Abstract:
We discuss the problem of N anyons in harmonic well, and derive the semi-classical spectrum as an exactly solvable limit of the many-anyon Hamiltonian. The relevance of our result to the solution of the anyon-gas model is discussed.

Abstract:
The anyon exciton model is generalized to the case of a neutral exciton consisting of a valence hole and an arbitrary number N of fractionally-charged quasielectrons (anyons). A complete set of exciton basis functions is obtained and these functions are classified using a result from the theory of partitions. Expressions are derived for the inter-particle interaction matrix elements of a six-particle system (N=5), which describes an exciton against the background of an incompressible quantum liquid with filling factor 2/5. Several exact results are obtained in a boson approximation, including the binding energy of a (N+1)-particle exciton with zero in-plane momentum and zero internal angular momentum.

Abstract:
The issue of the thermodynamics of a system of distinguishable particles is discussed in this paper. In constructing the statistical mechanics of distinguishable particles from the definition of Boltzmann entropy, it is found that the entropy is not extensive. The inextensivity leads to the so-called Gibbs paradox in which the mixing entropy of two identical classical gases increases. Lots of literature from different points of view were created to resolve the paradox. In this paper, starting from the Boltzmann entropy, we present the thermodynamics of the system of distinguishable particles. A straightforward way to get the corrected Boltzmann counting is shown. The corrected Boltzmann counting factor can be justified in classical statistical mechanics.

Abstract:
The issue of the thermodynamics of a system of distinguishable particles is discussed in this paper. In constructing the statistical mechanics of distinguishable particles from the definition of Boltzmann entropy, it is found that the entropy is not extensive. The inextensivity leads to the so-called Gibbs paradox in which the mixing entropy of two identical classical gases increases. Lots of literature from different points of view were created to resolve the paradox. In this paper, starting from the Boltzmann entropy, we present the thermodynamics of the system of distinguishable particles. A straightforward way to get the corrected Boltzmann counting is shown. The corrected Boltzmann counting factor can be justified in classical statistical mechanics.

Abstract:
Evaluating the propagator by the usual time-sliced manner, we use it to compute the second virial coefficient of an anyon gas interacting through the repulsive potential of the form $g/r^2 (g > 0)$. All the cusps for the unpolarized spin-1/2 as well as spinless cases disappear in the $\omega \to 0$ limit, where $\omega$ is a frequency of harmonic oscillator which is introduced as a regularization method. As $g$ approaches to zero, the result reduces to the noninteracting hard-core limit.

Abstract:
A new model for anyon is proposed, which exhibits the classical analogue of the quantum phenomenon - Zitterbewegung. The model is derived from existing spinning particle model and retains the essential features of anyon in the non-relativistic limit.

Abstract:
In this letter we study 1+1 anyon fields at finite temperature and density with non-vanishing chemical potentials. Our approach is based on an operator formalism for bosonization at finite temperature; the correlation functions for the system are given in an explicit form. Two are the main results of this construction: we point out the existence of persistent currents in 1+1 anyon systems; from the analysis of 2-point anyon field correlation function, a remarkable and new condensation phenomenon in momentum space is discovered. As a concrete example, the above formalism is applied to the Thirring model.

Abstract:
In this set of lectures, we give a pedagogical introduction to the subject of anyons. We discuss 1) basic concepts in anyon physics, 2) quantum mechanics of two anyon systems, 3) statistical mechanics of many anyon systems, 4) mean field approach to many anyon systems and anyon superconductivity, 5) anyons in field theory and 6) anyons in the Fractional Quantum Hall Effect (FQHE). (Based on lectures delivered at the VII SERC school in High Energy Physics at the Physical Research Laboratory, Ahmedabad, January 1992 and at the I SERC school in Statistical Mechanics at Puri, February 1994.)

Abstract:
We develop the concept of trajectories in anyon spectra, i.e., the continuous dependence of energy levels on the kinetic angular momentum. It provides a more economical and unified description, since each trajectory contains an infinite number of points corresponding to the same statistics. For a system of non-interacting anyons in a harmonic potential, each trajectory consists of two infinite straight line segments, in general connected by a nonlinear piece. We give the systematics of the three-anyon trajectories. The trajectories in general cross each other at the bosonic/fermionic points. We use the (semi-empirical) rule that all such crossings are true crossings, i.e.\ the order of the trajectories with respect to energy is opposite to the left and to the right of a crossing.

Abstract:
Bosonic end perturbative calculations for quantum mechanical anyon systems require a regularization. I regularize by adding a specific $\delta$-function potential to the Hamiltonian. The reliability of this regularization procedure is verified by comparing its results for the 2-anyon in harmonic potential system with the known exact solutions. I then use the $\delta$-function regularized bosonic end perturbation theory to test some recent conjectures concerning the unknown portion of the many-anyon spectra.