Quantum mechanics of anyons on a torus

We study a system of anyons on a torus, which are defined as nonrelativistic particles, and can be either bosons or fermions, coupled to a U(1) Chern-Simons field representing the dynamics of an intermediate statistics superposed to the original one. In the case of bosons we find the exact ground state for given total momentum, in the case of fermions we succeed in finding all the momentum and energy eigenstates of a translationally invariant mean field hamiltonian, which approximates the exact one for high densities. In the latter case we find particular momentum eigenstates, for which the energy has a sharp minimum, representing macroscopically quantized motions of the anyon fluid along a handle, which have the features of supercurrents. We also compute the corresponding magnetic field. © 1990.