX 78712 USA

[2] Rutgers State Univ, Dept Math, Piscataway, NJ 08854 USA

[3] Cent China Normal Univ, Dept Math & Appl Math, Wuhan, Hubei, Peoples R China

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2019年 / 276卷 / 03期

基金：

美国国家科学基金会;

关键词：

Bose gas; Mean field limit; Tracer particle; Well-posedness; NONLINEAR SCHRODINGER-EQUATION; GROSS-PITAEVSKII HIERARCHY; CLASSICAL-LIMIT; PAIR EXCITATIONS; DERIVATION; UNIQUENESS; STATES; APPROXIMATION; EXISTENCE;

D O I：

10.1016/j.jfa.2018.10.019

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the dynamics of a heavy quantum tracer particle coupled to a non-relativistic boson field in R-3. The pair interactions of the bosons are of mean-field type, with coupling strength proportional to 1/N, where N is the expected particle number. Assuming that the mass of the tracer particle is proportional to N, we derive generalized Hartree equations in the limit N -> infinity. Moreover, we prove the global well-posedness of the associated Cauchy problem for sufficiently weak interaction potentials. (C) 2018 Elsevier Inc. All rights reserved.

引用

页码：971 / 1006

页数：36

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