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. B, Condensed matter

Second virial coefficient for contact-interacting anyons

Paola Giacconi A, Fabio Maltoni B, Roberto Soldati

Published Apr 15, 1996• 14 citations
Publisher

Abstract

We study the thermodynamic properties of the anyon gas in the presence of a contact interaction. In particular, we use dimensional and analytical regularizations to calculate the second virial coefficient for free and contact-interacting anyons. The Bethe-Uhlenbeck formula is discussed and it is shown that the same result is regained using the \ensuremath{\zeta} regularization. Finally, the second virial coefficients for contact-interacting particles in two and three spatial dimensions are obtained as special cases. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physrevb.53.10065

Related papers

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

Ideal quantum gases in two dimensions

S. Viefers, F. Ravndal, T. Haugset

Thermodynamic properties of nonrelativistic bosons and fermions in two spatial dimensions and without interactions are derived. All the virial coefficients are the same except for the second, for which the signs are opposite. This results in the same specific heat for the two gases. Existing equations of state for the free anyon gas are also discussed and shown to break down at low temperatures or high densities.

arXiv:hep-th/9408011•American Journal of Physics•Apr 1, 1995•22 citations

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

Ideal quantum gases in two dimensions

S. Viefers, F. Ravndal, T. Haugset

Abstract: Thermodynamic properties of non-relativistic bosons and fermions in two spatial dimensions and without interactions are derived. All the virial coefficients are the same except for the second, for which the signs are opposite. This results in the same specific heat for the two gases. Existing equations of state for the free anyon gas are also discussed and shown to break down at low temperatures or high densities.

•Jan 1, 1994•10 citations

The second virial coefficient of spin- interacting anyon system

Sahng-Kyoon Yoo, D K Park

We evaluate the propagator by the usual time-sliced manner and use it to compute the second virial coefficient of an anyon gas interacting through the repulsive potential of the form . All the cusps for the unpolarized spin- as well as spinless cases disappear in the limit, where is a frequency of the harmonic oscillator which is introduced as a regularization method. As g approaches zero, the result reduces to the noninteracting hard-core limit.

arXiv:hep-th/9710056•Journal of Physics A Mathematical and General•Jan 1, 1999•0 citations

The Second Virial Coefficient of Spin-1/2 Interacting Anyon System

Yoo, S K, Daniel K. Park

Evaluating the propagator by the usual time-sliced manner, we use it to compute the second virial coefficient of an anyon gas interacting through the repulsive potential of the form $g/r^2 (g > 0)$. All the cusps for the unpolarized spin-1/2 as well as spinless cases disappear in the $\\omega \\to 0$ limit, where $\\omega$ is a frequency of harmonic oscillator which is introduced as a regularization method. As $g$ approaches to zero, the result reduces to the noninteracting hard-core limit.

•Jan 1, 1999•0 citations
We study the thermodynamic properties of the anyon gas in the presence of a contact interaction. In particular, we use dimensional and analytical regularizations to calculate the second virial coefficient for free and contact-interacting anyons. The Bethe-Uhlenbeck formula is discussed and it is shown that the same result is regained using the \ensuremath{\zeta} regularization. Finally, the second virial coefficients for contact-interacting particles in two and three spatial dimensions are obtained as special cases. \textcopyright{} 1996 The American Physical Society.
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.
Evaluating the propagator by the usual time-sliced manner, we use it to compute the second virial coefficient of an anyon gas interacting through the repulsive potential of the form g/r2(g>0)g/r^2 (g > 0)g/r2(g>0). All the cusps for the unpolarized spin-1/2 as well as spinless cases disappear in the omegato0\\omega \\to 0omegato0 limit, where omega\\omegaomega is a frequency of harmonic oscillator which is introduced as a regularization method. As ggg approaches to zero, the result reduces to the noninteracting hard-core limit.