AI 中文总结
研究从各向同性捕获势释放的自由费米气体的膨胀，用半经典技术推导费米子数很大时膨胀云的晚期轮廓，得到任意指数和维度幂律势的表达式，推广了相关定律和分布。
AI 中文摘要
我们考虑一个在任意维度的各向同性捕获势的多体基态中制备的非相互作用费米子系统，并研究势突然释放后费米子云的弹道膨胀。使用半经典技术，我们在费米子数很大的情况下推导了膨胀云的完整晚期轮廓。我们得到了任意指数\(a\)和所有维度\(d\)的幂律势的显式表达式。云的动量分布和空间轮廓呈现出通用边缘指数\(d/a\)，从而推广了维格纳半圆定律和托马斯 - 费米分布。
英文摘要
We consider a system of non-interacting fermions prepared in the many-body ground state of an isotropic trapping potential in any dimension, and investigate the ballistic expansion of the fermionic cloud after the potential is suddenly released. Using semi-classical techniques, we derive the full late-time profile of the expanding cloud in the regime when the fermion number is large. We thus obtain explicit expressions for power-law potentials with arbitrary exponent $a$ and in all dimensions $d$. The momentum distribution and the spatial profile of the cloud exhibit a universal edge exponent $d/a$, thus generalizing the Wigner semi-circle law and the Thomas-Fermi distribution.
Comments28 pages, 7 figures, 55 references
