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摘要翻译：
结果表明，三个玻色子在小碰撞能下的有效相互作用强度可以从它们在零能下的波函数中提取出来。导出了该波函数在大粒子间距下的渐近展开式，由此定义了三体散射超体积，它是两体散射长度的模拟量。在给定任何有限程相互作用势的情况下，我们可以从Schr\“{o}dinger方程的数值解中预测有效三体力。用这种方法计算了硬球玻色子的常数D$,从而得到了硬球稀玻色-爱因斯坦凝聚体(BEC)中每个粒子的基态能量的完整结果:$\Rho^2$,其中$\Rho$是数密度。在一个尺寸为$L$的有限盒中的三体能量和真空中的三体散射振幅中，也证明了$D$的效应。另一个重要的预测是，在稀BECs中的凝析油馏分中存在有效场理论(EFT)的违反，这是由短程物理引起的。EFT对基态能量和少体散射振幅的预测得到了证实。
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英文标题：
《Three-boson problem at low energy and Implications for dilute
Bose-Einstein condensates》
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作者：
Shina Tan
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最新提交年份：
2007
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分类信息：
一级分类：Physics 物理学
二级分类：Statistical Mechanics 统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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一级分类：Physics 物理学
二级分类：High Energy Physics - Lattice 高能物理-晶格
分类描述：Lattice field theory. Phenomenology from lattice field theory. Algorithms for lattice field theory. Hardware for lattice field theory.
晶格场论。从晶格场论到现象学。格场论的算法。晶格场论硬件。
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一级分类：Physics 物理学
二级分类：Nuclear Theory 核理论
分类描述：Nuclear Theory Theory of nuclear structure covering wide area from models of hadron structure to neutron stars. Nuclear equation of states at different external conditions. Theory of nuclear reactions including heavy-ion reactions at low and high energies. It does not include problems of data analysis, physics of nuclear reactors, problems of safety, reactor construction
核理论涵盖从强子结构模型到中子星等广泛领域的核结构理论。不同外部条件下的核状态方程。核反应理论，包括低能和高能的重离子反应。它不包括数据分析问题、核反应堆物理问题、安全问题、反应堆建设问题
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英文摘要：
It is shown that the effective interaction strength of three bosons at small collision energies can be extracted from their wave function at zero energy. An asymptotic expansion of this wave function at large interparticle distances is derived, from which is defined a quantity $D$ named three-body scattering hypervolume, which is an analog of the two-body scattering length. Given any finite-range interaction potentials, one can thus predict the effective three-body force from a numerical solution of the Schr\"{o}dinger equation. In this way the constant $D$ for hard-sphere bosons is computed, leading to the complete result for the ground state energy per particle of a dilute Bose-Einstein condensate (BEC) of hard spheres to order $\rho^2$, where $\rho$ is the number density. Effects of $D$ are also demonstrated in the three-body energy in a finite box of size $L$, which is expanded to the order $L^{-7}$, and in the three-body scattering amplitude in vacuum. Another key prediction is that there is a violation of the effective field theory (EFT) in the condensate fraction in dilute BECs, caused by short-range physics. EFT predictions for the ground state energy and few-body scattering amplitudes, however, are corroborated.
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PDF链接：
https://arxiv.org/pdf/709.253
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