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The Average Field Approximation for Almost Bosonic Extended Anyons
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0003-3456-5846
CNRS & LPMMC Grenoble.
2015 (English)In: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, Vol. 161, 1236-1267 p.Article in journal (Refereed) Published
Abstract [en]

Anyons are 2D or 1D quantum particles with intermediate statistics, interpolating between bosons and fermions. We study the ground state of a large number N of 2D anyons, in a scaling limit where the statistics parameter α is proportional to N−1 when N→∞. This means that the statistics is seen as a “perturbation from the bosonic end”. We model this situation in the magnetic gauge picture by bosons interacting through long-range magnetic potentials. We assume that these effective statistical gauge potentials are generated by magnetic charges carried by each particle, smeared over discs of radius R (extended anyons). Our method allows to take R→0 not too fast at the same time as N→∞. In this limit we rigorously justify the so-called “average field approximation”: the particles behave like independent, identically distributed bosons interacting via a self-consistent magnetic field.

Place, publisher, year, edition, pages
Springer-Verlag New York, 2015. Vol. 161, 1236-1267 p.
Keyword [en]
Anyons, Fractional statistics, Magnetic interaction, Mean-field theory, Quantum de Finetti theorem
National Category
Mathematical Analysis Condensed Matter Physics
Research subject
Mathematics; Physics
Identifiers
URN: urn:nbn:se:kth:diva-176070DOI: 10.1007/s10955-015-1382-yISI: 000365187700009Scopus ID: 2-s2.0-84947027030OAI: oai:DiVA.org:kth-176070DiVA: diva2:865925
Projects
VR 2013-4734:Spectral theory of quantum systems with exotic symmetries
Funder
Swedish Research Council, 67801, 2013-4734Knut and Alice Wallenberg Foundation, KAW 2010.0063
Note

QC 20151218

Available from: 2015-10-29 Created: 2015-10-29 Last updated: 2017-12-01Bibliographically approved

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Lundholm, Douglas

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