We study the minimizers of an energy functional with a self-consistent magnetic field, which describes a quantum gas of almost-bosonic anyons in the average-field approximation. For the homogeneous gas we prove the existence of the thermodynamic limit of the energy at fixed effective statistics parameter, and the independence of such a limit from the shape of the domain. This result is then used in a local density approximation to derive an effective Thomas–Fermi-like model for the trapped anyon gas in the limit of a large effective statistics parameter (i.e., “less-bosonic” anyons).
Local density approximation for the almost-bosonic anyon gas / Correggi, Michele; Lundholm, Douglas; Rougerie, Nicolas. - In: ANALYSIS & PDE. - ISSN 2157-5045. - ELETTRONICO. - 10:5(2017), pp. 1169-1200. [10.2140/apde.2017.10.1169]
Local density approximation for the almost-bosonic anyon gas
CORREGGI, MICHELE;
2017
Abstract
We study the minimizers of an energy functional with a self-consistent magnetic field, which describes a quantum gas of almost-bosonic anyons in the average-field approximation. For the homogeneous gas we prove the existence of the thermodynamic limit of the energy at fixed effective statistics parameter, and the independence of such a limit from the shape of the domain. This result is then used in a local density approximation to derive an effective Thomas–Fermi-like model for the trapped anyon gas in the limit of a large effective statistics parameter (i.e., “less-bosonic” anyons).File | Dimensione | Formato | |
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