Asymptotic analysis and spectrum of three anyons

TL;DR

This paper develops a method to analyze the spectrum of three anyons in a harmonic oscillator potential, revealing both linear and nonlinear dependencies on the statistical parameter through asymptotic analysis.

Contribution

It introduces a new approach to interpolate the spectrum nonlinearly by analyzing eigenvalue equations in different asymptotic regions for three anyons.

Findings

Spectrum exhibits both linear and nonlinear dependence on the statistical parameter.

Asymptotic analysis provides insights into the eigenvalue behavior in various regions.

Method suggests potential for more accurate spectrum interpolation.

Abstract

The spectrum of anyons confined in harmonic oscillator potential shows both linear and nonlinear dependence on the statistical parameter. While the existence of exact linear solutions have been shown analytically, the nonlinear dependence has been arrived at by numerical and/or perturbative methods. We develop a method which shows the possibility of nonlinearly interpolating spectrum. To be specific we analyse the eigenvalue equation in various asymptotic regions for the three anyon problem.