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

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

Haldane exclusion statistics and second virial coefficient

We show that Haldanes new definition of statistics, when generalised to infinite dimensional Hilbert spaces, is equal to the high temperature limit of the second virial coefficient. We thus show that this exclusion statistics parameter, g , of anyons is non-trivial and is completely determined by its exchange statistics parameter $\alpha$. We also compute g for quasiparticles in the Luttinger model and show that it is equal to $\alpha$.Comment: 11 pages, REVTEX 3.

Fractional Exclusion Statistics and Anyons

Do anyons, dynamically realized by the field theoretic Chern-Simons construction, obey fractional exclusion statistics? We find that they do if the statistical interaction between anyons and anti-anyons is taken into account. For this anyon model, we show perturbatively that the exchange statistical parameter of anyons is equal to the exclusion statistical parameter. We obtain the same result by applying the relation between the exclusion statistical parameter and the second virial coefficient in the non-relativistic limit.Comment: 9 pages, latex, IFT-498-UN

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

Persistent current in a one-dimensional ring of fractionally charged "exclusons''

The Aharonov-Bohm effect in a one-dimensional (1D) ring containing a gas of fractionally charged excitations is considered. It is shown that the low temperature behavior of the system is identical to that of free electrons with (integer) charge $e$. This is a direct consequence of the fact that the total charge in the ring is quantized in units of the electron charge. Anomalous oscillations of the persistent current amplitude with temperature are predicted to occur as a direct manifistation of the fractional nature of the quasiparticle charge. A 1D conducting ring with gate induced periodical potential is discussed as a possible set-up for an experimental observation of the predicted phenomenon.Comment: 4 pages, RevTex, uuencoded figure

Exclusonic Quasiparticles and Thermodynamics of Fractional Quantum Hall Liquids

Quasielectrons and quasiholes in the fractional quantum Hall liquids obey fractional (including nontrivial mutual) exclusion statistics. Their statistics matrix can be determined from several possible state-counting scheme, involving different assumptions on statistical correlations. Thermal activation of quasiparticle pairs and thermodynamic properties of the fractional quantum Hall liquids near fillings $1/m$ ($m$ odd) at low temperature are studied in the approximation of generalized ideal gas. The existence of hierarchical states in the fractional quantum Hall effect is shown to be a manifestation of the exclusonic nature of the relevant quasiparticles. For magnetic properties, a paramagnetism-diamagnetism transition appears to be possible at finite temperature.Comment: latex209, REVTE