We study the bound-state spectrum of many particles obeying fractional statistics (anyons) in a two-dimensional system in the presence of an external potential and a large magnetic field B. As a function of B, there occur periodic recurrences of quantized states at fixed energy. For fixed particle number, the period is determined by the fractional charge, while at fixed chemical potential, the fractional charge is masked by the fractional statistics. We discuss the relevance of these results to recent experiments in quantum Hall devices, and we propose a simple extension of these experiments which could measure the fractional statistics.

• Received 14 May 1990

DOI:https://doi.org/10.1103/PhysRevLett.65.3369