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Journal of Physics A Mathematical and General

On a class of noninterpolating solutions of the many-anyon problem

M. V. N. Murthy, J. Law, R. K. Bhaduri, Ghanashyam Date

Published Dec 7, 1992• 15 citations
Publisher

Abstract

In the many-anyon problem in two space dimensions, irregular but square integrable solutions of the Schrodinger equation may exist. A class of such solutions is constructed for anyons confined in a harmonic oscillator. It is shown that these may have lower energies than the usual regular solutions, but they do not exist throughout the range between the bosonic and fermionic limits, and as such do not interpolate continuously.

DOI
10.1088/0305-4470/25/23/013

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In the many-anyon problem in two space dimensions, irregular but square integrable solutions of the Schrodinger equation may exist. A class of such solutions is constructed for anyons confined in a harmonic oscillator. It is shown that these may have lower energies than the usual regular solutions, but they do not exist throughout the range between the bosonic and fermionic limits, and as such do not interpolate continuously.
The ground-state energy and wave function of many anyons in a harmonic oscillator potential is studied using perturbation theory from the fermionic and bosonic ends. As the number of anyons increases to infinity, the ground-state energy scales with the power 3/2. As the statistics parameter changes, there are repeated level crossings between states having different angular momenta. Hence the ground state is only piecewise continuous, and the number of pieces increases with the number of anyons. This is to be contrasted with the problem of interpolating statistics in one dimension where there are no level crossings in the ground state for any number of particles.