一维反常扩散和分数自相似的观测
Observation of anomalous diffusion and fractional self-similarity in one dimension
摘要：
实验研究了超冷原子在一维偏振光晶格中的反常扩散。在不同的时间记录原子的空间分布，并分析其动力学和形状。我们发现，云的宽度表现出幂律的时间依赖性与依赖于晶格深度的指数。此外，分布具有分数自相似性，具有相同的特征指数。的自相似形状的分布被发现是很好的拟合的Lévy分布，但与时间的一个不同的特征指数。数值模拟表明，这可能是由于原子的速度和飞行时间之间的相关性。
英文摘要：
We experimentally study anomalous diffusion of ultra-cold atoms in a one dimensional polarization optical lattice. The atomic spatial distribution is recorded at different times and its dynamics and shape are analyzed. We find that the width of the cloud exhibits a power-law time dependence with an exponent that depends on the lattice depth. Moreover, the distribution exhibits fractional self-similarity with the same characteristic exponent. The self-similar shape of the distribution is found to be well-fitted by a Lévy distribution, but with a characteristic exponent that differs from the temporal one. Numerical simulations suggest that this may be due to correlations between the atoms' velocity and flight duration.
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