Vol. 10, No. 5, 2017

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Local density approximation for the almost-bosonic anyon gas

Michele Correggi, Douglas Lundholm and Nicolas Rougerie

Vol. 10 (2017), No. 5, 1169–1200
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).

Keywords
mean-field energy, anyons, fractional statistics, Thomas–Fermi theory, magnetic Schrödinger operator
Mathematical Subject Classification 2010
Primary: 35Q40, 81V70, 81S05, 46N50
Milestones
Received: 3 November 2016
Revised: 3 March 2017
Accepted: 3 April 2017
Published: 1 July 2017
Authors
Michele Correggi
Dipartimento di Matematica “G. Castelnuovo”
Università degli Studi di Roma “La Sapienza”
P. le Aldo Moro, 5
00185 Rome
Italy
Douglas Lundholm
KTH Royal Institute of Technology
Department of Mathematics
SE-100 44 Stockholm
Sweden
Nicolas Rougerie
CNRS & Université Grenoble Alpes
LPMMC (UMR 5493)
B.P. 166
38042 Grenoble
France