Self-dual Ginzburg-Landau vortices in a disk

We study the properties of the Ginzburg-Laundau model in the self-dual point for a two-dimensional finite system . By a numerical calculation we analyze the solutions of the Euler-Lagrange equations for a cylindrically symmetric ansatz. We also study the self-dual equations for this case. We find that the minimal energy configurations are not given by the Bogomol'nyi equations but by solutions to the Euler Lagrange ones. With a simple approximation scheme we reproduce the result of the numerical calculation.Comment: 8 pages, 4 figures, RevTex macro

Three-dimensionality in quasi-two dimensional flows: recirculations and barrel effects

A scenario is put forward for the appearance of three-dimensionality both in quasi-2D rotating flows and quasi-2D magnetohydrodynamic (MHD) flows. We show that 3D recirculating flows and currents originate in wall boundary layers and that, unlike in ordinary hydrodynamic flows, they cannot be ignited by confinement alone. They also induce a second form of three-dimensionality with quadratic variations of velocities and current across the channel. This scenario explains both the common tendency of these flows to two-dimensionality and the mechanisms of the recirculations through a single formal analogy covering a wide class of flow including rotating and MHD flows. These trans-disciplinary effects are thus active in atmospheres, oceans or the cooling blankets of nuclear fusion reactors.Comment: 6 pages, 1 Figur

Effect of connecting wires on the decoherence due to electron-electron interaction in a metallic ring

We consider the weak localization in a ring connected to reservoirs through leads of finite length and submitted to a magnetic field. The effect of decoherence due to electron-electron interaction on the harmonics of AAS oscillations is studied, and more specifically the effect of the leads. Two results are obtained for short and long leads regimes. The scale at which the crossover occurs is discussed. The long leads regime is shown to be more realistic experimentally.Comment: LaTeX, 4 pages, 4 eps figure

Vortex nucleation through edge states in finite Bose-Einstein condensates

We study the vortex nucleation in a finite Bose-Einstein condensate. Using a set of non-local and chiral boundary conditions to solve the Schr$\ddot{o}$dinger equation of non-interacting bosons in a rotating trap, we obtain a quantitative expression for the characteristic angular velocity for vortex nucleation in a condensate which is found to be 35% of the transverse harmonic trapping frequency.Comment: 24 pages, 8 figures. Both figures and the text have been revise

Anderson localization of a Bose-Einstein condensate in a 3D random potential

We study the effect of Anderson localization on the expansion of a Bose-Einstein condensate, released from a harmonic trap, in a 3D random potential. We use scaling arguments and the self-consistent theory of localization to show that the long-time behavior of the condensate density is controlled by a single parameter equal to the ratio of the mobility edge and the chemical potential of the condensate. We find that the two critical exponents of the localization transition determine the evolution of the condensate density in time and space.Comment: 4 pages, 2 figure

Transverse confinement of waves in 3D random media

We study the transmission of a tightly focused beam through a thick slab of 3D disordered medium in the Anderson localized regime. We show that the transverse profile of the transmitted beam exhibits clear signatures of Anderson localization and that its mean square width provides a direct measure of the localization length. For a short incident pulse, the width is independent of absorption.Comment: 4 pages, 3 figure

Mesoscopic scattering of spin s particles

Quantum effects in weakly disordered systems are governed by the properties of the elementary interaction between propagating particles and impurities. Long range mesoscopic effects due to multiple scattering are derived by iterating the single scattering vertex, which has to be appropriately diagonalized. In the present contribution, we present a systematic and detailed diagonalisation of the diffuson and cooperon vertices responsible for weak localisation effects. We obtain general expressions for eigenvalues and projectors onto eigenmodes, for any spin and arbitrary elementary interaction with impurities. This description provides a common frame for a unified theory of mesoscopic spin physics for electrons, photons, and other quantum particles. We treat in detail the case of spin-flip scattering of electrons by freely orientable magnetic impurities and briefly review the case of photon scattering from degenerate dipole transitions in cold atomic gases.Comment: published version, with a new figure and new section

Heat Capacity of Mesoscopic Superconducting Disks

We study the heat capacity of isolated giant vortex states, which are good angular momentum ($L$) states, in a mesoscopic superconducting disk using the Ginzburg-Landau (GL) theory. At small magnetic fields the $L$=0 state qualitatively behaves like the bulk sample characterized by a discontinuity in heat capacity at $T_c$. As the field is increased the discontinuity slowly turns into a continuous change which is a finite size effect. The higher $L$ states show a continuous change in heat capacity at $T_c$ at all fields. We also show that for these higher $L$ states, the behavior of the peak position with change in field is related to the paramagnetic Meissner effect (irreversible) and can lead to an unambiguous observation of positive magnetization in mesoscopic superconductors.Comment: Final versio

Hanbury Brown and Twiss Correlations of Anderson Localized Waves

When light waves propagate through disordered photonic lattices, they can eventually become localized due to multiple scattering effects. Here we show experimentally that while the evolution and localization of the photon density distribution is similar in the two cases of diagonal and off-diagonal disorder, the density-density correlation carries a distinct signature of the type of disorder. We show that these differences reflect a symmetry in the spectrum and eigenmodes that exists in off-diagonally disordered lattices but is absent in lattices with diagonal disorder.Comment: 4 pages, 3 figures, comments welcom

Energy levels and their correlations in quasicrystals

Quasicrystals can be considered, from the point of view of their electronic properties, as being intermediate between metals and insulators. For example, experiments show that quasicrystalline alloys such as AlCuFe or AlPdMn have conductivities far smaller than those of the metals that these alloys are composed from. Wave functions in a quasicrystal are typically intermediate in character between the extended states of a crystal and the exponentially localized states in the insulating phase, and this is also reflected in the energy spectrum and the density of states. In the theoretical studies we consider in this review, the quasicrystals are described by a pure hopping tight binding model on simple tilings. We focus on spectral properties, which we compare with those of other complex systems, in particular, the Anderson model of a disordered metal.Comment: 15 pages including 19 figures. Review article, submitted to Phil. Ma