A Second Order Upper Bound for the Ground State Energy of a Hard-Sphere Gas in the Gross-Pitaevskii Regime

被引：9

作者：

Basti, Giulia ^{[1
]}

Cenatiempo, Serena ^{[1
]}

Olgiati, Alessandro ^{[2
]}

Pasqualetti, Giulio ^{[2
]}

Schlein, Benjamin ^{[2
]}

机构：

[1] Gran Sasso Sci Inst, Viale Francesco Crispi 7, I-67100 Laquila, Italy

[2] Univ Zurich, Inst Math, Winterthurerstr 190, CH-8057 Zurich, Switzerland

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2023年 / 399卷 / 01期

关键词：

MANY-BODY; BOSE; DYNAMICS;

D O I：

10.1007/s00220-022-04547-y

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We prove an upper bound for the ground state energy of a Bose gas consisting of N hard spheres with radius a/N, moving in the three-dimensional unit torus A. Our estimate captures the correct asymptotics of the ground state energy, up to errors that vanish in the limit N-* oo. The proof is based on the construction of an appropriate trial state, given by the product of a Jastrow factor (describing two-particle correlations on short scales) and of a wave function constructed through a (generalized) Bogoliubov transformation, generating orthogonal excitations of the Bose-Einstein condensate and describing correlations on large scales.

引用

页码：1 / 55

页数：55

共 35 条

[31] GROUND STATES OF LARGE BOSONIC SYSTEMS: THE GROSS-PITAEVSKII LIMIT REVISITED [J].