The Aharonov–Bohm effect and fractional statistics of distinguishable particles

Abstract

In two-dimensional space, the topological coupling arising between charged particles with attached magnetic fluxes, via the Aharonov–Bohm effect, causes distinguishable particles to effectively acquire quantum statistics: a nontrivial quantum phase is generated when a particle of one species encircles one of a different species. We discuss a number of exact and numerical results concerning distinguishable particles with fractional statistics. Just like for anyons, the spectrum of such particles confined to the lowest Landau level of a strong magnetic field can be found exactly. Then a system of particles in the presence of static magnetic fluxes (equivalent to particles with infinite mass) is considered, and the low-lying states of one particle in the presence of two fluxes and two particles in the presence of one flux are analyzed.