Polarization singularities in the clear sky

Ideas from singularity theory provide a simple account of the pattern of polarization directions in daylight. The singularities (two near the Sun and two near the anti-Sun) are points in the sky where the polarization line pattern has index +1/2 and the intensity of polarization is zero. The singularities are caused by multiple scattering that splits into two each of the unstable index +1 singularities at the Sun and anti-Sun, which occur in the single-dipole scattering (Rayleigh) theory. The polarization lines are contours of an elliptic integral. For the intensity of polarization (unnormalized degree), it is necessary to incorporate the strong depolarizing effect of multiple scattering near the horizon. Singularity theory is compared with new digital images of sky polarization, and gives an excellent description of the pattern of polarization directions. For the intensity of polarization, the theory can reproduce not only the zeros but also subtle variations in the polarization maxima

Vortex lines of the electromagnetic field

Relativistic definition of the phase of the electromagnetic field, involving two Lorentz invariants, based on the Riemann-Silberstein vector is adopted to extend our previous study [I. Bialynicki-Birula, Z. Bialynicka-Birula and C. Sliwa, Phys. Rev. A 61, 032110 (2000)] of the motion of vortex lines embedded in the solutions of wave equations from Schroedinger wave mechanics to Maxwell theory. It is shown that time evolution of vortex lines has universal features; in Maxwell theory it is very similar to that in Schroedinger wave mechanics. Connection with some early work on geometrodynamics is established. Simple examples of solutions of Maxwell equations with embedded vortex lines are given. Vortex lines in Laguerre-Gaussian beams are treated in some detail.Comment: 11 pages, 6 figures, to be published in Phys. Rev.

Universal spectral statistics of Andreev billiards: semiclassical approach

The classification of universality classes of random-matrix theory has recently been extended beyond the Wigner-Dyson ensembles. Several of the novel ensembles can be discussed naturally in the context of superconducting-normal hybrid systems. In this paper, we give a semiclassical interpretation of their spectral form factors for both quantum graphs and Andreev billiards.Comment: final improved version (to be published in Physical Review E), 6 pages, revtex

The JCMT Gould Belt survey: Dense core clusters in Orion B

The James Clerk Maxwell Telescope Gould Belt Legacy Survey obtained SCUBA-2 observations of dense cores within three sub-regions of OrionB: LDN1622, NGC2023/2024, and NGC2068/2071, all of which contain clusters of cores. We present an analysis of the clustering properties of these cores, including the two-point correlation function and Cartwright’s Q parameter. We identify individual clusters of dense cores across all three regions using a minimal spanning tree technique, and find that in each cluster, the most massive cores tend to be centrally located. We also apply the independent M–Σ technique and find a strong correlation between core mass and the local surface density of cores. These two lines of evidence jointly suggest that some amount of mass segregation in clusters has happened already at the dense core stage

Dynamics and Berry phase of two-species Bose-Einstein condensates

In terms of exact solutions of the time-dependent Schrodinger equation for an effective giant spin modeled from a coupled two-mode Bose-Einstein condensate (BEC) with adiabatic and cyclic time-varying Raman coupling between two hyperfine states of the BEC, we obtain analytic time-evolution formulas of the population imbalance and relative phase between two components with various initial states, especially the SU(2)coherent state. We find the Berry phase depending on the number parity of atoms, and particle number dependence of the collapse revival of population-imbalance oscillation. It is shown that self-trapping and phase locking can be achieved from initial SU(2) coherent states with proper parameters.Comment: 18 pages,5 figure

Current correlations and quantum localization in 2D disordered systems with broken time-reversal invariance

We study long-range correlations of equilibrium current densities in a two-dimensional mesoscopic system with the time reversal invariance broken by a random or homogeneous magnetic field. Our result is universal, i.e. it does not depend on the type (random potential or random magnetic field) or correlation length of disorder. This contradicts recent sigma-model calculations of Taras-Semchuk and Efetov (TS&E) for the current correlation function, as well as for the renormalization of the conductivity. We show explicitly that the new term in the sigma-model derived by TS&E and claimed to lead to delocalization does not exist. The error in the derivation of TS&E is traced to an incorrect ultraviolet regularization procedure violating current conservation and gauge invariance.Comment: 8 pages, 3 figure

