标题： 二维中散射长度为无限或零的粒子的三体散射面积 显示英文标题

标题： Three-body scattering area for particles with infinite or zero scattering length in two dimensions

摘要： 我们推导了具有有限范围相互作用且二维散射长度为无限大或零的三个等质量粒子在零能量和零轨道角动量下碰撞时的波函数的渐近展开式，并由此定义了一个三体参数$D$。 $D$的量纲为面积，我们将$D$称为三体散射面积。 我们发现，在零温下具有这些相互作用的稀薄玻色气体每个粒子的基态能量约为$\frac{\hbar^2 D }{6m}\rho^2$，其中$\rho$是玻色子的数密度，$m$是每个玻色子的质量，$\hbar$是普朗克常量除以$2\pi$。 这样的玻色气体在热力学极限下于 $D\geq 0$ 处是稳定的，在谐振子势阱中当粒子数少于 $N_{cr}\approx 3.6413 \sqrt{\frac{\hbar}{m\omega |D|}}$ 时于 $D<0$ 处是亚稳态的，其中 $\omega$ 是谐振子势阱的角频率。 如果两体相互作用支持束缚态，$D$ 通常会获得一个负的虚部，我们找到了这个虚部与成对玻色子产生过程振幅之间的关系。 我们根据 $D$ 的虚部推导出多玻色子系统的三体重组速率常数公式。 显示英文摘要

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 $\frac{\hbar^2 D }{6m}\rho^2$, where $\rho$ is the number density of the bosons, $m$ is the mass of each boson, and $\hbar$ is Planck's constant over $2\pi$. 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 $N_{cr}\approx 3.6413 \sqrt{\frac{\hbar}{m\omega |D|}}$, where $\omega$ 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 $D$.