论文标题
bose气体中的基态能量
Ground state energy of a Bose gas in the Gross-Pitaevskii regime
论文作者
论文摘要
我们回顾了一些严格的稀释玻色气体基态能量的估计。我们从Dyson的上限开始，该上限为硬球提供了正确的领先顺序渐近。之后，我们讨论了Bogoliubov理论的严格版本，该理论最近导致了在Gross-Pitaevskii制度中对基态能量的估计，该粒子通过可集成的电位相互作用。最后，我们解释了如何将这些想法组合起来，以建立一个新的上限，有效至二阶，以实现大球体中的硬球的能量。在这里，我们只绘制主要想法，细节将出现在其他地方。
We review some rigorous estimates for the ground state energy of dilute Bose gases. We start with Dyson's upper bound, which provides the correct leading order asymptotics for hard spheres. Afterwards, we discuss a rigorous version of Bogoliubov theory, which recently led to an estimate for the ground state energy in the Gross-Pitaevskii regime, valid up to second order, for particles interacting through integrable potentials. Finally, we explain how these ideas can be combined to establish a new upper bound, valid to second order, for the energy of hard spheres in the Gross-Pitaeavskii limit. Here we only sketch the main ideas, details will appear elsewhere.
