arXiv:cond-mat/9803061

A note on exclusion statistics parameter and Hausdorff dimension

Wellington da Cruz

Published Mar 5, 1998• 0 citations

Abstract

We obtain for an anyon gas in the high temperature limit a relation between the exclusion statistics parameter $g$ and the Hausdorff dimension $h$, given by $g=h(2-h)$. The anyonic excitations are classified into equivalence classes labeled by Hausdorff dimension, $h$, and in that limit, the parameter $g$ give us the second virial coefficient for any statistics, $ν$. The anyonic excitations into the same class $h$ get the same value of this virial coefficient.

DOI: 10.48550/arxiv.cond-mat/9803061

Related papers

Haldane exclusion statistics and second virial coefficient

M. V. N. Murthy, Ravi Shankar

We show that Haldane's new definition of statistics, when generalized to infinite dimensional Hilbert spaces, is determined by the high temperature limit of the second virial coefficient. We thus show that this exclusion statistics parameter g of anyone is nontrivial and is completely determined by its exchange statistics parameter \ensuremath{\alpha}. We also compute g for quasiparticles in the Luttinger model and show that it is equal to \ensuremath{\alpha}.

arXiv:cond-mat/9401071Physical Review LettersJun 6, 199480 citations

Fractional exclusion statistics and anyons

Wei Chen, Yee Jack Ng

arXiv:cond-mat/9411008Physical review. B, Condensed matterMay 15, 19956 citations

Comment on “Thermodynamics of a One-Dimensional Ideal Gas with Fractional Exclusion Statistics”

Alain Dasnières de Veigy, Stéphane Ouvry

arXiv:cond-mat/9503026Physical Review LettersJul 10, 199517 citations

Thermodynamic Properties of Generalized Exclusion Statistics

Hyun Seok Yang, Bum-Hoon Lee, Chanyong Park B

arXiv:cond-mat/9606165Jun 24, 199614 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 PhysicsJul 1, 19920 citations

Second virial coefficient of the interacting anyon gas

Nikitas I. Gidopoulos, A. K. Theophilou

Physical review. B, Condensed matterMar 1, 19941 citation

arXiv:cond-mat/9803061

A note on exclusion statistics parameter and Hausdorff dimension

Wellington da Cruz

Published Mar 5, 1998• 0 citations

arXiv HTML PDF

Abstract

We obtain for an anyon gas in the high temperature limit a relation between the exclusion statistics parameter

g

and the Hausdorff dimension

h

, given by

g=h(2-h)

. The anyonic excitations are classified into equivalence classes labeled by Hausdorff dimension,

h

, and in that limit, the parameter

g

give us the second virial coefficient for any statistics,

ν

. The anyonic excitations into the same class

h

get the same value of this virial coefficient.

DOI: 10.48550/arxiv.cond-mat/9803061

Related papers

Haldane exclusion statistics and second virial coefficient

M. V. N. Murthy, Ravi Shankar

arXiv:cond-mat/9401071Physical Review LettersJun 6, 199480 citations

Fractional exclusion statistics and anyons

Wei Chen, Yee Jack Ng

Do anyons, dynamically realized by the field theoretic Chern-Simons construction, obey fractional exclusion statistics? We find that they do if the statistical interaction between anyons and antianyons is taken into account. For this anyon model, we show perturbatively that the exchange statistical parameter of anyons is equal to the exclusion statistical parameter. We obtain the same result by applying the relation between the exclusion statistical parameter and the second virial coefficient in the nonrelativistic limit.Do anyons, dynamically realized by the field theoretic Chern-Simons construction, obey fractional exclusion statistics? We find that they do if the statistical interaction between anyons and antianyons is taken into account. For this anyon model, we show perturbatively that the exchange statistical parameter of anyons is equal to the exclusion statistical parameter. We obtain the same result by applying the relation between the exclusion statistical parameter and the second virial coefficient in the nonrelativistic limit.

arXiv:cond-mat/9411008Physical review. B, Condensed matterMay 15, 19956 citations

Comment on “Thermodynamics of a One-Dimensional Ideal Gas with Fractional Exclusion Statistics”

Alain Dasnières de Veigy, Stéphane Ouvry

In a recent letter -Phys. Rev. Lett. 73, 3331 (1995)-, the conclusion was reached that, in the one-dimensional Calogero model, only the second virial coefficient is affected by the statistical parameter $α$ , where $α$ is related to the coupling constant $κ/ x_{ij}^2$ of the Calogero interaction by $κ=α(α+1)$ . We argue that it is not so, i.e. all virial coefficients are affected, if the thermodynamic limit is properly taken.In a recent letter -Phys. Rev. Lett. 73, 3331 (1995)-, the conclusion was reached that, in the one-dimensional Calogero model, only the second virial coefficient is affected by the statistical parameter $α$, where $α$ is related to the coupling constant $κ/ x_{ij}^2$ of the Calogero interaction by $κ=α(α+1)$. We argue that it is not so, i.e. all virial coefficients are affected, if the thermodynamic limit is properly taken.

