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
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
收藏
页码:971 / 1006
页数:36
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