A (p, q)-deformed Landau problem in a spherical harmonic well: Spectrum and noncommuting coordinatesJ. Ben Geloun1, J. Govaerts1, 2 and M. N. Hounkonnou1
1 International Chair of Mathematical Physics and Applications (ICMPA-UNESCO Chair) 072 B.P. 50 Cotonou, Republic of Benin
2 Institute of Theoretical Physics, Department of Physics, University of Stellenbosch Stellenbosch 7600, Republic of South Africa
received 25 June 2007; accepted in final form 7 September 2007; published November 2007
published online 1 October 2007
A (p, q)-deformation of the Landau problem in a spherically symmetric harmonic potential is considered. The quantum spectrum as well as space noncommutativity are established, whether for the full Landau problem or its quantum Hall projections. The well-known noncommutative geometry in each Landau level is recovered in the appropriate limit p, q = 1. However, a novel noncommutative algebra for space coordinates is obtained in the (p, q)-deformed case, which could also be of interest to collective phenomena in condensed-matter systems.
02.40.Gh - Noncommutative geometry.
02.20.-a - Group theory.
02.20.Uw - Quantum groups.
© Europhysics Letters Association 2007