Realization of Haldane's Exclusion Statistics in a Model of Electron-Phonon Interactions

We discuss an integrable model describing one-dimensional electrons interacting with two-dimensional anharmonic phonons. In the low temperature limit it is possible to decouple phonons and consider one-dimensional excitations separately. They have a trivial two-body scattering matrix and obey fractional statistics. As far as we know the original model presents the first example of a model with local bare interactions generating purely statistical interactions between renormalized particles. As a by-product we obtain non-trivial thermodynamic equations for the interacting system of two-dimensional phonons.Comment: 4 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

`Composite particles' and the eigenstates of Calogero-Sutherland and Ruijsenaars-Schneider

We establish a one-to-one correspondance between the ''composite particles'' with $N$ particles and the Young tableaux with at most $N$ rows. We apply this correspondance to the models of Calogero-Sutherland and Ruijsenaars-Schneider and we obtain a momentum space representation of the ''composite particles'' in terms of creation operators attached to the Young tableaux. Using the technique of bosonisation, we obtain a position space representation of the ''composite particles'' in terms of products of vertex operators. In the special case where the ''composite particles'' are bosons and if we add one extra quasiparticle or quasihole, we construct the ground state wave functions corresponding to the Jain series $\nu =p/(2np\pm 1)$ of the fractional quantum Hall effect.Comment: latex calcomp2.tex, 5 files, 30 pages [SPhT-T99/080], submitted to J. Math. Phy

Haldane's Fractional Statistics and the Lowest Landau Level on a Torus

The Lowest Landau Level on a torus is studied. The dimension of the many-body Hilbert space is obtained and is found to be different from the formula given by Haldane. Our result can be tested in numerical investigations of the low-energy spectrum of fractional quantum Hall states on a torus.Comment: 4 pages, Revtex. Small modifications. The modified version to appear in Phys. Rev. Lett., Feb., 199

Exclusion statistics,operator algebras and Fock space representations

We study exclusion statistics within the second quantized approach. We consider operator algebras with positive definite Fock space and restrict them in a such a way that certain state vectors in Fock space are forbidden ab initio.We describe three characteristic examples of such exclusion, namely exclusion on the base space which is characterized by states with specific constraint on quantum numbers belonging to base space M (e.g. Calogero-Sutherland type of exclusion statistics), exclusion in the single-oscillator Fock space, where some states in single oscillator Fock space are forbidden (e.g. the Gentile realization of exclusion statistics) and a combination of these two exclusions (e.g. Green's realization of para-Fermi statistics). For these types of exclusions we discuss extended Haldane statistics parameters g, recently introduced by two of us in Mod.Phys.Lett.A 11, 3081 (1996), and associated counting rules. Within these three types of exclusions in Fock space the original Haldane exclusion statistics cannot be realized.Comment: Latex,31 pages,no figures,to appear in J.Phys.A : Math.Ge

Approximate formula for the ground state energy of anyons in 2D parabolic well

We determine approximate formula for the ground state energy of anyons in 2D parabolic well which is valid for the arbitrary anyonic factor \nu and number of particles N in the system. We assume that centre of mass motion energy is not excluded from the energy of the system. Formula for ground state energy calculated by variational principle contains logarithmic divergence at small distances between two anyons which is regularized by cut-off parameter. By equating this variational formula to the analogous formula of Wu near bosonic limit (\nu ~ 0)we determine the value of the cut-off and thus derive the approximate formula for the ground state energy for the any \nu and N. We checked this formula at \nu=1, when anyons become fermions, for the systems containing two to thirty particles. We find that our approximate formula has an accuracy within 6%. It turns out, at the big number N limit the ground state energy has square root dependence on factor \nu.Comment: 7 page

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

Perturbative Renormalizations of Anyon Quantum Mechanics

In bosonic end perturbative calculations for quantum mechanical anyon systems a regularization and renormalization procedure, analogous to those used in field theory, is necessary. I examine the reliability and the physical interpretation of the most commonly used bosonic end regularization procedures. I then use the regularization procedure with the most transparent physical interpretation to derive some bosonic end perturbation theory results on anyon spectra, including a 3-anyon ground state energy.Comment: 19 pages, Plain LaTex, MIT-CTP-232

Calculation of the Aharonov-Bohm wave function

A calculation of the Aharonov-Bohm wave function is presented. The result is a series of confluent hypergeometric functions which is finite at the forward direction.Comment: 12 pages in LaTeX, and 3 PostScript figure

Finite-size anyons and perturbation theory

We address the problem of finite-size anyons, i.e., composites of charges and finite radius magnetic flux tubes. Making perturbative calculations in this problem meets certain difficulties reminiscent of those in the problem of pointlike anyons. We show how to circumvent these difficulties for anyons of arbitrary spin. The case of spin 1/2 is special because it allows for a direct application of perturbation theory, while for any other spin, a redefinition of the wave function is necessary. We apply the perturbative algorithm to the N-body problem, derive the first-order equation of state and discuss some examples.Comment: 18 pages (RevTex) + 4 PS figures (all included); a new section on equation of state adde