Two anyons on the sphere: nonlinear states and spectrum

TL;DR

This paper investigates the energy spectrum of two anyons on a spherical surface under a magnetic field, employing symmetry reduction and advanced mathematical methods to compute energy states, including those not solvable analytically.

Contribution

It introduces a novel approach to analyze two-anyon systems on a sphere using rotational invariance and generalized Frobenius methods for the first time.

Findings

Derived differential equations for the two-anyon system on a sphere.

Numerical results for energy levels, including non-analytical states.

Demonstrated the reduction of the problem to a single-variable differential equation.

Abstract

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.