González-García Luis Antonio, Alva-Sánchez Héctor, Paredes Rosario
Instituto de Física, Universidad Nacional Autónoma de México, Apartado Postal 20-364, México D. F. 01000, Mexico.
Entropy (Basel). 2022 Nov 10;24(11):1628. doi: 10.3390/e24111628.
We investigate the emergence of localization in a weakly interacting Bose gas confined in quasicrystalline lattices with three different rotational symmetries: five, eight, and twelve. The analysis, performed at a mean field level and from which localization is detected, relies on the study of two observables: the inverse participation ratio (IPR) and the Shannon entropy in the coordinate space. Those physical quantities were determined from a robust statistical study for the stationary density profiles of the interacting condensate. Localization was identified for each lattice type as a function of the potential depth. Our analysis revealed a range of the potential depths for which the condensate density becomes localized, from partially at random lattice sites to fully in a single site. We found that localization in the case of five-fold rotational symmetry appears for (6ER,9ER), while it occurs in the interval (12ER,15ER) for octagonal and dodecagonal symmetries.
我们研究了限制在具有三种不同旋转对称性（五重、八重和十二重）的准晶格子中的弱相互作用玻色气体中局域化的出现情况。该分析是在平均场水平上进行的，通过研究两个可观测量来检测局域化：逆参与率（IPR）和坐标空间中的香农熵。这些物理量是通过对相互作用凝聚体的稳态密度分布进行稳健的统计研究确定的。针对每种晶格类型，根据势阱深度确定了局域化情况。我们的分析揭示了一系列势阱深度，在此范围内凝聚体密度会发生局域化，从部分随机晶格位点的局域化到完全在单个位点的局域化。我们发现，对于五重旋转对称性，局域化出现在（6ER，9ER）范围内，而对于八边形和十二边形对称性，局域化发生在区间（12ER，15ER）内。
