Beyond lowest order mean-field theory for light interacting with atom arrays

Light propagation beyond the mean-field theory of standard optics.

With ready access to massive computer clusters we may now study light propagation in a dense cold atomic gas by means of basically exact numerical simulations. We report on a direct comparison between traditional optics, that is, electrodynamics of a polarizable medium, and numerical simulations in an elementary problem of light propagating through a slab of matter. The standard optics fails al...

Mean Field Theory for Josephson Junction Arrays with Charge Frustration

Using the path integral approach, we provide an explicit derivation of the equation for the phase boundary for quantum Josephson junction arrays with offset charges and non-diagonal capacitance matrix. For the model with nearest neighbor capacitance matrix and uniform offset charge q/2e = 1/2, we determine, in the low critical temperature expansion, the most relevant contributions to the equati...

Beyond Gross-Pitaevskii Mean Field Theory

Mean-field theory for arrays of Josephson-coupled wires

We describe a mean-field theory for phase transitions in a Josephson junction array consisting of two sets of parallel wire networks, arranged at right angles and coupled together by Josephson interactions. In contrast to earlier treatments, we include the variation of the superconducting phase along the individual wires; such variation is always present if the wires have finite thickness and a...

Mean-field theory of statistical assemblies of sterically interacting lines

2014 Statistical assemblies of lines on simple cubic lattices are considered. Beginning with a gas of diffusion loops we add steric interaction and chains. The interaction is treated by a mean-field ansatz strictly valid only for d > 4. Phase transitions are characterized by the appearance of infinite lines. The formalism can be applied to thermally equilibrated polymers, defect models of ...