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.

引用

页数：17

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