International Journal of Modern Physics B

ANYONS IN A MAGNETIC FIELD

A. Karlhede, E. Westerberg

Published May 20, 1992• 10 citations

Abstract

We consider N anyons, with statistical parameter ν, in a homogeneous magnetic fieldand discuss exact and perturbative solutions. We show that the energy, E(ν), obeys[Formula: see text] for any bose or fermi state and that the extremal cases correspondto the states where the relative angular momenta of all pairs of particles are negativeand non-negative, respectively. The anyonic continuations of these extremal states aregiven, their energy is linear in ν. We conjecture that the above bounds on [Formula: see text] hold forany ν. This implies that the energy of any many-anyon state decreases monotonicallywith the statistical parameter ν (ν taking any real value). For small enough ν, E=const. [Formula: see text] and the wave function is known. Increasing ν, the wave functionbecomes singular at some bose point. In the following intermediate region (which maybe absent), E(ν) decreases more slowly; the exact form of E(ν) and the wave functionare unknown. Increasing ν further, above some bose point the energy becomes constantand the wave function is again known.

DOI: 10.1142/s0217979292000797

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