One-Dimensional Statistical Mechanics for Identical Particles : The Calogero and Anyon Cases

The thermodynamic of particles with intermediate statistics interpolating between Bose and Fermi statistics is adressed in the simple case where there is one quantum number per particle. Such systems are essentially one-dimensional. As an illustration, one considers the anyon model restricted to the lowest Landau level of a strong magnetic field at low temperature, the generalization of this model to several particles species, and the one dimensional Calogero model. One reviews a unified algorithm to compute the statistical mechanics of these systems. It is pointed out that Haldane's generalization of the Pauli principle can be deduced from the anyon model in a strong magnetic field at low temperature.Comment: 17 page

Equation of State of an Anyon Gas in a Strong Magnetic Field

The statistical mechanics of an anyon gas in a magnetic field is addressed. An harmonic regulator is used to define a proper thermodynamic limit. When the magnetic field is sufficiently strong, only exact $N$-anyon groundstates, where anyons occupy the lowest Landau level, contribute to the equation of state. Particular attention is paid to the interval of definition of the statistical parameter $\alpha\in[-1,0]$ where a gap exists. Interestingly enough, one finds that at the critical filling $\nu=-{1/\alpha}$ where the pressure diverges, the external magnetic field is entirely screened by the flux tubes carried by the anyons.Comment: 14 pages, PACS numbers: 03.65.-w, 05.30.-d, 05.70.Ce, IPNO/TH 93-16 (MAY 1993), e-mail: OUVRY@FRCPN1