Diffusion at constant speed in a model phase space

We reconsider the problem of diffusion of particles at constant speed and present a generalization of the Telegrapher process to higher dimensional stochastic media ($d>1$), where the particle can move along $2^d$ directions. We derive the equations for the probability density function using the ``formulae of differentiation'' of Shapiro and Loginov. The model is an advancement over similiar models of photon migration in multiply scattering media in that it results in a true diffusion at constant speed in the limit of large dimensions.Comment: Final corrected version RevTeX, 6 pages, 1 figur

Near Field Lenses in Two Dimensions

It has been shown that a slab of materials with refractive index = -1 behaves like a perfect lens focussing all light to an exact electromagnetic copy of an object. The original lens is limited to producing images the same size as the object, but here we generalise the concept so that images can be magnified. For two dimensional systems, over distances much shorter than the free space wavelength, we apply conformal transformations to the original parallel sided slab generating a variety of new lenses. Although the new lenses are not `perfect' they are able to magnify two dimensional objects. The results apply equally to imaging of electric or magnetic sub wavelength objects in two dimensions. The concepts have potential applications ranging from microwave frequencies to the visible.Comment: PDF fil

Imaging the Near Field

In an earlier paper we introduced the concept of the perfect lens which focuses both near and far electromagnetic fields, hence attaining perfect resolution. Here we consider refinements of the original prescription designed to overcome the limitations of imperfect materials. In particular we show that a multi-layer stack of positive and negative refractive media is less sensitive to imperfections. It has the novel property of behaving like a fibre-optic bundle but one that acts on the near field, not just the radiative component. The effects of retardation are included and minimized by making the slabs thinner. Absorption then dominates image resolution in the near-field. The deleterious effects of absorption in the metal are reduced for thinner layers.Comment: RevTeX, (9 pages, 8 figures

Complete controllability of quantum systems

Sufficient conditions for complete controllability of $N$-level quantum systems subject to a single control pulse that addresses multiple allowed transitions concurrently are established. The results are applied in particular to Morse and harmonic-oscillator systems, as well as some systems with degenerate energy levels. Morse and harmonic oscillators serve as models for molecular bonds, and the standard control approach of using a sequence of frequency-selective pulses to address a single transition at a time is either not applicable or only of limited utility for such systems.Comment: 8 pages, expanded and revised versio

Atomic-scale coexistence of short-range magnetic order and superconductivity in Fe1+y_{1+y}Se0.1_{0.1}Te0.9_{0.9}

The ground state of the parent compounds of many high temperature superconductors is an antiferromagnetically (AFM) ordered phase, where superconductivity emerges when the AFM phase transition is suppressed by doping or application of pressure. This behaviour implies a close relation between the two orders. Understanding the interplay between them promises a better understanding of how the superconducting condensate forms from the AFM ordered background. Here we explore this relation in real space at the atomic scale using low temperature spin-polarized scanning tunneling microscopy (SP-STM) and spectroscopy. We investigate the transition from antiferromagnetically ordered $\mathrm{Fe}_{1+y}\mathrm{Te}$ via the spin glass phase in $\mathrm{Fe}_{1+y}\mathrm{Se}_{0.1}\mathrm{Te}_{0.9}$ to superconducting $\mathrm{Fe}_{1+y}\mathrm{Se}_{0.15}\mathrm{Te}_{0.85}$. In $\mathrm{Fe}_{1+y}\mathrm{Se}_{0.1}\mathrm{Te}_{0.9}$ we observe an atomic-scale coexistence of superconductivity and short-ranged bicollinear antiferromagnetic order.Comment: 7 pages, 6 figure

A spherical perfect lens

It has been recently proved that a slab of negative refractive index material acts as a perfect lens in that it makes accessible the sub-wavelength image information contained in the evanescent modes of a source. Here we elaborate on perfect lens solutions to spherical shells of negative refractive material where magnification of the near-field images becomes possible. The negative refractive materials then need to be spatially dispersive with $\epsilon(r) \sim 1/r$ and $\mu(r)\sim 1/r$. We concentrate on lens-like solutions for the extreme near-field limit. Then the conditions for the TM and TE polarized modes become independent of $\mu$ and $\epsilon$ respectively.Comment: Revtex4, 9 pages, 2 figures (eps