Charge and Statistics of Quantum Hall Quasi-Particles. A numerical study of mean values and fluctuations

We present Monte Carlo studies of charge expectation values and charge fluctuations for quasi-particles in the quantum Hall system. We have studied the Laughlin wave functions for quasi-hole and quasi-electron, and also Jain's definition of the quasi-electron wave function. The considered systems consist of from 50 to 200 electrons, and the filling fraction is 1/3. For all quasi-particles our calculations reproduce well the expected values of charge; -1/3 times the electron charge for the quasi-hole, and 1/3 for the quasi-electron. Regarding fluctuations in the charge, our results for the quasi-hole and Jain quasi-electron are consistent with the expected value zero in the bulk of the system, but for the Laughlin quasi-electron we find small, but significant, deviations from zero throughout the whole electron droplet. We also present Berry phase calculations of charge and statistics parameter for the Jain quasi-electron, calculations which supplement earlier studies for the Laughlin quasi-particles. We find that the statistics parameter is more well behaved for the Jain quasi-electron than it is for the Laughlin quasi-electron.Comment: 39 pages, 27 figure

Charge and Statistics of Quasiparticles in Fractional Quantum Hall Effec

We have studied here the charge and statistics of quasiparticle excitations in FQH states on the basis of the Berry phase approach incorporating the fact that even number of flux quanta can be gauged away when the Berry phase is removed to the dynamical phase. It is observed that the charge $q$ and statistical parameter $\theta$ of a quasiparticle at filling factor $\nu=\frac{n}{2pn+1}$ are given by $q=(\frac{n}{2pn+1})e$ and $\theta=\frac{n}{2pn+1}$, with the fact that the charge of the quasihole is opposite to that of the quasielectron. Using Laughlin wave function for quasiparticles, numerical studies have been done following the work of Kj{\o}nsberg and Myrheim \cite{KM} for FQH states at $\nu=1/3$ and it is pointed out that as in case of quasiholes, the statistics parameter can be well defined for quasielectrons having the value $\theta=1/3$.Comment: 12 pages, 4 figure

Classical phase space and statistical mechanics of identical particles

Starting from the quantum theory of identical particles, we show how to define a classical mechanics that retains information about the quantum statistics. We consider two examples of relevance for the quantum Hall effect: identical particles in the lowest Landau level, and vortices in the Chern-Simons Ginzburg-Landau model. In both cases the resulting {\em classical} statistical mechanics is shown to be a nontrivial classical limit of Haldane's exclusion statistics.Comment: 40 pages, Late