Localization in Two-Dimensional Quasicrystalline Lattices

Localization in Two-Dimensional Quasicrystalline Lattices

Blog Article

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 h22a4 transmission 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 swuart 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.