Duality in Josephson junction arrays

Various properties of mesoscopic two-dimensional Josephson junction arrays are reviewed. Particular attention is paid to structure of the topological excitations, charges and vortices, which are shown to be dual to each other. This duality persists in the presence of external magnetic fields and offset charges, which influence vortices and charges in an equivalent way. A double-layer junction array is also considered, where an even further reaching duality is discovered.