An approach to nonstandard quantum mechanics

We use nonstandard analysis to formulate quantum mechanics in hyperfinite-dimensional spaces. Self-adjoint operators on hyperfinite-dimensional spaces have complete eigensets, and bound states and continuum states of a Hamiltonian can thus be treated on an equal footing. We show that the formalism extends the standard formulation of quantum mechanics. To this end we develop the Loeb-function calculus in nonstandard hulls. The idea is to perform calculations in a hyperfinite-dimensional space, but to interpret expectation values in the corresponding nonstandard hull. We further apply the framework to non-relativistic quantum scattering theory. For time-dependent scattering theory, we identify the starting time and the finishing time of a scattering experiment, and we obtain a natural separation of time scales on which the preparation process, the interaction process, and the detection process take place. For time-independent scattering theory, we derive rigorously explicit formulas for the M{\o}ller wave operators and the S-Matrix

On the origin dependence of multipole moments in electromagnetism

The standard description of material media in electromagnetism is based on multipoles. It is well known that these moments depend on the point of reference chosen, except for the lowest order. It is shown that this "origin dependence" is not unphysical as has been claimed in the literature but forms only part of the effect of moving the point of reference. When also the complementary part is taken into account then different points of reference lead to different but equivalent descriptions of the same physical reality. This is shown at the microscopic as well as at the macroscopic level. A similar interpretation is valid regarding the "origin dependence" of the reflection coefficients for reflection on a semi infinite medium. We show that the "transformation theory" which has been proposed to remedy this situation (and which is thus not needed) is unphysical since the transformation considered does not leave the boundary conditions invariant.Comment: 14 pages, 0 figure

Nonlinear optical response of a gold surface in the visible range: A study by two-color sum-frequency generation spectroscopy. II. Model for metal nonlinear susceptibility

We present a modeling of the nonlinear optical response of a metal surface in order to account for recent experimental results from two-color Sum-Frequency Generation experiments on gold. The model allows calculating the surface and bulk contributions, and explicitly separates free and bound electron terms. Contrary to the other contributions, the perpendicular surface component is strongly model-dependent through the surface electron density profiles. We consider three electron density schemes at the surface, with free and bound electrons overlapping or spilling out of the bulk, for its calculation. The calculated SFG signals from the metal rely only on bulk quantities and do not need an explicit definition of the density profiles. In the particular case of gold, when the free electrons overlap with the bound ones or spill out of the bulk, the free electron response completely dominates through the perpendicular surface terms. When the bound electrons spill out, the situation is more balanced, still in favor of the free electrons, with lower amplitudes and different dispersion lineshapes. As for silver, the free electron contributions dominate, and the calculated slow amplitude growth from blue to red follows the experimental trends

Genetic structure of the threatened West-Pannonian population of Great Bustard (Otis tarda).

The genetic diversity, population structure and gene flow of the Great Bustards (Otis tarda) living in Austria-Slovakia-West Hungary (West-Pannonian region), one of the few populations of this globally threatened species that survives across the Palaearctic, has been assessed for the first time in this study. Fourteen recently developed microsatellite loci identified one single population in the study area, with high values of genetic diversity and gene flow between two different genetic subunits. One of these subunits (Heideboden) was recognized as a priority for conservation, as it could be crucial to maintain connectivity with the central Hungarian population and thus contribute to keeping contemporary genetic diversity. Current conservation efforts have been successful in saving this threatened population from extinction two decades ago, and should continue to guarantee its future survival

Magnetic dipole moments in single and coupled split-ring resonators

We examine the role of magnetic dipoles in single and coupled pairs of metallic split-ring resonators by numerically computing their magnitude and examining their relative contributions to the scattering cross section. We demonstrate that magnetic dipoles can strongly influence the scattering cross section along particular directions. It is also found that the magnetic dipole parallel to the incident magnetic field and/or high-order multipoles may play a significant role in the linear response of coupled split-ring resonators.Comment: 7 pages, 3 figures, 1 tabl

Motional sidebands and direct measurement of the cooling rate in the resonance fluorescence of a single trapped ion

Resonance fluorescence of a single trapped ion is spectrally analyzed using a heterodyne technique. Motional sidebands due to the oscillation of the ion in the harmonic trap potential are observed in the fluorescence spectrum. From the width of the sidebands the cooling rate is obtained and found to be in agreement with the theoretical prediction.Comment: 4 pages, 4 figures. Final version after minor changes, 1 figure replaced; to be published in PRL, July 10, 200

Electromagnetic multipole theory for optical nanomaterials

Optical properties of natural or designed materials are determined by the electromagnetic multipole moments that light can excite in the constituent particles. In this work we present an approach to calculate the multipole excitations in arbitrary arrays of nanoscatterers in a dielectric host medium. We introduce a simple and illustrative multipole decomposition of the electric currents excited in the scatterers and link this decomposition to the classical multipole expansion of the scattered field. In particular, we find that completely different multipoles can produce identical scattered fields. The presented multipole theory can be used as a basis for the design and characterization of optical nanomaterials

A simple and versatile analytical approach for planar metamaterials

We present an analytical model which permits the calculation of effective material parameters for planar metamaterials consisting of arbitrary unit cells (metaatoms) formed by a set of straight wire sections of potentially different shape. The model takes advantage of resonant electric dipole oscillations in the wires and their mutual coupling. The pertinent form of the metaatom determines the actual coupling features. This procedure represents a kind of building block model for quite different metaatoms. Based on the parameters describing the individual dipole oscillations and their mutual coupling the entire effective metamaterial tensor can be determined. By knowing these parameters for a certain metaatom it can be systematically modified to create the desired features. Performing such modifications effective material properties as well as the far field intensities remain predictable. As an example the model is applied to reveal the occurrence of optical activity if the split ring resonator metaatom is modified to L- or S-shaped metaatoms.Comment: 5 figures, 1 tabl

Multipole nonlinearity of metamaterials

We report on the linear and nonlinear optical response of metamaterials evoked by first and second order multipoles. The analytical ground on which our approach bases permits for new insights into the functionality of metamaterials. For the sake of clarity we focus here on a key geometry, namely the split-ring resonator, although the introduced formalism can be applied to arbitrary structures. We derive the equations that describe linear and nonlinear light propagation where special emphasis is put on second harmonic generation. This contribution basically aims at stretching versatile and existing concepts to describe light propagation in nonlinear media towards the realm of metamaterials.Comment: 7 pages, 3 figure