论文标题
二维玻色气的基态能
The Ground State Energy of a Two-Dimensional Bose Gas
论文作者
论文摘要
我们证明了以下公式，用于稀有bose气体的基态能量密度，密度$ρ$ $ 2 $ 2 $尺寸在热力学极限\ begin \ begin {align*} e^{\ rm {2d}}}}}}（ρ）=4πρ^2 y \ left（1 - y \ vert y \ y y \ y \ y \ y \ welet + wewt（2 2 y） \ frac {1} {2} + \ log（π）\ right）y \ right） + o（ρ^2 y^{2}）。 \ end {align*}这里$ y = | \ log（ρa^2）|^{ - 1} $和$ a $是两体电位的散射长度。 $ 2 $尺寸的结果与$ 3 $尺寸相对应。该证明对于具有有限散射长度的所有正面潜力是有效的，特别是它涵盖了硬核能的关键情况。
We prove the following formula for the ground state energy density of a dilute Bose gas with density $ρ$ in $2$ dimensions in the thermodynamic limit \begin{align*} e^{\rm{2D}}(ρ) = 4πρ^2 Y\left(1 - Y \vert \log Y \vert + \left( 2Γ+ \frac{1}{2} + \log(π) \right) Y \right) + o(ρ^2 Y^{2}). \end{align*} Here $Y= |\log(ρa^2)|^{-1}$ and $a$ is the scattering length of the two-body potential. This result in $2$ dimensions corresponds to the famous Lee-Huang-Yang formula in $3$ dimensions. The proof is valid for essentially all positive potentials with finite scattering length, in particular it covers the crucial case of the hard core potential.
