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Local density approximation for the almost-bosonic anyon gas
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0003-3456-5846
Università degli Studi di Roma “La Sapienza”.
CNRS & Université Grenoble Alpes.
2017 (English)In: Analysis & PDE, ISSN 2157-5045, E-ISSN 1948-206X, Vol. 10, no 5, 1169-1200 p.Article in journal (Refereed) Published
Abstract [en]

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).

Place, publisher, year, edition, pages
Mathematical Sciences Publishers , 2017. Vol. 10, no 5, 1169-1200 p.
Keyword [en]
mean-field energy, anyons, fractional statistics, Thomas–Fermi theory, magnetic Schrödinger operator
National Category
Mathematical Analysis
Research subject
Mathematics; Physics
Identifiers
URN: urn:nbn:se:kth:diva-211092DOI: 10.2140/apde.2017.10.1169OAI: oai:DiVA.org:kth-211092DiVA: diva2:1127456
Funder
Swedish Research Council, 2013-4734
Available from: 2017-07-14 Created: 2017-07-14 Last updated: 2017-07-14

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