Equations of motion in the linear approximation

Gauge invariant theory of motion of singularities in linear approximatio

Electromagnetic vortex lines riding atop null solutions of the Maxwell equations

New method of introducing vortex lines of the electromagnetic field is outlined. The vortex lines arise when a complex Riemann-Silberstein vector $({\bm E} + i{\bm B})/\sqrt{2}$ is multiplied by a complex scalar function $\phi$. Such a multiplication may lead to new solutions of the Maxwell equations only when the electromagnetic field is null, i.e. when both relativistic invariants vanish. In general, zeroes of the $\phi$ function give rise to electromagnetic vortices. The description of these vortices benefits from the ideas of Penrose, Robinson and Trautman developed in general relativity.Comment: NATO Workshop on Singular Optics 2003 To appear in Journal of Optics

Gauss-Bonnet black holes with non-constant curvature horizons

We investigate static and dynamical n(\ge 6)-dimensional black holes in Einstein-Gauss-Bonnet gravity of which horizons have the isometries of an (n-2)-dimensional Einstein space with a condition on its Weyl tensor originally given by Dotti and Gleiser. Defining a generalized Misner-Sharp quasi-local mass that satisfies the unified first law, we show that most of the properties of the quasi-local mass and the trapping horizon are shared with the case with horizons of constant curvature. It is shown that the Dotti-Gleiser solution is the unique vacuum solution if the warp factor on the (n-2)-dimensional Einstein space is non-constant. The quasi-local mass becomes constant for the Dotti-Gleiser black hole and satisfies the first law of the black-hole thermodynamics with its Wald entropy. In the non-negative curvature case with positive Gauss-Bonnet constant and zero cosmological constant, it is shown that the Dotti-Gleiser black hole is thermodynamically unstable. Even if it becomes locally stable for the non-zero cosmological constant, it cannot be globally stable for the positive cosmological constant.Comment: 15 pages, 1 figure; v2, discussion clarified and references added; v3, published version; v4, Eqs.(4.22)-(4.24) corrected, which do not change Eqs.(4.25)-(4.27

Schuster and Robinson Reply

A Reply to the Comment by A. C. Egsgaard Madsen, et al

Quantum and classical surface acoustic wave induced magnetoresistance oscillations in a 2D electron gas

We study theoretically the geometrical and temporal commensurability oscillations induced in the resistivity of 2D electrons in a perpendicular magnetic field by surface acoustic waves (SAWs). We show that there is a positive anisotropic dynamical classical contribution and an isotropic non-equilibrium quantum contribution to the resistivity. We describe how the commensurability oscillations modulate the resonances in the SAW-induced resistivity at multiples of the cyclotron frequency. We study the effects of both short-range and long-range disorder on the resistivity corrections for both the classical and quantum non-equilibrium cases. We predict that the quantum correction will give rise to zero-resistance states with associated geometrical commensurability oscillations at large SAW amplitude for sufficiently large inelastic scattering times. These zero resistance states are qualitatively similar to those observed under microwave illumination, and their nature depends crucially on whether the disorder is short- or long-range. Finally, we discuss the implications of our results for current and future experiments on two dimensional electron gases.Comment: 16 pages, 8 figure

Radiation-driven rotational motion of nanoparticles

Focused synchrotron beams can influence a studied sample via heating, or radiation pressure effects due to intensity gradients. The high angular sensitivity of rotational X-ray tracking of crystalline particles via their Bragg reflections can detect extremely small forces such as those caused by field gradients. By tracking the rotational motion of single-crystal nanoparticles embedded in a viscous or viscoelastic medium, the effects of heating in a uniform gradient beam and radiation pressure in a Gaussian profile beam were observed. Changes in viscosity due to X-ray heating were measured for 42 µm crystals in glycerol, and angular velocities of 10-6 rad s-1 due to torques of 10-24 N m were measured for 340 nm crystals in a colloidal gel matrix. These results show the ability to quantify small forces using rotation motion of tracer particles

Probe-diverse ptythography

We propose an extension of ptychography where the target sample is scanned separately through several probes with distinct amplitude and phase profiles and a diffraction image is recorded for each probe and each sample translation. The resulting probe-diverse dataset is used to iteratively retrieve high-resolution images of the sample and all probes simultaneously. The method is shown to yield significant improvement in the reconstructed sample image compared to the image obtained using the standard single-probe ptychographic phase-retrieval scheme