Archive ouverte HAL – Two anyons on the sphere: nonlinear states and spectrum

Alexios P. PolychronakosStéphane Ouvry 1

Alexios P. Polychronakos, Stéphane Ouvry. Two anyons on the sphere: nonlinear states and spectrum. Nucl.Phys.B, 2020, 951, pp.114906. ⟨10.1016/j.nuclphysb.2019.114906⟩. ⟨hal-02340259⟩

We study the energy spectrum of two anyons on the sphere in a constant magnetic field. Making use of rotational invariance we reduce the energy eigenvalue equation to a system of linear differential equations for functions of a single variable, a reduction analogous to separating center of mass and relative coordinates on the plane. We solve these equations by a generalization of the Frobenius method and derive numerical results for the energies of non-analytically derivable states.

  • 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques