自由膨胀Lieb-Liniger气体的动量分布
Momentum distribution of a freely expanding Lieb-Liniger gas
摘要：
本文数值研究了几个初始处于无限深硬壁阱基态的Lieb-Liniger玻色子的自由膨胀。采用标准傅里叶变换进行数值计算，如下从费米玻色变换的时间相关的Lieb-Liniger气体。我们研究了动量分布、实空间单粒子密度和自然轨道的占位性的演化。我们的数值计算使我们能够探索这些观测量的行为在瞬态制度的膨胀，在那里他们是非平凡的粒子相互作用的影响。我们推导出解析（通过使用固定相近似）的公式，它连接的渐近形状的动量分布和初始状态。对于足够大的时间，动量分布（直到一个简单的标度变换）与实空间单粒子密度的形状一致（膨胀是渐近弹道的）。我们的分析和数值结果是一致的。
英文摘要：
We numerically study free expansion of a few Lieb-Liniger bosons, which are initially in the ground state of an infinitely deep hard-wall trap. Numerical calculation is carried out by employing a standard Fourier transform, as follows from the Fermi-Bose transformation for a time-dependent Lieb-Liniger gas. We study the evolution of the momentum distribution, the real-space single-particle density, and the occupancies of natural orbitals. Our numerical calculation allows us to explore the behavior of these observables in the transient regime of the expansion, where they are non-trivially affected by the particle interactions. We derive analytically (by using the stationary phase approximation) the formula which connects the asymptotic shape of the momentum distribution and the initial state. For sufficiently large times the momentum distribution coincides (up to a simple scaling transformation) with the shape of the real-space single-particle density (the expansion is asymptotically ballistic). Our analytical and numerical results are in good agreement.
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