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We investigate the properties of strongly interacting bosons in two dimensions at zero temperature using mean-field theory, a variational Ansatz for the ground state wave function, and Monte Carlo methods. With on-site and short-range interactions a rich phase diagram is obtained. Apart from the homogeneous superfluid and Mott-insulating phases, inhomogeneous chargedensity wave phases appear, that are stabilized by the finite-range interaction.Furthermore, our analysis demonstrates the existence of a supersolid phase, in which both long-range order (related to the charge-density wave) and offdiagonal long-range order coexist. We also obtain the critical exponents for the various phase transitions.

We present a microscopic derivation of the equation of motion for a vortex in a superconductor. A coherent view on vortex dynamics is obtained, in which both hydrodynamics and the vortex core contribute to the forces acting on a vortex. The competition between these two provides an interpretation of the observed sign change in the Hall angle in superconductors with mean free path l of the order of the coherence length ξ in terms of broken particlehole symmetry, which is related to details of the microscopic mechanism of superconductivity.Typeset using REVT E X 1

We study the superconductor-insulator transition of a 2-dimensional Bose-Hubbard model, considering as a speci c example, an array of Josephson junctions. Within a coarse-graining approach w e derive an e ective free-energy functional from which w e determine the phase diagram. At zero temperature it consists of a superconducting phase and Mott-insulating lobes. The phase boundaries of some of these lobes display reentrant behaviour as a function of temperature. Next, we e v aluate the electromagnetic response functions of the system. The real part of the longitudinal conductivity i s c haracterized by an excitation gap, whereas the imaginary part describes a capacitor. In an ideal system, under certain conditions a universal conductance is found at the transition. If we add low frequency dissipation to the model a di erent v alue of the universal conductance is found, but still it is independent of the strength of the dissipation. Qualitatively di ering results are obtained for frustrated and unfrustrated systems. We also discuss the Hall conductance of the system. PACS numbers: 72.20.-i 74.65.+n