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

International Journal of Modern Physics B

MEAN FIELD APPROXIMATION FOR ANYONS IN A MAGNETIC FIELD

E. Westerberg

Published May 15, 1993• 7 citations
Publisher

Abstract

The mean field equations for anyons in an external homogeneous magnetic field are studied and two classes of mean field solutions are explicitly constructed. The first class of solutions, corresponding to one filled Landau level in the combined external and smeared out statistical magnetic fields, is compared to the corresponding exact groundstate solutions. The energies are found to agree well at low densities and when the statistical field is not too strong compared to the background field. At high densities the fermi pressure increases the mean field energy indefinitely. The mean field solutions also miss the lower part of the energy spectrum. To the second class of mean field solutions no corresponding anyon state is known. These solutions represent the anyonic continuation of the fermi state with two filled Landau levels.

DOI
10.1142/s0217979293002833

Related papers

ANYONS IN A MAGNETIC FIELD

A. Karlhede, E. Westerberg

We consider N anyons, with statistical parameter ν, in a homogeneous magnetic fieldand discuss exact and perturbative solutions. We show that the energy, E(ν), obeys[Formula: see text] for any bose or fermi state and that the extremal cases correspondto the states where the relative angular momenta of all pairs of particles are negativeand non-negative, respectively. The anyonic continuations of these extremal states aregiven, their energy is linear in ν. We conjecture that the above bounds on [Formula: see text] hold forany ν. This implies that the energy of any many-anyon state decreases monotonicallywith the statistical parameter ν (ν taking any real value). For small enough ν, E=const. [Formula: see text] and the wave function is known. Increasing ν, the wave functionbecomes singular at some bose point. In the following intermediate region (which maybe absent), E(ν) decreases more slowly; the exact form of E(ν) and the wave functionare unknown. Increasing ν further, above some bose point the energy becomes constantand the wave function is again known.

International Journal of Modern Physics B•May 20, 1992•10 citations

Equation of state of an anyon gas in a strong magnetic field

Alain Dasnières de Veigy, Stéphane Ouvry

The statistical mechanics of an anyon gas in a magnetic field is addressed. A harmonic regulator is used to define a proper thermodynamic limit. When the magnetic field is sufficiently strong, only exact N-anyon ground states, where anyons occupy the lowest Landau level, contribute to the equation of state. Particular attention is paid to the interval of definition of the statistical parameter \ensuremath{\alpha}\ensuremath{\in}[-1,0] where a gap exists. Interestingly enough, one finds that at the critical filling \ensuremath{\nu}=-1/\ensuremath{\alpha} where the pressure diverges, the external magnetic field is entirely screened by the flux tubes carried by the anyons.

arXiv:hep-th/9306039•Physical Review Letters•Jan 31, 1994•152 citations

ANYONS IN A MAGNETIC FIELD: LANDAU LEVELS AND VERTEX OPERATOR REPRESENTATION

Gerald V. Dunne, Alberto Lerda A, Carlo A. Trugenberger

We construct exact many-body eigenstates of both energy and angular momentum for the N-anyon problem in an external magnetic field. Such states span the full ground-state eigenspace and have a natural representation in terms of the Fubini-Veneziano vertex operators of string theory.

International Journal of Modern Physics B•Jun 1, 1991•18 citations

EXACT GROUND STATE WAVE FUNCTIONS FOR N ANYONS IN A MAGNETIC FIELD ON A TORUS

ANSAR FAYYAZUDDIN

The complete set of ground state wave functions for N anyons in an external magnetic field on the torus is found. The cases when the filling factor is less than or equal to one are considered. The single valued description of anyons is employed throughout by coupling bosons to a Chern-Simons field. At the end, the Chern-Simons interaction is removed by a singular gauge transformation as a result of which the wave functions become multi-component in agreement with other studies. It is shown that for statistics of the type θ=πq/p the exactly filled lowest Landau level has a q-fold degeneracy. Statistics of type π/p, which are relevant for the Laughlin theory of the FQHE, are singled out as those with non-degenerate filled ground states.

arXiv:hep-th/9303120•Modern Physics Letters A•Oct 30, 1993•3 citations

AVERAGE FIELD APPROXIMATION FOR ALMOST BOSONIC ANYONS IN A MAGNETIC FIELD

Théotime Girardot

We study the ground state of a large number N of 2D anyons in an external magnetic field. We consider a scaling limit where the statistics parameter α tends to zero when N tends to infinity which allows the statistics to be seen as a "perturbation from the bosonic end". Our model is that of bosons in a magnetic field and interacting through long-range magnetic potential generated by magnetic charges carried by each particle, smeared over discs of radius R. Our method allows to take R tends to not too fast at the same time as N tends to infinity. We use the information theoretic version of the de Finetti theorem of Brandão and Harrow to justify the so-called "average field approximation": the particles behave like independent, identically distributed bosons interacting via a self-consistent magnetic field.

