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

Yoo, S K, Daniel K. Park

Published Jan 1, 1999• 0 citations

Abstract

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.

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

Yoo, S K, Daniel K. Park

Published Jan 1, 1999• 0 citations

OpenAlex

Abstract

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.

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Communications in Theoretical PhysicsJul 1, 19920 citations

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.

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.

{\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.