Model of statistically coupled chiral fields on the circle

Starting from a field theoretical description of multicomponent anyons with mutual statistical interactions in the lowest Landau level, we construct a model of interacting chiral fields on the circle, with the energy spectrum characterized by a symmetric matrix $g_{\alpha\beta}$ with nonnegative entries. Being represented in a free form, the model provides a field theoretical realization of (ideal) fractional exclusion statistics for particles with linear dispersion, with $g_{\alpha\beta}$ as a statistics matrix. We derive the bosonized form of the model and discuss the relation to the effective low-energy description of the edge excitations for abelian fractional quantum Hall states in multilayer systems.Comment: 26 pages, Latex, 1 Latex figure included. The figure has been correcte

Algebra of Observables for Identical Particles in One Dimension

The algebra of observables for identical particles on a line is formulated starting from postulated basic commutation relations. A realization of this algebra in the Calogero model was previously known. New realizations are presented here in terms of differentiation operators and in terms of SU(N)-invariant observables of the Hermitian matrix models. Some particular structure properties of the algebra are briefly discussed.Comment: 13 pages, Latex, uses epsf, 1 eps figure include

Equation of State for Exclusion Statistics in a Harmonic Well

We consider the equations of state for systems of particles with exclusion statistics in a harmonic well. Paradygmatic examples are noninteracting particles obeying ideal fractional exclusion statistics placed in (i) a harmonic well on a line, and (ii) a harmonic well in the Lowest Landau Level (LLL) of an exterior magnetic field. We show their identity with (i) the Calogero model and (ii) anyons in the LLL of an exterior magnetic field and in a harmonic well.Comment: latex file, 11 page

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

Algebra of one-particle operators for the Calogero model

An algebra ${\cal G}$ of symmetric {\em one-particle} operators is constructed for the Calogero model. This is an infinite-dimensional Lie-algebra, which is independent of the interaction parameter $\lambda$ of the model. It is constructed in terms of symmetric polynomials of raising and lowering operators which satisfy the commutation relations of the $S_N$-{\em extended} Heisenberg algebra. We interpret ${\cal G}$ as the algebra of observables for a system of identical particles on a line. The parameter $\lambda$, which characterizes (a class of) irreducible representations of the algebra, is interpreted as a statistics parameter for the identical particles.Comment: 23 pages, LaTe

ON THERMODYNAMICS OF MULTISPECIES ANYONS

We address the problem of multispecies anyons, i.e. particles of different species whose wave function is subject to anyonlike conditions. The cluster and virial coefficients are considered. Special attention is paid to the case of anyons in the lowest Landau level of a strong magnetic field, when it is possible (i) to prove microscopically the equation of state, in particular in terms of Aharonov-Bohm charge-flux composite systems, and (ii) to formulate the problem in terms of single-state statistical distributions.Comment: Latex, 19 page

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

Exclusion statistics: A resolution of the problem of negative weights

We give a formulation of the single particle occupation probabilities for a system of identical particles obeying fractional exclusion statistics of Haldane. We first derive a set of constraints using an exactly solvable model which describes an ideal exclusion statistics system and deduce the general counting rules for occupancy of states obeyed by these particles. We show that the problem of negative probabilities may be avoided with these new counting rules.Comment: REVTEX 3.0, 14 page

Conductance and Shot Noise for Particles with Exclusion Statistics

The first quantized Landauer approach to conductance and noise is generalized to particles obeying exclusion statistics. We derive an explicit formula for the crossover between the shot and thermal noise limits and argue that such a crossover can be used to determine experimentally whether charge carriers in FQHE devices obey exclusion statistics.Comment: 4 pages, revtex, 1 eps figure 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