论文标题
GROSS-PITAEVSKII制度中二维bose气体的激发光谱
The excitation spectrum of two dimensional Bose gases in the Gross-Pitaevskii regime
论文作者
论文摘要
我们在二维单位圆环中考虑了$ n $玻色子的系统。我们假设颗粒通过排斥的两体电位相互作用，其散射长度在$ n $中呈指数较小（Gross-Pitaevskii制度）。在这种情况下，我们确定了Bogoliubov理论的预测的有效性，确定了汉密尔顿操作员及其低能激发频谱的基态能量，直到在极限$ n \ to \ iffty $中消失的错误。
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 $N \to \infty$.
