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

World Scientific series in 20th century physics

STATISTICAL MECHANICS OF ANYONS

Daniel P. Arovas, Robert Schrieffer, Frank A. Wilczek, A. Zee

Published Nov 1, 2002• 0 citations
Publisher

Abstract

We study the statistical mechanics of a two-dimensional gas of free anyons-particles which interpolate between Bose-Einstein and Fermi-Dirac character. Thermodynamic quantities are discussed in the low-density regime. In particular, the second virial coefficient is evaluated by two different methods and is found to exhibit a simple, periodic, but nonanalytic behavior as a function of the statistics determining parameter.

DOI
10.1142/9789812777041_0027

Related papers

Second Virial Coefficient of Anyons with Spins

Shun-Qing Shen, Jianming Cai, Ruibao Tao

We study the statistical properties of a two-dimensional gas of free anyone with spin. The concept of spin carried by anyons has been discussed in detail based on the two-dimensional Dirac equation. The second virial coefficient for the gas is evaluated and is found that it is the result of Arovas et al.[1] but not the result of Blum et al.[2] that is recovered, which is periodical for the statistical parameter with the length .

Communications in Theoretical Physics•Jul 1, 1992•0 citations

Second virial coefficient of the interacting anyon gas

Nikitas I. Gidopoulos, A. K. Theophilou

Arovas and co-workers, in their well-known paper on the statistical mechanics of anyons [D. P. Arovas, R. Schrieffer, F. Wilczek, and A. Zee, Nucl. Phys. B251, 117 (1985)], found that the second virial coefficient of a two-dimensional gas of free anyons exhibits nonanalytic behavior as the statistical parameter is varied in the neighborhood of the Bose point. In this paper we consider the anyons to be interacting, via a two-body interaction U(\ensuremath{\Vert}${\mathbf{r}}_{1}$-${\mathbf{r}}_{2}$\ensuremath{\Vert}), where ${\mathit{r}}^{2}$U(r)\ensuremath{\rightarrow}0 as r\ensuremath{\rightarrow}0. Expanding the second virial coefficient in the vicinity of the Bose point, we show that the nonanalyticity is still present and independent of the particular form of U. Furthermore, we calculate explicitly, the second virial coefficient in the case of a short-range interaction.

Physical review. B, Condensed matter•Mar 1, 1994•1 citation

Second virial coefficient of an interacting anyon gas

Daniel Loss, Yaotian Fu

We consider the statistical mechanics of an interacting anyon gas with a repulsive pair potential of the form g/${\mathit{r}}^{2}$. The second virial coefficient is calculated and shown to be a smooth function of the statistical parameter \ensuremath{\alpha} for g>0, without the cusps previously found at the Bose point in a noninteracting anyon gas. As g\ensuremath{\rightarrow}0 the cusps remain absent but a different type of singularity develops at the Bose point, showing that the order of limits is crucial.

Physical Review Letters•Jul 15, 1991•16 citations

Improved calculation of the third virial coefficient of a free anyon gas

J. Law, Avinash Khare, R. K. Bhaduri +1 more

For three anyons confined in a harmonic oscillator, only the class of states that interpolates nonlinearly with the statistical parameter contributes to the third virial coefficient of a free anyon gas. Rather than evaluating the full three-body partition function as was done in an earlier publication [J. Law, A. Suzuki, and R. Bhaduri, Phys. Rev. A 46, 4693 (1992)], here only the nonlinear contribution is calculated, thus avoiding delicate cancellations between the irrelevant linear part and the two-body partition function. Our numerical results are consistent with the simple analytical form suggested recently by Myrheim and Olaussen [Phys. Lett. B 299, 267 (1993)].

arXiv:hep-th/9310106•Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Feb 1, 1994•4 citations

Statistical mechanics of anyons

R. Acharya, P. Narayana Swamy

We propose a new generalized statistical mechanics for anyons based on a simple ansatz that has the correct familiar limiting cases. We derive the anyon equation of state from the grand partition function. We develop the virial expansion and obtain all the virial coefficients. Furthermore, we demonstrate how thermodynamic quantities such as the molar specific heat can readily be calculated. We discuss the properties of semions and also demonstrate that ideal non-relativistic anyons do not exhibit finite temperature condensation.

