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

arXiv:hep-th/9303078 · Modern Physics Letters A

PARITY VIOLATION AND THE MEAN FIELD APPROXIMATION FOR THE ANYON GAS

Didier Caenepeel, R. MacKenzie

Published Jun 28, 1993• 3 citations
arXivHTMLPDF

Abstract

We examine an approach to justifying the mean field approximation for the anyon gas, using the scattering of anyons. Parity violation permits a nonzero average scattering angle, from which one can extract a mean radius of curvature for anyons. If this is larger than the interparticle separation, one expects that the graininess of the statistical magnetic field is unimportant, and that the mean field approximation is good. We argue that a non-conventional interaction between anyons is crucial, in which case the criterion for validity of the approximation is identical to the one deduced using a self-consistency argument.

DOI
10.1142/s021773239300163x

Related papers

Parity violation, anyon scattering, and the mean field approximation

Didier Caenepeel, R. MacKenzie

Some genreal features of the scattering of boson-based anyons with an added nonstatistical interaction are discussed. Periodicity requirements of the phase shifts are derived, and used to illustrate the danger inherent in separating these phase shifts into the well-known pure Aharanov-Bohm phase shifts, and an additional set which arises due to the interaction. It is proven that the added phase shifts, although due to the nonstatistical interaction, necessarily change as the statistical parameter is varied, keeping the interaction fixed. A hard-disk interaction provides a concrete illustration of these general ideas. In the latter part of the paper, scattering with an additional hard-disk interaction is studied in detail, with an eye towards providing a criterion for the validity of the mean-field approximation for anyons, which is the first step in virtually any treatment of this system. We find, consistent with previous work, that the approximation is justified if the statistical interaction is weak, and that it must be more weak for boson-based than for fermion-based anyons.

arXiv:hep-th/9405027•Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•Oct 15, 1994•4 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

MEAN-FIELD THEORY OF ANYONS NEAR BOSE STATISTICS

JOHN MCCABE, R. MacKenzie

We argue the validity of a mean-field approximation for a free anyon gas near Bose statistics, and show that the anyon gas can exhibit a Meissner effect in the domain of validity of the approximation only due to a hard-core repulsion.

Modern Physics Letters B•Jan 10, 1994•0 citations

Average-field approximation for dilute almost-bosonic anyons

François Louis Antoine Visconti

Abstract We study the ground state of a system of N two-dimensional trapped almost-bosonic anyons. This setup can equivalently be viewed as bosons interacting through long-range magnetic potentials generated by magnetic charges carried by each particle. These magnetic charges are assumed to be smeared over discs of radius R —a model known as extended anyons . To recover the point-like anyons perspective, we consider the joint limit $$R \rightarrow 0$$ R → 0 as $$N \rightarrow \infty $$ N → ∞ . We rigorously justify the average-field approximation for any radius R that decays polynomially, and even for certain exponentially decaying R . The average-field approximation asserts that the particles behave like independent, identical bosons interacting through a self-consistent magnetic field. Our result significantly improves upon the best-known estimates from [1, 2], and it in particular covers radii that are much smaller than the mean interparticle distance. The proof strategy builds on a recent work on two-dimensional attractive Bose gases by Junge and the author [3].

arXiv:2507.01102•Calculus of Variations and Partial Differential Equations•Sep 1, 2026•0 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 extended anyons in an external magnetic field. We consider a scaling limit where the statistics parameter α is proportional to N−1 when N → ∞, which allows the statistics to be seen as a “perturbation around the bosonic end.” Our model is that of bosons in a magnetic field interacting through long-range magnetic potential generated by magnetic charges carried by each particle, smeared over discs of radius R. Our method allows us to take R → 0 not too fast at the same time as N → ∞ : R = N−1/4+ɛ. 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.

arXiv:1910.09310•Journal of Mathematical Physics•Jul 1, 2020•15 citations

Self-consistent mean-field approach for the ideal anyon gas

Lizeng Zhang, Michael Ma, Fu‐Chun Zhang

Using a self-consistent mean-field theory, where the anyon gauge field is approximated by its expectation value, we obtain a linear excitation spectrum for noninteracting anyon systems. The sound velocity is found to be \ensuremath{\surd}3 /2 of the value obtained by the random-phase approximation. The uniform liquid state of the anyon gas is shown to be locally stable against solid formation.

Physical review. B, Condensed matter•Nov 1, 1990•14 citations
We examine an approach to justifying the mean field approximation for the anyon gas, using the scattering of anyons. Parity violation permits a nonzero average scattering angle, from which one can extract a mean radius of curvature for anyons. If this is larger than the interparticle separation, one expects that the graininess of the statistical magnetic field is unimportant, and that the mean field approximation is good. We argue that a non-conventional interaction between anyons is crucial, in which case the criterion for validity of the approximation is identical to the one deduced using a self-consistency argument.
Some genreal features of the scattering of boson-based anyons with an added nonstatistical interaction are discussed. Periodicity requirements of the phase shifts are derived, and used to illustrate the danger inherent in separating these phase shifts into the well-known pure Aharanov-Bohm phase shifts, and an additional set which arises due to the interaction. It is proven that the added phase shifts, although due to the nonstatistical interaction, necessarily change as the statistical parameter is varied, keeping the interaction fixed. A hard-disk interaction provides a concrete illustration of these general ideas. In the latter part of the paper, scattering with an additional hard-disk interaction is studied in detail, with an eye towards providing a criterion for the validity of the mean-field approximation for anyons, which is the first step in virtually any treatment of this system. We find, consistent with previous work, that the approximation is justified if the statistical interaction is weak, and that it must be more weak for boson-based than for fermion-based anyons.
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.
Abstract We study the ground state of a system of N two-dimensional trapped almost-bosonic anyons. This setup can equivalently be viewed as bosons interacting through long-range magnetic potentials generated by magnetic charges carried by each particle. These magnetic charges are assumed to be smeared over discs of radius R —a model known as extended anyons . To recover the point-like anyons perspective, we consider the joint limit R→0R \rightarrow 0R→0 R → 0 as N→∞N \rightarrow \infty N→∞ N → ∞ . We rigorously justify the average-field approximation for any radius R that decays polynomially, and even for certain exponentially decaying R . The average-field approximation asserts that the particles behave like independent, identical bosons interacting through a self-consistent magnetic field. Our result significantly improves upon the best-known estimates from [1, 2], and it in particular covers radii that are much smaller than the mean interparticle distance. The proof strategy builds on a recent work on two-dimensional attractive Bose gases by Junge and the author [3].
We study the ground state of a large number N of 2D extended anyons in an external magnetic field. We consider a scaling limit where the statistics parameter α is proportional to N−1 when N → ∞, which allows the statistics to be seen as a “perturbation around the bosonic end.” Our model is that of bosons in a magnetic field interacting through long-range magnetic potential generated by magnetic charges carried by each particle, smeared over discs of radius R. Our method allows us to take R → 0 not too fast at the same time as N → ∞ : R = N−1/4+ɛ. 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.