Solitons and fractional statistics

Solitons in the continuum limit of the Calogero model are derived and shown to correspond to one-particle excitations. The statistical mechanics of exclusion statistics particles is then formulated in terms of a priori probabilities and a path integral is thereoff constructed. (Talk delivered at the Trieste April 1995 Conference on statistical mechanics and QFT and at the Oslo August 1995 Worskhop on low-dimensional systems.)Comment: 7 pages, Latex, no figures; References correcte

The Lowest Landau Level Anyon Equation of State in the Anti-screening Regime

The thermodynamics of the anyon model projected on the lowest Landau level (LLL) of an external magnetic field is addressed in the anti-screening regime, where the flux tubes carried by the anyons are parallel to the magnetic field. It is claimed that the LLL-anyon equation of state, which is known in the screening regime, can be analytically continued in the statistical parameter across the Fermi point to the antiscreening regime up to the vicinity (whose width tends to zero when the magnetic field becomes infinite) of the Bose point. There, an unphysical discontinuity arises due to the dropping of the non-LLL eigenstates which join the LLL, making the LLL approximation no longer valid. However, taking into account the effect of the non-LLL states at the Bose point would only smoothen the discontinuity and not alter the physics which is captured by the LLL projection: Close to the Bose point, the critical filling factor either goes to infinity (usual bosons) in the screening situation, or to 1/2 in the anti-screening situation, the difference between the flux tubes orientation being relevant even when they carry an infinitesimal fraction of the flux quantum. An exclusion statistics interpretation is adduced, which explains this situation in semiclassical terms. It is further shown how the exact solutions of the 3-anyon problem support this scenario as far as the third cluster coefficient is concerned.Comment: 14 pages, 3 figures, LaTex 2

Quantum liquids of particles with generalized statistics

We propose a phenomenological approach to quantum liquids of particles obeying generalized statistics of a fermionic type, in the spirit of the Landau Fermi liquid theory. The approach is developed for fractional exclusion statistics. We discuss both equilibrium (specific heat, compressibility, and Pauli spin susceptibility) and nonequilibrium (current and thermal conductivities, thermopower) properties. Low temperature quantities have the same temperature dependences as for the Fermi liquid, with the coefficients depending on the statistics parameter. The novel quantum liquids provide explicit realization of systems with a non-Fermi liquid Lorentz ratio in two and more dimensions. Consistency of the theory is verified by deriving the compressibility and $f$-sum rules.Comment: 14 pages, Revtex, no figures; typos correcte

Thermodynamics for Fractional Exclusion Statistics

We discuss the thermodynamics of a gas of free particles obeying Haldane's exclusion statistics, deriving low temperature and low density expansions. For gases with a constant density of states, we derive an exact equation of state and find that temperature-dependent quantities are independent of the statistics parameter.Comment: 9 pages, Revtex, no figures. References correcte

Non-Abelian Chern-Simons Particles in an External Magnetic Field

The quantum mechanics and thermodynamics of SU(2) non-Abelian Chern-Simons particles (non-Abelian anyons) in an external magnetic field are addressed. We derive the N-body Hamiltonian in the (anti-)holomorphic gauge when the Hilbert space is projected onto the lowest Landau level of the magnetic field. In the presence of an additional harmonic potential, the N-body spectrum depends linearly on the coupling (statistics) parameter. We calculate the second virial coefficient and find that in the strong magnetic field limit it develops a step-wise behavior as a function of the statistics parameter, in contrast to the linear dependence in the case of Abelian anyons. For small enough values of the statistics parameter we relate the N-body partition functions in the lowest Landau level to those of SU(2) bosons and find that the cluster (and virial) coefficients dependence on the statistics parameter cancels.Comment: 35 pages, revtex, 3 eps figures include

Bosonic and fermionic single-particle states in the Haldane approach to statistics for identical particles

We give two formulations of exclusion statistics (ES) using a variable number of bosonic or fermionic single-particle states which depend on the number of particles in the system. Associated bosonic and fermionic ES parameters are introduced and are discussed for FQHE quasiparticles, anyons in the lowest Landau level and for the Calogero-Sutherland model. In the latter case, only one family of solutions is emphasized to be sufficient to recover ES; appropriate families are specified for a number of formulations of the Calogero-Sutherland model. We extend the picture of variable number of single-particle states to generalized ideal gases with statistical interaction between particles of different momenta. Integral equations are derived which determine the momentum distribution for single-particle states and distribution of particles over the single-particle states in the thermal equilibrium.Comment: 6 pages, REVTE