•Oct 18, 2019•14 citations

GROUND STATE OF N HARMONICALLY BOUND ANYONS IN A MAGNETIC FIELD

R. Chitra

The properties of the ground state of N anyons in an external magnetic field and a harmonic oscillator potential are computed in the large-N limit using the Thomas-Fermi approximation. The number of level crossings in the ground state as a function of the harmonic frequency, the strength and the direction of the magnetic field and N are also studied.

Modern Physics Letters A•Dec 14, 1992•0 citations
The mean field equations for anyons in an external homogeneous magnetic field are studied and two classes of mean field solutions are explicitly constructed. The first class of solutions, corresponding to one filled Landau level in the combined external and smeared out statistical magnetic fields, is compared to the corresponding exact groundstate solutions. The energies are found to agree well at low densities and when the statistical field is not too strong compared to the background field. At high densities the fermi pressure increases the mean field energy indefinitely. The mean field solutions also miss the lower part of the energy spectrum. To the second class of mean field solutions no corresponding anyon state is known. These solutions represent the anyonic continuation of the fermi state with two filled Landau levels.
We consider N anyons, with statistical parameter ν, in a homogeneous magnetic fieldand discuss exact and perturbative solutions. We show that the energy, E(ν), obeys[Formula: see text] for any bose or fermi state and that the extremal cases correspondto the states where the relative angular momenta of all pairs of particles are negativeand non-negative, respectively. The anyonic continuations of these extremal states aregiven, their energy is linear in ν. We conjecture that the above bounds on [Formula: see text] hold forany ν. This implies that the energy of any many-anyon state decreases monotonicallywith the statistical parameter ν (ν taking any real value). For small enough ν, E=const. [Formula: see text] and the wave function is known. Increasing ν, the wave functionbecomes singular at some bose point. In the following intermediate region (which maybe absent), E(ν) decreases more slowly; the exact form of E(ν) and the wave functionare unknown. Increasing ν further, above some bose point the energy becomes constantand the wave function is again known.
The statistical mechanics of an anyon gas in a magnetic field is addressed. A harmonic regulator is used to define a proper thermodynamic limit. When the magnetic field is sufficiently strong, only exact N-anyon ground states, where anyons occupy the lowest Landau level, contribute to the equation of state. Particular attention is paid to the interval of definition of the statistical parameter \ensuremath{\alpha}\ensuremath{\in}[-1,0] where a gap exists. Interestingly enough, one finds that at the critical filling \ensuremath{\nu}=-1/\ensuremath{\alpha} where the pressure diverges, the external magnetic field is entirely screened by the flux tubes carried by the anyons.
The complete set of ground state wave functions for N anyons in an external magnetic field on the torus is found. The cases when the filling factor is less than or equal to one are considered. The single valued description of anyons is employed throughout by coupling bosons to a Chern-Simons field. At the end, the Chern-Simons interaction is removed by a singular gauge transformation as a result of which the wave functions become multi-component in agreement with other studies. It is shown that for statistics of the type θ=πq/p the exactly filled lowest Landau level has a q-fold degeneracy. Statistics of type π/p, which are relevant for the Laughlin theory of the FQHE, are singled out as those with non-degenerate filled ground states.
We study the ground state of a large number N of 2D anyons in an external magnetic field. We consider a scaling limit where the statistics parameter α tends to zero when N tends to infinity which allows the statistics to be seen as a "perturbation from the bosonic end". Our model is that of bosons in a magnetic field and interacting through long-range magnetic potential generated by magnetic charges carried by each particle, smeared over discs of radius R. Our method allows to take R tends to not too fast at the same time as N tends to infinity. We use the information theoretic version of the de Finetti theorem of Brandão and Harrow to justify the so-called "average field approximation": the particles behave like independent, identically distributed bosons interacting via a self-consistent magnetic field.