The Excitation Spectrum of Two-Dimensional Bose Gases in the Gross-Pitaevskii Regime

被引：8

作者：

Caraci, Cristina ^{[1
]}

Cenatiempo, Serena ^{[2
]}

Schlein, Benjamin ^{[1
]}

机构：

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

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

来源：

ANNALES HENRI POINCARE | 2023年 / 24卷 / 08期

基金：

欧洲研究理事会; 瑞士国家科学基金会;

关键词：

GROUND-STATE ENERGY;

D O I：

10.1007/s00023-023-01278-1

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We consider a system of N bosons, in the two-dimensional unit torus. We assume particles to interact through a repulsive two body potential, with a scattering length that is exponentially small in N (Gross-Pitaevskii regime). In this setting, we establish the validity of the predictions of Bogoliubov theory, determining the ground state energy of the Hamilton operator and its low-energy excitation spectrum, up to errors that vanish in the limit N ? 8.

引用

页码：2877 / 2928

页数：52

共 37 条

[1] Bose-Einstein Condensation Beyond the Gross-Pitaevskii Regime [J].

Adhikari, Arka ;

Brennecke, Christian ;

Schlein, Benjamin .

ANNALES HENRI POINCARE, 2021, 22 (04) :1163-1233

[2] Ground state pressure and energy density of an interacting homogeneous Bose gas in two dimensions [J].

Andersen, JO .

EUROPEAN PHYSICAL JOURNAL B, 2002, 28 (04) :389-396

[3]

[Anonymous], 2003, International Series of Monographs on Physics

[4]

Basti G., 2022, COMMUN MATH PHYS, V5, P89

[5] Quantitative Derivation of the Gross-Pitaevskii Equation [J].

Benedikter, Niels ;

de Oliveira, Gustavo ;

Schlein, Benjamin .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2015, 68 (08) :1399-1482

[6] STUDY OF SUPERFLUID TRANSITION IN 2-DIMENSIONAL HE-4 FILMS [J].

BISHOP, DJ ;

REPPY, JD .

PHYSICAL REVIEW LETTERS, 1978, 40 (26) :1727-1730

[7] The excitation spectrum of Bose gases interacting through singular potentials [J].

Boccato, Chiara ;

Brennecke, Christian ;

Cenatiempo, Serena ;

Schlein, Benjamin .

JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 2020, 22 (07) :2331-2403

[8] Optimal Rate for Bose-Einstein Condensation in the Gross-Pitaevskii Regime [J].

Boccato, Chiara ;

Brennecke, Christian ;

Cenatiempo, Serena ;

Schlein, Benjamin .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2020, 376 (02) :1311-1395

[9] Bogoliubov theory in the Gross-Pitaevskii limit [J].

Boccato, Chiara ;

Brennecke, Christian ;

Cenatiempo, Serena ;

Schlein, Benjamin .

ACTA MATHEMATICA, 2019, 222 (02) :219-335

[10]

Bogolyubov N., 1947, Izv. Akad. Nauk Ser. Fiz., V11, P77

← 1 2 3 4 →