UPPER BOUND FOR THE GRAND CANONICAL FREE ENERGY OF THE BOSE GAS IN THE GROSS-PITAEVSKII LIMIT

被引：5

作者：

Boccato, Chiara ^{[1
]}

Deuchert, Andreas ^{[2
]}

Stocker, David ^{[2
]}

机构：

[1] Univ Milan, Inst Math, I-20133 Milan, Italy

[2] Univ Zurich, Inst Math, CH-8057 Zurich, Switzerland

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2024年 / 56卷 / 02期

基金：

瑞士国家科学基金会;

关键词：

mathematical physics; quantum mechanics; quantum statistical mechanics; calculus of variations; GROUND-STATE ENERGY; EINSTEIN CONDENSATION; HARD SPHERES; DILUTE; BOSONS; SYSTEM;

D O I：

10.1137/23M1580930

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a homogeneous Bose gas in the Gross-Pitaevskii limit at temperatures that are comparable to the critical temperature for Bose-Einstein condensation in the ideal gas. Our main result is an upper bound for the grand canonical free energy in terms of two new contributions: (a) The free energy of the interacting condensate is given in terms of an effective theory describing its particle number fluctuations, and (b) the free energy of the thermally excited particles equals that of a temperature-dependent Bogoliubov Hamiltonian.

引用

页码：2611 / 2660

页数：50