The Bose-Hubbard model:: from Josephson junction arrays to optical lattices

The Bose-Hubbard model is a paradigm for the study of strongly correlated bosonic systems. We review some of its properties with emphasis on the implications on quantum phase transitions of Josephson junction arrays and quantum dynamics of topological excitations as well as the properties of ultra-cold atoms in optical lattices. (c) 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.