Path integral approach to eikonal and next-to-eikonal exponentiation

We approach the issue of exponentiation of soft gauge boson corrections to scattering amplitudes from a path integral point of view. We show that if one represents the amplitude as a first quantized path integral in a mixed coordinate-momentum space representation, a charged particle interacting with a soft gauge field is represented as a Wilson line for a semi-infinite line segment, together with calculable fluctuations. Combining such line segments, we show that exponentiation in an abelian field theory follows immediately from standard path-integral combinatorics. In the non-abelian case, we consider color singlet hard interactions with two outgoing external lines, and obtain a new viewpoint for exponentiation in terms of ``webs'', with a closed form solution for their corresponding color factors. We investigate and clarify the structure of next-to-eikonal corrections.Comment: 43 pages, 16 figure

Path integral approach to eikonal and next-to-eikonal exponentiation

We approach the issue of exponentiation of soft gauge boson corrections to scattering amplitudes from a path integral point of view. We show that if one represents the amplitude as a first quantized path integral in a mixed coordinate-momentum space representation, a charged particle interacting with a soft gauge field is represented as a Wilson line for a semi-infinite line segment, together with calculable fluctuations. Combining such line segments, we show that exponentiation in an abelian field theory follows immediately from standard path-integral combinatorics. In the non-abelian case, we consider color singlet hard interactions with two outgoing external lines, and obtain a new viewpoint for exponentiation in terms of ``webs'', with a closed form solution for their corresponding color factors. We investigate and clarify the structure of next-to-eikonal corrections.Comment: 43 pages, 16 figure

Angular sensitivity of blowfly photoreceptors: intracellular measurements and wave-optical predictions

The angular sensitivity of blowfly photoreceptors was measured in detail at wavelengths λ = 355, 494 and 588 nm. The measured curves often showed numerous sidebands, indicating the importance of diffraction by the facet lens. The shape of the angular sensitivity profile is dependent on wavelength. The main peak of the angular sensitivities at the shorter wavelengths was flattened. This phenomenon as well as the overall shape of the main peak can be quantitatively described by a wave-optical theory using realistic values for the optical parameters of the lens-photoreceptor system. At a constant response level of 6 mV (almost dark adapted), the visual acuity of the peripheral cells R1-6 is at longer wavelengths mainly diffraction limited, while at shorter wavelengths the visual acuity is limited by the waveguide properties of the rhabdomere. Closure of the pupil narrows the angular sensitivity profile at the shorter wavelengths. This effect can be fully described by assuming that the intracellular pupil progressively absorbs light from the higher order modes. In light-adapted cells R1-6 the visual acuity is mainly diffraction limited at all wavelengths.

Nonrelativistic Chern-Simons Vortices on the Torus

A classification of all periodic self-dual static vortex solutions of the Jackiw-Pi model is given. Physically acceptable solutions of the Liouville equation are related to a class of functions which we term Omega-quasi-elliptic. This class includes, in particular, the elliptic functions and also contains a function previously investigated by Olesen. Some examples of solutions are studied numerically and we point out a peculiar phenomenon of lost vortex charge in the limit where the period lengths tend to infinity, that is, in the planar limit.Comment: 25 pages, 2+3 figures; improved exposition, corrected typos, added one referenc

Metarhodopsin control by arrestin, light-filtering screening pigments, and visual pigment turnover in invertebrate microvillar photoreceptors

The visual pigments of most invertebrate photoreceptors have two thermostable photo-interconvertible states, the ground state rhodopsin and photo-activated metarhodopsin, which triggers the phototransduction cascade until it binds arrestin. The ratio of the two states in photoequilibrium is determined by their absorbance spectra and the effective spectral distribution of illumination. Calculations indicate that metarhodopsin levels in fly photoreceptors are maintained below ~35% in normal diurnal environments, due to the combination of a blue-green rhodopsin, an orange-absorbing metarhodopsin and red transparent screening pigments. Slow metarhodopsin degradation and rhodopsin regeneration processes further subserve visual pigment maintenance. In most insect eyes, where the majority of photoreceptors have green-absorbing rhodopsins and blue-absorbing metarhodopsins, natural illuminants are predicted to create metarhodopsin levels greater than 60% at high intensities. However, fast metarhodopsin decay and rhodopsin regeneration also play an important role in controlling metarhodopsin in green receptors, resulting in a high rhodopsin content at low light intensities and a reduced overall visual pigment content in bright light. A simple model for the visual pigment–arrestin cycle is used to illustrate the dependence of the visual pigment population states on light intensity, arrestin levels and pigment turnover

Coloration mechanisms and phylogeny of Morpho butterflies

Morpho butterflies are universally admired for their iridescent blue coloration, which is due to nanostructured wing scales. We performed a comparative study on the coloration of 16 Morpho species, investigating the morphological, spectral and spatial scattering properties of the differently organized wing scales. In numerous previous studies, the bright blue Morpho coloration has been fully attributed to the multi-layered ridges of the cover scales' upper laminae, but we found that the lower laminae of the cover and ground scales play an important additional role, by acting as optical thin film reflectors. We conclude that Morpho coloration is a subtle combination of overlapping pigmented and/or unpigmented scales, multilayer systems, optical thin films and sometimes undulated scale surfaces. Based on the scales' architecture and their organization, five main groups can be distinguished within the genus Morpho, largely agreeing with the accepted phylogeny

Rainbow peacock spiders inspire miniature super-iridescent optics

Colour produced by wavelength-dependent light scattering is a key component of visual communication in nature and acts particularly strongly in visual signalling by structurally-coloured animals during courtship. Two miniature peacock spiders (Maratus robinsoni and M. chrysomelas) court females using tiny structured scales (similar to 40 x 10 mu m(2)) that reflect the full visual spectrum. Using TEM and optical modelling, we show that the spiders' scales have 2D nanogratings on microscale 3D convex surfaces with at least twice the resolving power of a conventional 2D diffraction grating of the same period. Whereas the long optical path lengths required for light-dispersive components to resolve individual wavelengths constrain current spectrometers to bulky sizes, our nano-3D printed prototypes demonstrate that the design principle of the peacock spiders' scales could inspire novel, miniature light-dispersive components