标题： 二维玻色气体在Gross-Pitaevskii区域的激发谱 显示英文标题

标题： The excitation spectrum of two dimensional Bose gases in the Gross-Pitaevskii regime

摘要： 我们考虑一个二维单位环面上的$N$个玻色子系统。 我们假设粒子通过排斥性的两体势相互作用，其散射长度在$N$中呈指数小（Gross-Pitaevskii 理论）。 在这种情况下，我们确定了哈密顿算符的基态能量及其低能激发谱，误差在$N \to \infty$极限下消失。 显示英文摘要

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 $N \to \infty$.