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Local density approximation for the almost-bosonic anyon gas

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).
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Dates and versions

hal-01391205 , version 1 (03-11-2016)
hal-01391205 , version 2 (04-03-2017)
hal-01391205 , version 3 (10-04-2017)

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Michele Correggi, Douglas Lundholm, Nicolas Rougerie. Local density approximation for the almost-bosonic anyon gas . 2017. ⟨hal-01391205v2⟩
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