多粒子量子系统中的Levy分布
Levy distribution in many-particle quantum systems
摘要：
Levy分布，以前用来描述经典系统的复杂行为，表现出的特点，量子多体系统。使用两种互补的方法，正则和巨正则形式主义，我们发现，Tonks-Girardeau气体的动量分布，-一维气体的$N$不可穿透（硬核）玻色子，谐波限制在有限温度下的晶格，服从Levy分布。最后，我们将我们的分析扩展到不同的限制设置，并证明了可调Levy分布正确地再现了实验可访问区域的动量分布。我们的发现允许复杂的多体量子态的校准，通过使用一个独特的标度指数。
英文摘要：
Levy distribution, previously used to describe complex behavior of classical systems, is shown to characterize that of quantum many-body systems. Using two complimentary approaches, the canonical and grand-canonical formalisms, we discovered that the momentum profile of a Tonks-Girardeau gas, -- a one-dimensional gas of $N$ impenetrable (hard-core) bosons, harmonically confined on a lattice at finite temperatures, obeys Levy distribution. Finally, we extend our analysis to different confinement setups and demonstrate that the tunable Levy distribution properly reproduces momentum profiles in experimentally accessible regions. Our finding allows for calibration of complex many-body quantum states by using a unique scaling exponent.
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