arXiv:cond-mat/9503026Physical Review LettersJul 10, 199517 citations

Thermodynamic Properties of Generalized Exclusion Statistics

Hyun Seok Yang, Bum-Hoon Lee, Chanyong Park B

We analytically calculate some thermodynamic quantities of an ideal $g$ -on gas obeying generalized exclusion statistics. We show that the specific heat of a $g$ -on gas ( $g \neq 0$ ) vanishes linearly in any dimension as $T \to 0$ when the particle number is conserved and exhibits an interesting dual symmetry that relates the particle-statistics at $g$ to the hole-statistics at $1/g$ at low temperatures. We derive the complete solution for the cluster coefficients $b_l(g)$ as a function of Haldane's statistical interaction $g$ in $D$ dimensions. We also find that the cluster coefficients $b_l(g)$ and the virial coefficients $a_l(g)$ are exactly mirror symmetric ( $l$ =odd) or antisymmetric ( $l$ =even) about $g=1/2$ . In two dimensions, we completely determine the closed forms about the cluster and the virial coefficients of the generalized exclusion statistics, which exactly agree with the virial coefficients of an anyon gas of linear energies. We show that the $g$ -on gas with zero chemical potential shows thermodynamic properties similar to the photon statistics. We discuss some physical implications of our results.We analytically calculate some thermodynamic quantities of an ideal $g$-on gas obeying generalized exclusion statistics. We show that the specific heat of a $g$-on gas ($g \neq 0$) vanishes linearly in any dimension as $T \to 0$ when the particle number is conserved and exhibits an interesting dual symmetry that relates the particle-statistics at $g$ to the hole-statistics at $1/g$ at low temperatures. We derive the complete solution for the cluster coefficients $b_l(g)$ as a function of Haldane's statistical interaction $g$ in $D$ dimensions. We also find that the cluster coefficients $b_l(g)$ and the virial coefficients $a_l(g)$ are exactly mirror symmetric ($l$=odd) or antisymmetric ($l$=even) about $g=1/2$. In two dimensions, we completely determine the closed forms about the cluster and the virial coefficients of the generalized exclusion statistics, which exactly agree with the virial coefficients of an anyon gas of linear energies. We show that the $g$-on gas with zero chemical potential shows thermodynamic properties similar to the photon statistics. We discuss some physical implications of our results.

arXiv:cond-mat/9606165Jun 24, 199614 citations

Second Virial Coefficient of Anyons with Spins

Shun-Qing Shen, Jianming Cai, Ruibao Tao

Communications in Theoretical PhysicsJul 1, 19920 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.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 matterMar 1, 19941 citation

We obtain for an anyon gas in the high temperature limit a relation between the exclusion statistics parameter

g

and the Hausdorff dimension

h

, given by

g=h(2-h)

. The anyonic excitations are classified into equivalence classes labeled by Hausdorff dimension,

h

, and in that limit, the parameter

g

give us the second virial coefficient for any statistics,

ν

. The anyonic excitations into the same class

h

get the same value of this virial coefficient.

α

, where

α

is related to the coupling constant

κ/ x_{ij}^2

of the Calogero interaction by

κ=α(α+1)

. We argue that it is not so, i.e. all virial coefficients are affected, if the thermodynamic limit is properly taken.

We analytically calculate some thermodynamic quantities of an ideal

g

-on gas obeying generalized exclusion statistics. We show that the specific heat of a

g

-on gas (

g \neq 0

) vanishes linearly in any dimension as

T \to 0

when the particle number is conserved and exhibits an interesting dual symmetry that relates the particle-statistics at

g

to the hole-statistics at

1/g

at low temperatures. We derive the complete solution for the cluster coefficients

b_l(g)

as a function of Haldane's statistical interaction

g

D

dimensions. We also find that the cluster coefficients

b_l(g)

and the virial coefficients

a_l(g)

are exactly mirror symmetric (

l

=odd) or antisymmetric (

l

=even) about

g=1/2

. In two dimensions, we completely determine the closed forms about the cluster and the virial coefficients of the generalized exclusion statistics, which exactly agree with the virial coefficients of an anyon gas of linear energies. We show that the

g

-on gas with zero chemical potential shows thermodynamic properties similar to the photon statistics. We discuss some physical implications of our results.

{\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.