On the 3-anyon harmonics

W.Y Ruan, Tingwan Wu, R.Y Lie +1 more

Weerachart Kilenthong, Virulh Sa-yakanit

In this thesis, the case of two anyons in a harmonic potential in two dimensions is studied by using Feynman path integration. Following Wilczek's ideas, in the concept of the anyon the extraordinary spin and statistics are fractional. Significant applications of anyons are to the fractional quantum Hall effect and anyon superconductivity. Moreover, the configuration space of anyonic systems is multiply connected, and then the path integral is very useful to solve such problems. Nevertheless, there is the alternative approach that can be applied to the same problem, namely, the Chern-Simons construction. By adding the Chern-Simons term into the ordinary Lagrangian, normal particles, particles with the usual statistics, cna become anyons. In this thesis we show that the ground-state energy of two anyons in a harmonic potential can be evaluated both by applying the path integral technique and by the use of the Chern-Simons theory. We show that the complexity of the topology of the anyonic system can be handled readily. It is shown that the ground-state energy of two anyons in a harmonic potential depends on the statistical parameter, alpha, representing the statistics of the anyon.

Stefan V. Mashkevich

Stefan V. Mashkevich, Jan Myrheim, Kåre Olaussen +1 more

M. Sporre, J. J. M. Verbaarschot, Ismail Zahed A

We construct numerically the spectrum of four anyons in a harmonic potential. As a function of the statistical flux, the anyon spectrum interpolates continuously between bosons and fermions. We show that its generic structure follows from semiclassical arguments. The relation of these results to the spectrum of four anyons in a constant magnetic field is also discussed.

H. Mori