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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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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Alva-Sánchez, Héctor
Paredes, Rosario
description 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.
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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
title Localization in Two-Dimensional Quasicrystalline Lattices
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