Lieb-Liniger气体的自由膨胀：波函数的渐近形式
Free expansion of a Lieb-Liniger gas: Asymptotic form of the wave functions
摘要：
利用含时态的费米玻色变换和定相近似，导出了描述自由膨胀Lieb-Liniger气体的波函数的渐近形式。我们发现，渐近的波函数接近Tonks-Girardeau（TG）结构，因为它们消失时，任何两个粒子坐标重合。我们指出，这些渐近状态的性质可以显着不同的性质的TG气体在基态的外部潜力。讨论了渐近波函数对初态的依赖性。该分析包括一个大类的初始条件，包括物理上现实的外部电位的Lieb-Liniger气体的基态。它还表明，相互作用能渐近衰减的普遍的幂律与时间，$E_\mathrm{int}\propto t^{-3}$。
英文摘要：
The asymptotic form of the wave functions describing a freely expanding Lieb-Liniger gas is derived by using a Fermi-Bose transformation for time-dependent states, and the stationary phase approximation. We find that asymptotically the wave functions approach the Tonks-Girardeau (TG) structure as they vanish when any two of the particle coordinates coincide. We point out that the properties of these asymptotic states can significantly differ from the properties of a TG gas in a ground state of an external potential. The dependence of the asymptotic wave function on the initial state is discussed. The analysis encompasses a large class of initial conditions, including the ground states of a Lieb-Liniger gas in physically realistic external potentials. It is also demonstrated that the interaction energy asymptotically decays as a universal power law with time, $E_\mathrm{int}\propto t^{-3}$.
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