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Local density
approximation for the almost-bosonic anyon gas
Michele Correggi, Douglas Lundholm and Nicolas Rougerie |
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Vol. 10 (2017), No. 5, 1169–1200
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Abstract |
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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
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Mathematical Subject Classification 2010
Primary: 35Q40, 81V70, 81S05, 46N50
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Milestones
Received: 3 November 2016
Revised: 3 March 2017
Accepted: 3 April 2017
Published: 1 July 2017
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Authors |
| Michele Correggi | |
| Dipartimento di Matematica “G.
Castelnuovo” Università degli Studi di Roma “La Sapienza” P. le Aldo Moro, 5 00185 Rome Italy |
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| Douglas Lundholm | |
| KTH Royal Institute of
Technology Department of Mathematics SE-100 44 Stockholm Sweden |
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| Nicolas Rougerie | |
| CNRS & Université Grenoble
Alpes LPMMC (UMR 5493) B.P. 166 38042 Grenoble France |
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