Exact results for the Spectra of Bosons and Fermions with Contact Interaction
arXiv:cond-mat/0609668 · doi:10.1016/j.nuclphysb.2006.11.022
Abstract
An N-body bosonic model with delta-contact interactions projected on the lowest Landau level is considered. For a given number of particles in a given angular momentum sector, any energy level can be obtained exactly by means of diagonalizing a finite matrix: they are roots of algebraic equations. A complete solution of the three-body problem is presented, some general properties of the N-body spectrum are pointed out, and a number of novel exact analytic eigenstates are obtained. The FQHE N-fermion model with Laplacian-delta interactions is also considered along the same lines of analysis. New exact eigenstates are proposed, along with the Slater determinant, whose eigenvalues are shown to be related to Catalan numbers.
arXiv comment16 pages, LaTeX 2e
References in corpus (8)
- Vortex formation in a stirred Bose-Einstein condensate
- Vortices in a Bose-Einstein Condensate
- Stationary states of a rotating Bose-Einstein condensate: routes to vortex nucleation
- Nonequilibrium effects of anisotropic compression applied to vortex lattices in Bose-Einstein condensates
- Equation of State of an Anyon Gas in a Strong Magnetic Field
- Yrast line for weakly interacting trapped bosons
- Exact Eigenstates for Repulsive Bosons in Two Dimensions
- Rotational spectra of weakly interacting Bose-Einstein condensates