论文标题
二阶阶在GROSS-PITAEVSKII制度中硬球气的基态能
A second order upper bound for the ground state energy of a hard-sphere gas in the Gross-Pitaevskii regime
论文作者
论文摘要
我们证明了由$ n $硬球组成的bose气体的基态能量，其半径为$ \ mathfrak {a}/n $，以三维单位torus $λ$移动。我们的估计捕获了基态能量的正确渐近学，直到在限制$ n \ to \ iftty $中消失的错误。该证明是基于由jastrow因子的乘积（描述短尺度上的两个粒子相关性）和通过（广义的）Bogoliubov转换构建的波函数的乘积给出的，基于适当的试验状态的构建，从而产生了Bose-Eintein冷凝物的正交激发，并在大尺度上描述了相关性。
We prove an upper bound for the ground state energy of a Bose gas consisting of $N$ hard spheres with radius $\mathfrak{a}/N$, moving in the three-dimensional unit torus $Λ$. Our estimate captures the correct asymptotics of the ground state energy, up to errors that vanish in the limit $N \to \infty$. The proof is based on the construction of an appropriate trial state, given by the product of a Jastrow factor (describing two-particle correlations on short scales) and of a wave function constructed through a (generalized) Bogoliubov transformation, generating orthogonal excitations of the Bose-Einstein condensate and describing correlations on large scales.
