A ring-shaped array of Bose-Einstein condensed atomic gases can display
circular currents if the relative phase of neighboring condensates becomes
locked to certain values. It is shown that, irrespective of the mechanism
responsible for generating these states, only a restricted set of currents are
stable, depending on the number of condensates, on the interaction and
tunneling energies, and on the total number of particles. Different
instabilities due to quasiparticle excitations are characterized and possible
experimental setups for testing the stability prediction are also discussed.Comment: 7 pages, REVTex