DUALITY IN JOSEPHSON-JUNCTION ARRAYS

Various properties of mesoscopic two-dimensional Josephson junction ar rays are reviewed. Particular attention is paid to structure of the to pological excitations, charges and vortices, which are shown to be dua l to each other. This duality persists in the presence of external mag netic 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.