Incompressible quantum states in Josephson junction arrays

We consider arrays of small Josephson junctions (Ec ∼ Ej) in the case of small and uniform charge and flux frustrations. The dynamics of this system can be described in terms of interacting quantum particles-charges (for small Ej) or vortices (for large Ej). We show that at low concentrations of the particles, i.e. in the limit of a short range interaction, the system is intimately related to the hard core bosons in the fractional quantum Hall regime. In particular, the ground state can be described by the Laughlin type wave function Ψ(f)m = IIiuniversal values (2e)2/hm (for small Ej).