Coherently Scattering Atoms from an Excited Bose-Einstein Condensate

We consider scattering atoms from a fully Bose-Einstein condensed gas. If we take these atoms to be identical to those in the Bose-Einstein condensate, this scattering process is to a large extent analogous to Andreev reflection from the interface between a superconducting and a normal metal. We determine the scattering wave function both in the absence and the presence of a vortex. Our results show a qualitative difference between these two cases that can be understood as due to an Aharonov-Bohm effect. It leads to the possibility to experimentally detect and study vortices in this way.Comment: 5 pages of ReVTeX and 2 postscript figure

Globally-Linked Vortex Clusters in Trapped Wave Fields

We put forward the existence of a rich variety of fully stationary vortex structures, termed H-clusters, made of an increasing number of vortices nested in paraxial wave fields confined by trapping potentials. However, we show that the constituent vortices are globally linked, rather than products of independent vortices. Also, they always feature a monopolar global wave front and exist in nonlinear systems, such as Bose-Einstein condensates. Clusters with multipolar global wave fronts are non-stationary or at best flipping.Comment: 4 pages, 5 PostScript figure

A Solvable Regime of Disorder and Interactions in Ballistic Nanostructures, Part I: Consequences for Coulomb Blockade

We provide a framework for analyzing the problem of interacting electrons in a ballistic quantum dot with chaotic boundary conditions within an energy $E_T$ (the Thouless energy) of the Fermi energy. Within this window we show that the interactions can be characterized by Landau Fermi liquid parameters. When $g$, the dimensionless conductance of the dot, is large, we find that the disordered interacting problem can be solved in a saddle-point approximation which becomes exact as $g\to\infty$ (as in a large-N theory). The infinite $g$ theory shows a transition to a strong-coupling phase characterized by the same order parameter as in the Pomeranchuk transition in clean systems (a spontaneous interaction-induced Fermi surface distortion), but smeared and pinned by disorder. At finite $g$, the two phases and critical point evolve into three regimes in the $u_m-1/g$ plane -- weak- and strong-coupling regimes separated by crossover lines from a quantum-critical regime controlled by the quantum critical point. In the strong-coupling and quantum-critical regions, the quasiparticle acquires a width of the same order as the level spacing $\Delta$ within a few $\Delta$'s of the Fermi energy due to coupling to collective excitations. In the strong coupling regime if $m$ is odd, the dot will (if isolated) cross over from the orthogonal to unitary ensemble for an exponentially small external flux, or will (if strongly coupled to leads) break time-reversal symmetry spontaneously.Comment: 33 pages, 14 figures. Very minor changes. We have clarified that we are treating charge-channel instabilities in spinful systems, leaving spin-channel instabilities for future work. No substantive results are change

Sequential design of computer experiments for the estimation of a probability of failure

This paper deals with the problem of estimating the volume of the excursion set of a function $f:\mathbb{R}^d \to \mathbb{R}$ above a given threshold, under a probability measure on $\mathbb{R}^d$ that is assumed to be known. In the industrial world, this corresponds to the problem of estimating a probability of failure of a system. When only an expensive-to-simulate model of the system is available, the budget for simulations is usually severely limited and therefore classical Monte Carlo methods ought to be avoided. One of the main contributions of this article is to derive SUR (stepwise uncertainty reduction) strategies from a Bayesian-theoretic formulation of the problem of estimating a probability of failure. These sequential strategies use a Gaussian process model of $f$ and aim at performing evaluations of $f$ as efficiently as possible to infer the value of the probability of failure. We compare these strategies to other strategies also based on a Gaussian process model for estimating a probability of failure.Comment: This is an author-generated postprint version. The published version is available at http://www.springerlink.co