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

被引:0
作者
Cristina Caraci
Serena Cenatiempo
Benjamin Schlein
机构
[1] University of Zurich,Institute of Mathematics
[2] Gran Sasso Science Institute,undefined
来源
Annales Henri Poincaré | 2023年 / 24卷
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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→∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N \rightarrow \infty $$\end{document}.
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页码:2877 / 2928
页数:51
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