Casimir Force between a Dielectric Sphere and a Wall: A Model for Amplification of Vacuum Fluctuations

The interaction between a polarizable particle and a reflecting wall is examined. A macroscopic approach is adopted in which the averaged force is computed from the Maxwell stress tensor. The particular case of a perfectly reflecting wall and a sphere with a dielectric function given by the Drude model is examined in detail. It is found that the force can be expressed as the sum of a monotonically decaying function of position and of an oscillatory piece. At large separations, the oscillatory piece is the dominant contribution, and is much larger than the Casimir-Polder interaction that arises in the limit that the sphere is a perfect conductor. It is argued that this enhancement of the force can be interpreted in terms of the frequency spectrum of vacuum fluctuations. In the limit of a perfectly conducting sphere, there are cancellations between different parts of the spectrum which no longer occur as completely in the case of a sphere with frequency dependent polarizability. Estimates of the magnitude of the oscillatory component of the force suggest that it may be large enough to be observable.Comment: 18pp, LaTex, 7 figures, uses epsf. Several minor errors corrected, additional comments added in the final two sections, and references update

Spontaneous emission of an atom in front of a mirror

Motivated by a recent experiment [J. Eschner {\it et al.}, Nature {\bf 413}, 495 (2001)], we now present a theoretical study on the fluorescence of an atom in front of a mirror. On the assumption that the presence of the distant mirror and a lens imposes boundary conditions on the electric field in a plane close to the atom, we derive the intensities of the emitted light as a function of an effective atom-mirror distance. The results obtained are in good agreement with the experimental findings.Comment: 8 pages, 6 figures, revised version, references adde

Who I Am: The Meaning of Early Adolescents’ Most Valued Activities and Relationships, and Implications for Self-Concept Research

Self-concept research in early adolescence typically measures young people’s self-perceptions of competence in specific, adult-defined domains. However, studies have rarely explored young people’s own views of valued self-concept factors and their meanings. For two major self domains, the active and the social self, this mixed-methods study identified factors valued most by 526 young people from socioeconomically diverse backgrounds in Ireland (10-12 years), and explored the meanings associated with these in a stratified subsample (n = 99). Findings indicate that self-concept scales for early adolescence omit active and social self factors and meanings valued by young people, raising questions about content validity of scales in these domains. Findings also suggest scales may under-represent girls’ active and social selves; focus too much on some school-based competencies; and, in omitting intrinsically salient self domains and meanings, may focus more on contingent (extrinsic) rather than true (intrinsic) self-esteem

Why 'scaffolding' is the wrong metaphor : the cognitive usefulness of mathematical representations.

The metaphor of scaffolding has become current in discussions of the cognitive help we get from artefacts, environmental affordances and each other. Consideration of mathematical tools and representations indicates that in these cases at least (and plausibly for others), scaffolding is the wrong picture, because scaffolding in good order is immobile, temporary and crude. Mathematical representations can be manipulated, are not temporary structures to aid development, and are refined. Reflection on examples from elementary algebra indicates that Menary is on the right track with his ‘enculturation’ view of mathematical cognition. Moreover, these examples allow us to elaborate his remarks on the uniqueness of mathematical representations and their role in the emergence of new thoughts.Peer reviewe

Moving Atom-Field Interaction: Correction to Casimir-Polder Effect from Coherent Back-action

The Casimir-Polder force is an attractive force between a polarizable atom and a conducting or dielectric boundary. Its original computation was in terms of the Lamb shift of the atomic ground state in an electromagnetic field (EMF) modified by boundary conditions along the wall and assuming a stationary atom. We calculate the corrections to this force due to a moving atom, demanding maximal preservation of entanglement generated by the moving atom-conducting wall system. We do this by using non-perturbative path integral techniques which allow for coherent back-action and thus can treat non-Markovian processes. We recompute the atom-wall force for a conducting boundary by allowing the bare atom-EMF ground state to evolve (or self-dress) into the interacting ground state. We find a clear distinction between the cases of stationary and adiabatic motions. Our result for the retardation correction for adiabatic motion is up to twice as much as that computed for stationary atoms. We give physical interpretations of both the stationary and adiabatic atom-wall forces in terms of alteration of the virtual photon cloud surrounding the atom by the wall and the Doppler effect.Comment: 16 pages, 2 figures, clarified discussions; to appear in Phys. Rev.

