Localization in Two-Dimensional Quasicrystalline Lattices

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 o...

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Bibliographic Details
Published in:Entropy (Basel, Switzerland) Switzerland), 2022-11, Vol.24 (11), p.1628
Main Authors: González-García, Luis Antonio, Alva-Sánchez, Héctor, Paredes, Rosario
Format: Article
Language:English
Subjects:
Bose-Einstein condensation
Bose–Einstein condensates
Condensates
Crystal lattices
Density
Energy
Entropy (Information theory)
Gases
Gross–Pitaevskii equation
Lattice sites
Lattices
Localization
localization in quasicrystals
Quasicrystals
Symmetry
Weakly interacting massive particles
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Summary: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.
ISSN:1099-4300
1099-4300
DOI:10.3390/e24111628