Dimensional reduction on a sphere

Details Dimensional reduction on a sphere Dimensional reduction on a sphere

2005-09-22

arxiv.org/abs/cond-mat/0509580v1

Int. J. Mod. Phys. B 20 (2006) 3533

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

10 pages, 1 figure

Scientific paper

10.1142/S0217979206035503

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 \omega or on a circle of radius R - both parameters \omega 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 the same radius. 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.

Affiliated with

Also associated with

No associations

Rating

Dimensional reduction on a sphere does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Dimensional reduction on a sphere, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Dimensional reduction on a sphere will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-504903