Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review Letters

Quantum spectrum of three anyons in an oscillator potential

M. V. N. Murthy, J. Law, M. Brack, R. K. Bhaduri

Published Sep 30, 1991• 75 citations
Publisher

Abstract

The low-lying quantum states of three anyons confined in a harmonic-oscillator well are obtained numerically. The interpolation of these states between the limits of noninteracting bosons to noninteracting fermions in the well is established. Particular attention is paid to the transformation of the fermionic ground state to an excited Bosonic state, and its overlap with Laughlin-Wu-type correlated states.

DOI
10.1103/physrevlett.67.1817

Related papers

Spectrum of three anyons in a harmonic-oscillator potential

M. V. N. Murthy, J. Law, M. Brack +1 more

The Hamiltonian of three anyons in a harmonic-oscillator potential is diagonalized using a set of harmonic-oscillator states, by treating these as bosons or fermions with an appropriate statistical interaction. The interpolation between the bosonic and fermionic limits is established, and the spectrum of the low-lying states is displayed.

Physical review. B, Condensed matter•Feb 15, 1992•9 citations

Analytic wave functions for understanding the spectrum of the three-anyon problem

Siu A. Chin, Chia-Ren Hu

We show that the low-lying spectrum of three noninteracting anyons in a harmonic potential can be qualitatively and quantitatively understood on the basis of a simple set of analytic wave functions. These wave functions are exact in both the boson and fermion limits and satisfy the anyone wave-function phase condition at all intermediate values of the statistical parameter 01. The resulting nonlinear spectrum agrees with those of exact numerical calculations to better than a few parts in a thousand.

Physical Review Letters•Jul 13, 1992•13 citations

Multianyon spectra and wave functions

Chihong Chou

We study a many-body system consisting of $N$ identical anyons in an external harmonic-oscillator potential. A partial set of exact solutions is obtained by using Jacobi coordinates. For completing the full investigation, we employ a perturbative method to compute those spectra, which have not been analytically obtained. Near the boson limit, we point out that the requirement of the boson being hard core is needed for performing the perturbative calculations, and the first-order $N$-anyon ground-state energies are explicitly presented by using a proper regulation procedure. Up to third perturbative order from the fermion limit, the three-anyon ground-state energy corrections are explicitly presented. Finally we compute the first-order three-anyon ground-state wave function near the fermion limit.

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•Oct 15, 1991•62 citations

ASYMPTOTIC ANALYSIS AND SPECTRUM OF THREE ANYONS

Ghanashyam Date, M. Krishna, M. V. N. Murthy

The spectrum of anyons confined in a harmonic oscillator potential shows both linear and nonlinear dependence on the statistical parameter. While the existence of exact linear solutions has 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 a nonlinearly interpolating spectrum. To be specific we analyze the eigenvalue equation in various asymptotic regions for the three-anyon problem.

arXiv:cond-mat/9301021•International Journal of Modern Physics A•Jun 20, 1994•7 citations

Ground state of many anyons in a harmonic potential

R. Chitra, Diptiman Sen

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.

Physical review. B, Condensed matter•Nov 1, 1992•28 citations

Four anyons in a harmonic well

M. Sporre, J. J. M. Verbaarschot, Ismail Zahed A

We construct numerically the spectrum of four anyons in a harmonic potential. As a function of the statistical flux, the anyon spectrum interpolates continuously between bosons and fermions. We show that its generic structure follows from semiclassical arguments. The relation of these results to the spectrum of four anyons in a constant magnetic field is also discussed.

Physical review. B, Condensed matter•Sep 1, 1992•28 citations
The low-lying quantum states of three anyons confined in a harmonic-oscillator well are obtained numerically. The interpolation of these states between the limits of noninteracting bosons to noninteracting fermions in the well is established. Particular attention is paid to the transformation of the fermionic ground state to an excited Bosonic state, and its overlap with Laughlin-Wu-type correlated states.
We show that the low-lying spectrum of three noninteracting anyons in a harmonic potential can be qualitatively and quantitatively understood on the basis of a simple set of analytic wave functions. These wave functions are exact in both the boson and fermion limits and satisfy the anyone wave-function phase condition at all intermediate values of the statistical parameter 01. The resulting nonlinear spectrum agrees with those of exact numerical calculations to better than a few parts in a thousand.
We study a many-body system consisting of NNN identical anyons in an external harmonic-oscillator potential. A partial set of exact solutions is obtained by using Jacobi coordinates. For completing the full investigation, we employ a perturbative method to compute those spectra, which have not been analytically obtained. Near the boson limit, we point out that the requirement of the boson being hard core is needed for performing the perturbative calculations, and the first-order NNN-anyon ground-state energies are explicitly presented by using a proper regulation procedure. Up to third perturbative order from the fermion limit, the three-anyon ground-state energy corrections are explicitly presented. Finally we compute the first-order three-anyon ground-state wave function near the fermion limit.
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.