Journal of Physics A Mathematical and General•Nov 21, 1994•49 citations

Statistics of q-oscillators, quons and relations to fractional statistics

Масуд Чайчиан, R. González Felipe, Claus Montonen

The statistics of q-oscillators, quons, and, to some extent, of anyons are studied and the basic differences among these objects are pointed out In particular, the statistical distributions for different bosonic and fermionic q-oscillators are found for their corresponding Fock space representations in the case when the Hamiltonian is identified with the number operator. In this case and for non-relativistic particles, the single-particle temperature Green function is defined with q-deformed periodicity conditions. The equations of state for nonrelativistic and ultrarelativistic bosonic q-gases in an arbitrary space dimension are found near Bose statistics, as well as that for an anyonic gas near Bose and Fermi statistics. The first corrections to the second virial coefficients are also evaluated.

arXiv:hep-th/9304111•Journal of Physics A Mathematical and General•Aug 21, 1993•159 citations
We study the statistical mechanics of a two-dimensional gas of free anyons-particles which interpolate between Bose-Einstein and Fermi-Dirac character. Thermodynamic quantities are discussed in the low-density regime. In particular, the second virial coefficient is evaluated by two different methods and is found to exhibit a simple, periodic, but nonanalytic behavior as a function of the statistics determining parameter.
Arovas and co-workers, in their well-known paper on the statistical mechanics of anyons [D. P. Arovas, R. Schrieffer, F. Wilczek, and A. Zee, Nucl. Phys. B251, 117 (1985)], found that the second virial coefficient of a two-dimensional gas of free anyons exhibits nonanalytic behavior as the statistical parameter is varied in the neighborhood of the Bose point. In this paper we consider the anyons to be interacting, via a two-body interaction U(\ensuremath{\Vert}r1{\mathbf{r}}_{1}r1​-r2{\mathbf{r}}_{2}r2​\ensuremath{\Vert}), where r2{\mathit{r}}^{2}r2U(r)\ensuremath{\rightarrow}0 as r\ensuremath{\rightarrow}0. Expanding the second virial coefficient in the vicinity of the Bose point, we show that the nonanalyticity is still present and independent of the particular form of U. Furthermore, we calculate explicitly, the second virial coefficient in the case of a short-range interaction.
We consider the statistical mechanics of an interacting anyon gas with a repulsive pair potential of the form g/r2{\mathit{r}}^{2}r2. The second virial coefficient is calculated and shown to be a smooth function of the statistical parameter \ensuremath{\alpha} for g>0, without the cusps previously found at the Bose point in a noninteracting anyon gas. As g\ensuremath{\rightarrow}0 the cusps remain absent but a different type of singularity develops at the Bose point, showing that the order of limits is crucial.
For three anyons confined in a harmonic oscillator, only the class of states that interpolates nonlinearly with the statistical parameter contributes to the third virial coefficient of a free anyon gas. Rather than evaluating the full three-body partition function as was done in an earlier publication [J. Law, A. Suzuki, and R. Bhaduri, Phys. Rev. A 46, 4693 (1992)], here only the nonlinear contribution is calculated, thus avoiding delicate cancellations between the irrelevant linear part and the two-body partition function. Our numerical results are consistent with the simple analytical form suggested recently by Myrheim and Olaussen [Phys. Lett. B 299, 267 (1993)].
We propose a new generalized statistical mechanics for anyons based on a simple ansatz that has the correct familiar limiting cases. We derive the anyon equation of state from the grand partition function. We develop the virial expansion and obtain all the virial coefficients. Furthermore, we demonstrate how thermodynamic quantities such as the molar specific heat can readily be calculated. We discuss the properties of semions and also demonstrate that ideal non-relativistic anyons do not exhibit finite temperature condensation.
The statistics of q-oscillators, quons, and, to some extent, of anyons are studied and the basic differences among these objects are pointed out In particular, the statistical distributions for different bosonic and fermionic q-oscillators are found for their corresponding Fock space representations in the case when the Hamiltonian is identified with the number operator. In this case and for non-relativistic particles, the single-particle temperature Green function is defined with q-deformed periodicity conditions. The equations of state for nonrelativistic and ultrarelativistic bosonic q-gases in an arbitrary space dimension are found near Bose statistics, as well as that for an anyonic gas near Bose and Fermi statistics. The first corrections to the second virial coefficients are also evaluated.