论文标题
上限的稀铁球的稀岩气的基态能
Upper bound for the ground state energy of a dilute Bose gas of hard spheres
论文作者
论文摘要
我们认为，在热力学极限中，通过硬球电势与半径$ \ frak {a} $相互作用的玻色子的气体相互作用。我们在低密度下为每个粒子的基态能提供了一个简单的上限。我们的界限捕获了领先的$4πρ\ frak {a} $，并表明更正小于$cρ\ frak {a}（ρ\ frak {a}^3）^3）^{1/2} $，对于足够大的常数$ c> 0 $。结合已知的下限，我们的结果意味着基态能量的第一个子领导术语实际上是$ρ\ frak {a}（ρ\ frak {a}^3）^{1/2} $的顺序，与Lee-huang-yang-yang-yang-yang-yang预测一致。
We consider a gas of bosons interacting through a hard-sphere potential with radius $\frak{a}$ in the thermodynamic limit. We derive a simple upper bound for the ground state energy per particle at low density. Our bound captures the leading term $4πρ\frak{a}$ and shows that corrections are smaller than $C ρ\frak{a} (ρ\frak{a}^3)^{1/2}$, for a sufficiently large constant $C > 0$. In combination with a known lower bound, our result implies that the first sub-leading term to the ground state energy is, in fact, of the order $ρ\frak{a} (ρ\frak{a}^3)^{1/2}$, in agreement with the Lee-Huang-Yang prediction.
