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Dimensional Reduction on a Sphere

Möller, Gunnar, Matveenko, Sergey, Ouvry, Stephane (2006) Dimensional Reduction on a Sphere. International Journal of Modern Physics B, 20 (24). pp. 3533-3546. ISSN 0217-9792. E-ISSN 1793-6578. (doi:10.1142/S0217979206035503) (KAR id:55564)


The question of the dimensional reduction of two-dimensional (2d) quantum models on a sphere to one-dimensional (1d) models on a circle is adressed. A possible application is to look at a relation between the 2d anyon model and the 1d Calogero-Sutherland model, which would allow for a better understanding of the connection between 2d anyon exchange statistics and Haldane exclusion statistics. The latter is realized microscopically in the 2d LLL anyon model and in the 1d Calogero model. In a harmonic well of strength ? or on a circle of radius R – both parameters ? and R have to be viewed as long distance regulators – the Calogero spectrum is discrete. It is well known that by confining the anyon model in a 2d harmonic well and projecting it on a particular basis of the harmonic well eigenstates, one obtains the Calogero-Moser model. It is then natural to consider the anyon model on a sphere of radius R and look for a possible dimensional reduction to the Calogero-Sutherland model on a circle of radius R. First, the free one-body case is considered, where a mapping from the 2d sphere to the 1d chiral circle is established by projection on a special class of spherical harmonics. Second, the N-body interacting anyon model is considered : it happens that the standard anyon model on the sphere is not adequate for dimensional reduction. One is thus lead to define a new spherical anyon-like model deduced from the Aharonov-Bohm problem on the sphere where each flux line pierces the sphere at one point and exits it at its antipode.

Item Type: Article
DOI/Identification number: 10.1142/S0217979206035503
Uncontrolled keywords: Physics of Quantum Materials
Subjects: Q Science > QC Physics > QC20 Mathematical Physics
Divisions: Divisions > Division of Natural Sciences > Physics and Astronomy
Depositing User: Gunnar Moeller
Date Deposited: 05 Dec 2017 14:38 UTC
Last Modified: 16 Nov 2021 10:23 UTC
Resource URI: (The current URI for this page, for reference purposes)

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