Gibbs measures based on 1d (an)harmonic oscillators as mean-field limits

被引：19
|
作者：
Lewin, Mathieu [1 ,2 ]
Phan Thanh Nam [3 ]
Rougerie, Nicolas [4 ,5 ]
机构：
[1] PSL Res Univ, Univ Paris Dauphine, CNRS, Pl Lattre de Tassigny, F-75016 Paris, France
[2] PSL Res Univ, Univ Paris Dauphine, CEREMADE, Pl Lattre de Tassigny, F-75016 Paris, France
[3] Masaryk Univ, Dept Math & Stat, Kotlarska 2, CS-61137 Brno, Czech Republic
[4] Univ Grenoble 1, BP 166, F-38042 Grenoble, France
[5] CNRS, LPMMC, UMR 5493, BP 166, F-38042 Grenoble, France
来源：
JOURNAL OF MATHEMATICAL PHYSICS | 2018年 / 59卷 / 04期
关键词：
NONLINEAR SCHRODINGER-EQUATION; REDUCED DENSITY-MATRICES; GLOBAL WELL-POSEDNESS; THERMODYNAMIC LIMIT; INVARIANT-MEASURES; QUANTUM GASES; CORRELATION INEQUALITIES; CLASSICAL LIMIT; SYSTEMS;
D O I：
10.1063/1.5026963
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
We prove that Gibbs measures based on 1D defocusing nonlinear Schrodinger functionals with sub-harmonic trapping can be obtained as the mean-field/large temperature limit of the corresponding grand-canonical ensemble for many bosons. The limit measure is supported on Sobolev spaces of negative regularity, and the corresponding density matrices are not trace-class. The general proof strategy is that of a previous paper of ours, but we have to complement it with Hilbert-Schmidt estimates on reduced density matrices. Published by AIP Publishing.
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收藏
页数：17
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