## Abstract

The problem of the statistical mechanics of an anyon gas is addressed. A perturbative analysis in the anyonic coupling constant {alpha} is reviewed, and the thermodynamical potential is computed at first and second order. An adequate second quantized formalism (field theory at finite temperature) is proposed. At first order in perturbation theory, the results are strikingly simple: only the second virial coefficient close to bosonic statistics is corrected. At second order, however, the complexity of the anyon model appears. One can compute exactly the perturbative correction to each cluster coefficient. However, and contrary to first order, a closed expression for the equation of state seems out of reach. As an illustration, the perturbative expressions of a{sub 3}, a{sub 4}, a{sub 5} and a{sub 6} are given at second order. Finally, using the same formalism, the equation of state of an anyon gas in a constant magnetic field is analyzed at first order in perturbation theory. (K.A.) 16 refs.; 3 figs.; 7 tabs.

Dasnieres de Veigy, A;

^{[1] }Ouvry, S^{[1] }- Paris-11 Univ., 91 - Orsay (France). Inst. de Physique Nucleaire

## Citation Formats

Dasnieres de Veigy, A, and Ouvry, S.
Perturbative anyon gas.
France: N. p.,
1992.
Web.

Dasnieres de Veigy, A, & Ouvry, S.
Perturbative anyon gas.
France.

Dasnieres de Veigy, A, and Ouvry, S.
1992.
"Perturbative anyon gas."
France.

@misc{etde_10109814,

title = {Perturbative anyon gas}

author = {Dasnieres de Veigy, A, and Ouvry, S}

abstractNote = {The problem of the statistical mechanics of an anyon gas is addressed. A perturbative analysis in the anyonic coupling constant {alpha} is reviewed, and the thermodynamical potential is computed at first and second order. An adequate second quantized formalism (field theory at finite temperature) is proposed. At first order in perturbation theory, the results are strikingly simple: only the second virial coefficient close to bosonic statistics is corrected. At second order, however, the complexity of the anyon model appears. One can compute exactly the perturbative correction to each cluster coefficient. However, and contrary to first order, a closed expression for the equation of state seems out of reach. As an illustration, the perturbative expressions of a{sub 3}, a{sub 4}, a{sub 5} and a{sub 6} are given at second order. Finally, using the same formalism, the equation of state of an anyon gas in a constant magnetic field is analyzed at first order in perturbation theory. (K.A.) 16 refs.; 3 figs.; 7 tabs.}

place = {France}

year = {1992}

month = {Jun}

}

title = {Perturbative anyon gas}

author = {Dasnieres de Veigy, A, and Ouvry, S}

abstractNote = {The problem of the statistical mechanics of an anyon gas is addressed. A perturbative analysis in the anyonic coupling constant {alpha} is reviewed, and the thermodynamical potential is computed at first and second order. An adequate second quantized formalism (field theory at finite temperature) is proposed. At first order in perturbation theory, the results are strikingly simple: only the second virial coefficient close to bosonic statistics is corrected. At second order, however, the complexity of the anyon model appears. One can compute exactly the perturbative correction to each cluster coefficient. However, and contrary to first order, a closed expression for the equation of state seems out of reach. As an illustration, the perturbative expressions of a{sub 3}, a{sub 4}, a{sub 5} and a{sub 6} are given at second order. Finally, using the same formalism, the equation of state of an anyon gas in a constant magnetic field is analyzed at first order in perturbation theory. (K.A.) 16 refs.; 3 figs.; 7 tabs.}

place = {France}

year = {1992}

month = {Jun}

}