二维中具有无穷或零散射长度粒子的三体散射面积
Three-body scattering area for particles with infinite or zero scattering length in two dimensions
AI总结：
本文推导了二维零能碰撞的三体波函数渐近展开，定义了三体散射面积 $D$，并据此求出了稀薄玻色气体的基态能量、稳定性条件以及三体复合速率常数。
摘要：
我们推导了具有等质量、有限程相互作用且二维散射长度为无穷或零的三个粒子在零能量和零轨道角动量下碰撞的波函数渐近展开，由此定义了三体参数 $D$。$D$ 的量纲是长度的平方，我们称 $D$ 为三体散射面积。我们发现具有此类相互作用的零温稀薄玻色气体的每粒子基态能量约为 $\frac{\hbar^2 D }{6m}ρ^2$，其中 $ρ$ 是玻色子的数密度，$m$ 是每个玻色子的质量，$\hbar$ 是普朗克常数除以 $2π$。在热力学极限下，该玻色气体在 $D\geq 0$ 时稳定；在谐振阱中，若玻色子数小于 $N_{cr}\approx 3.6413 \sqrt{\frac{\hbar}{mω|D|}}$，则在 $D<0$ 时亚稳，其中 $ω$ 是谐振阱的角频率。如果两体相互作用支持束缚态，$D$ 通常获得负虚部，我们发现了该虚部与玻色子对产生过程振幅之间的关系。我们推导了多玻色子系统三体复合速率常数用 $D$ 的虚部表示的公式。
英文摘要：
We derive the asymptotic expansions of the wave function of three particles having equal mass with finite-range interactions and infinite or zero two-dimensional scattering length colliding at zero energy and zero orbital angular momentum, from which a three-body parameter $D$ is defined. The dimension of $D$ is length squared, and we call $D$ three-body scattering area. We find that the ground state energy per particle of a zero-temperature dilute Bose gas with these interactions is approximately $\frac{\hbar^2 D }{6m}ρ^2$, where $ρ$ is the number density of the bosons, $m$ is the mass of each boson, and $\hbar$ is Planck's constant over $2π$. Such a Bose gas is stable at $D\geq 0$ in the thermodynamic limit, and metastable at $D<0$ in the harmonic trap if the number of bosons is less than $N_{cr}\approx 3.6413 \sqrt{\frac{\hbar}{mω|D|}}$, where $ω$ is the angular frequency of the harmonic trap. If the two-body interaction supports bound states, $D$ typically acquires a negative imaginary part, and we find the relation between this imaginary part and the amplitudes of the pair-boson production processes. We derive a formula for the three-body recombination rate constant of the many-boson system in terms of the imaginary part of $D$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
