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

Scattering of anyons with hard-disk repulsion and the second virial coefficient

Akira Suzuki, M. K. Srivastava, R. K. Bhaduri, J. Law

Published Nov 15, 1991• 8 citations
Publisher

Abstract

We have considered two-anyon hard-disk scattering and found marked asymmetry in the differential cross section, and sensitivity to the strength of the statistical interaction parameter \ensuremath{\alpha}. For the second virial coefficient B(T), the hard-disk interaction suppresses the differences due to statistics except for very low temperatures. In this regime, we give an analytical low-temperature expansion of B(T) for semions.

DOI
10.1103/physrevb.44.10731

Related papers

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

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

Mott scattering of anyons: some exact results

J. Law, M. K. Srivastava, R. K. Bhaduri +1 more

The planar differential cross section for the Mott scattering of two identical charge anyons is obtained in a closed form. This expression exhibits a marked asymmetry between forward and backward angles, and is especially simple for the semion-semion scattering. At low energies, a pronounced dip in the differential cross section due to planar Coulomb-anyonic interference appears at the forward angles, whose implication is discussed.

Journal of Physics A Mathematical and General•Feb 21, 1992•13 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

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

STATISTICAL MECHANICS OF ANYONS

Daniel P. Arovas, Robert Schrieffer, Frank A. Wilczek +1 more

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.

World Scientific series in 20th century physics•Nov 1, 2002•0 citations
We have considered two-anyon hard-disk scattering and found marked asymmetry in the differential cross section, and sensitivity to the strength of the statistical interaction parameter \ensuremath{\alpha}. For the second virial coefficient B(T), the hard-disk interaction suppresses the differences due to statistics except for very low temperatures. In this regime, we give an analytical low-temperature expansion of B(T) for semions.
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.
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.