Non-Abelian Chern-Simons particles in an external magnetic field

The quantum mechanics and thermodynamics of SU(2) non-Abelian Chem-Simons p articles (non-Abelian anyons) in an external magnetic field are addressed. We derive the N-body Hamiltonian in the (anti-)holomorphic gauge when the H ilbert space is projected onto the lowest Landau level of the magnetic fiel d. In the presence of an additional harmonic potential, the N-body spectrum depends linearly on the coupling (statistics) parameter. We calculate the second virial coefficient and find that in the strong magnetic field limit it develops a step-wise behavior as a function of the statistics parameter, in contrast to the linear dependence in the case of Abelian anyons. For sm all enough values of the statistics parameter we relate the N-body partitio n functions in the lowest Landau level to those of SU(2) bosons and find th at the cluster land virial) coefficients dependence on the statistics param eter cancels. (C) 1999 Elsevier Science B.V. All rights reserved.