Using atomic interference to probe atom-surface interaction

We show that atomic interference in the reflection from two suitably polarized evanescent waves is sensitive to retardation effects in the atom-surface interaction for specific experimental parameters. We study the limit of short and long atomic de Broglie wavelength. The former case is analyzed in the semiclassical approximation (Landau-Zener model). The latter represents a quantum regime and is analyzed by solving numerically the associated coupled Schroedinger equations. We consider a specific experimental scheme and show the results for rubidium (short wavelength) and the much lighter meta-stable helium atom (long wavelength). The merits of each case are then discussed.Comment: 11 pages, including 6 figures, submitted to Phys. Rev. A, RevTeX sourc

Theory of decoherence in a matter wave Talbot-Lau interferometer

We present a theoretical framework to describe the effects of decoherence on matter waves in Talbot-Lau interferometry. Using a Wigner description of the stationary beam the loss of interference contrast can be calculated in closed form. The formulation includes both the decohering coupling to the environment and the coherent interaction with the grating walls. It facilitates the quantitative distinction of genuine quantum interference from the expectations of classical mechanics. We provide realistic microscopic descriptions of the experimentally relevant interactions in terms of the bulk properties of the particles and show that the treatment is equivalent to solving the corresponding master equation in paraxial approximation.Comment: 20 pages, 4 figures (minor corrections; now in two-column format

Coherent radiation from neutral molecules moving above a grating

We predict and study the quantum-electrodynamical effect of parametric self-induced excitation of a molecule moving above the dielectric or conducting medium with periodic grating. In this case the radiation reaction force modulates the molecular transition frequency which results in a parametric instability of dipole oscillations even from the level of quantum or thermal fluctuations. The present mechanism of instability of electrically neutral molecules is different from that of the well-known Smith-Purcell and transition radiation in which a moving charge and its oscillating image create an oscillating dipole. We show that parametrically excited molecular bunches can produce an easily detectable coherent radiation flux of up to a microwatt.Comment: 4 page

Advanced InSAR atmospheric correction: MERIS/MODIS combination and stacked water vapour models

A major source of error for repeat-pass Interferometric Synthetic Aperture Radar (InSAR) is the phase delay in radio signal propagation through the atmosphere (especially the part due to tropospheric water vapour). Based on experience with the Global Positioning System (GPS)/Moderate Resolution Imaging Spectroradiometer (MODIS) integrated model and the Medium Resolution Imaging Spectrometer (MERIS) correction model, two new advanced InSAR water vapour correction models are demonstrated using both MERIS and MODIS data: (1) the MERIS/MODIS combination correction model (MMCC); and (2) the MERIS/MODIS stacked correction model (MMSC). The applications of both the MMCC and MMSC models to ENVISAT Advanced Synthetic Aperture Radar (ASAR) data over the Southern California Integrated GPS Network (SCIGN) region showed a significant reduction in water vapour effects on ASAR interferograms, with the root mean square (RMS) differences between GPS- and InSAR-derived range changes in the line-of-sight (LOS) direction decreasing from ,10mm before correction to ,5mm after correction, which is similar to the GPS/MODIS integrated and MERIS correction models. It is expected that these two advanced water vapour correction models can expand the application of MERIS and MODIS data for InSAR atmospheric correction. A simple but effective approach has been developed to destripe Terra MODIS images contaminated by radiometric calibration errors. Another two limiting factors on the MMCC and MMSC models have also been investigated in this paper: (1) the impact of the time difference between MODIS and SAR data; and (2) the frequency of cloud-free conditions at the global scale