Flat lens without optical axis: Theory of imaging

We derive a general theory for imaging by a flat lens without optical axis. We show that the condition for imaging requires a material having elliptic dispersion relations with negative group refraction, equivalent to an effective anisotropic refractive index n(theta). Imaging can be achieved with both negative (n0) refractive indices. The Veselago-Pendry lens is a special case with isotropic negative refractive index of n(theta)=-1. Realizations of the imaging conditions using anisotropic media and inhomogeneous media, particularly photonic crystals, are discussed. Numerical examples of imaging and requirements for sub-wavelength imaging are also presented.Comment: 5 pages, 4 figure

GRB 060206: hints of precession of the central engine?

Aims. The high-redshift (z=4.048) gamma-ray burst GRB 060206 showed unusual behavior, with a significant rebrightening by a factor of ~4 at about 3000 s after the burst. We argue that this rebrightening implies that the central engine became active again after the main burst produced by the first ejecta, then drove another more collimated jet-like ejecta with a larger viewing angle. The two ejecta both interacted with the ambient medium, giving rise to forward shocks that propagated into the ambient medium and reverse shocks that penetrated into the ejecta. The total emission was a combination of the emissions from the reverse- and forward- shocked regions. We discuss how this combined emission accounts for the observed rebrightening. Methods. We apply numerical models to calculate the light curves from the shocked regions, which include a forward shock originating in the first ejecta and a forward-reverse shock for the second ejecta. Results. We find evidence that the central engine became active again 2000 s after the main burst. The combined emission produced by interactions of these two ejecta with the ambient medium can describe the properties of the afterglow of this burst. We argue that the rapid rise in brightness at ~3000 s in the afterglow is due to the off-axis emission from the second ejecta. The precession of the torus or accretion disk of the central engine is a natural explanation for the departure of the second ejecta from the line of sight

GRB 060206: Evidence of Precession of Central Engine

The high-redshift (z = 4.048) gamma-ray burst GRB 060206 showed unusual behavior, with a significant re-brightening about 3000 s after the burst. We assume that the central engine became active again 2000 s after the main burst and drove another more collimated off-axis jet. The two jets both interacted with the ambient medium and contributed to the whole emission. We numerically fit this optical afterglow from the two jets using the forward-shock model and the forward-reverse shock model. Combining with the zero time effect, we suggest that the fast rise at ~3000 s in the afterglow was due to the off-axis emission from the second jet. The precession of the torus or accretion disk of the gamma ray burst engine is the natural explanation for the symmetry axes of these two jets not to lie on the same line

Negative refraction and plano-concave lens focusing in one-dimensional photonic crystals

Negative refraction is demonstrated in one-dimensional (1D) dielectric photonic crystals (PCs) at microwave frequencies. Focusing by plano-concave lens made of 1D PC due to negative refraction is also demonstrated. The frequency-dependent negative refractive indices, calculated from the experimental data matches very well with those determined from band structure calculations. The easy fabrication of one-dimensional photonic crystals may open the door for new applications.Comment: 3 pages and 5 figure

Generalized Fibonacci numbers and dimer statistics

We establish new product identities involving the $q$-analogue of the Fibonacci numbers. We show that the identities lead to alternate expressions of generating functions for close-packed dimers on non-orientable surfaces.Comment: 4 pages, no figure, International Symposium on Frontiers of Science - In celebration of the 80th birthday of C. N. Yang, to appear in Modern Physics Letters

Superconductivity mediated by the antiferromagnetic spin-wave in chalcogenide iron-base superconductors

The ground state of K$_{0.8+x}$Fe$_{1.6+y}$Se$_2$ and other iron-based selenide superconductors are doped antiferromagnetic semiconductors. There are well defined iron local moments whose energies are separated from those of conduction electrons by a large band gap in these materials. We propose that the low energy physics of this system is governed by a model Hamiltonian of interacting electrons with on-site ferromagnetic exchange interactions and inter-site superexchange interactions. We have derived the effective pairing potential of electrons under the linear spin-wave approximation and shown that the superconductivity can be driven by mediating coherent spin wave excitations in these materials. Our work provides a natural account for the coexistence of superconducting and antiferromagnetic long range orders observed by neutron scattering and other experiments.Comment: 4 pages, 3 figure

The Cosmic Evolution of Faint Satellite Galaxies as a Test of Galaxy Formation and the Nature of Dark Matter

The standard cosmological model based on cold dark matter (CDM) predicts a large number of subhalos for each galaxy-size halo. It is well known that matching the subhalos to the observed properties of luminous satellites of galaxies in the local universe poses a significant challenge to our understanding of the astrophysics of galaxy formation. We show that the cosmic evolution and host mass dependence of the luminosity function of satellites provides a powerful new diagnostic to disentangle astrophysical effects from variations in the underlying dark matter mass function. We illustrate this by comparing the results of recent observations of satellites out to $z=0.8$ based on Hubble Space Telescope images with the predictions of three different sets of state-of-the art semi-analytic models with underlying CDM power spectra and one semi-analytic model with an underlying Warm Dark Matter (WDM) power spectrum. We find that even though CDM models provide a reasonable fit to the local luminosity function of satellites around galaxies comparable or slightly larger than the Milky Way, they do not reproduce the data as well for different redshift and host galaxy stellar mass. This tension indicates that further improvements are likely to be needed in the description of star formation if the models are to be reconciled with the data. The WDM model matches the observed mass dependence and redshift evolution of satellite galaxies more closely than any of the CDM models, indicating that a modification of the underlying power spectrum may offer an alternative solution to this tension. We conclude by presenting predictions for the color magnitude relation of satellite galaxies to demonstrate how future observations will be able to further distinguish between these models and help constrain baryonic and non-baryonic physics.Comment: Accepted for publication in ApJ, revised to incorporate referee comment

Duality between quantum and classical dynamics for integrable billiards

We establish a duality between the quantum wave vector spectrum and the eigenmodes of the classical Liouvillian dynamics for integrable billiards. Signatures of the classical eigenmodes appear as peaks in the correlation function of the quantum wave vector spectrum. A semiclassical derivation and numerical calculations are presented in support of the results. These classical eigenmodes can be observed in physical experiments through the auto-correlation of the transmission coefficient of waves in quantum billiards. Exact classical trace formulas of the resolvent are derived for the rectangle, equilateral triangle, and circle billiards. We also establish a correspondence between the classical periodic orbit length spectrum and the quantum spectrum for integrable polygonal billiards.Comment: 12 pages, 4 figure