Hopf instantons, Chern-Simons vortices, and Heisenberg ferromagnets

The dimensional reduction of the three-dimensional fermion-Chern-Simons model (related to Hopf maps) of Adam et el. is shown to be equivalent to (i) either the static, fixed--chirality sector of our non-relativistic spinor-Chern-Simons model in 2+1 dimensions, (ii) or a particular Heisenberg ferromagnet in the plane.Comment: 4 pages, Plain Tex, no figure

Galilean Lee Model of the Delta Function Potential

The scattering cross section associated with a two dimensional delta function has recently been the object of considerable study. It is shown here that this problem can be put into a field theoretical framework by the construction of an appropriate Galilean covariant theory. The Lee model with a standard Yukawa interaction is shown to provide such a realization. The usual results for delta function scattering are then obtained in the case that a stable particle exists in the scattering channel provided that a certain limit is taken in the relevant parameter space. In the more general case in which no such limit is taken finite corrections to the cross section are obtained which (unlike the pure delta function case) depend on the coupling constant of the model.Comment: 7 pages, latex, no figure

Galilean Limit of Equilibrium Relativistic Mass Distribution

The low-temperature form of the equilibrium relativistic mass distribution is subject to the Galilean limit by taking $c\rightarrow \infty .$ In this limit the relativistic Maxwell-Boltzmann distribution passes to the usual nonrelativistic form and the Dulong-Petit law is recovered.Comment: TAUP-2081-9

Spontaneous formation of optically induced surface relief gratings

A model based on Fick's law of diffusion as a phenomenological description of the molecular motion, and on the coupled mode theory, is developped to describe single-beam surface relief grating formation in azopolymers thin films. It allows to explain the mechanism of spontaneous patterning, and self-organization. It allows also to compute the surface relief profile and its evolution in time with good agreement with experiments

Short-term changes in particulate fluxes measured by drifting sediment traps during end summer oligotrophic regime in the NW Mediterranean Sea

Short-term changes in the flux of particulate matter were determined in the central north western Mediterranean Sea (near DYFAMED site) using drifting sediment traps at 200 m depth in the course of the DYNAPROC 2 cruise (14 September–17 October 2004). In this period of marked water column stratification, POC fluxes varied by an order of magnitude, in the range of 0.03–0.29 mgC m<sup>−2</sup> h<sup>−1</sup> over the month and showed very rapid and high variations. Particulate carbon export represented less than 5% of integrated primary production, suggesting that phytoplankton production was essentially sustained by internal recycling of organic matter and retained within the photic zone. While PON and POP fluxes paralleled one another, the elemental ratios POC/PON and POC/POP, varied widely over short-term periods. Values of these ratios generally higher than the conventional Redfield ratio, together with the very low chlorophyll a flux recorded in the traps (mean 0.017 μg m<sup>−2</sup> h<sup>−1</sup>), and the high phaeopigment and acyl lipid hydrolysis metabolite concentrations of the settling material, indicated that the organic matter reaching 200 m depth was reworked (by grazing, fecal pellets production, degradation) and that algal sinking, dominated by nano- and picoplankton, made a small contribution to the downward flux. Over time, the relative abundance of individual lipid classes in organic matter (OM) changed from glycolipids-dominated to neutral (wax esters, triacylglycerols) and phospholipids-dominated, suggesting ecosystem maturation as well as rapid and continual exchanges between dissolved, suspended and sinking pools. Our most striking result was documenting the rapid change in fluxes of the various measured parameters. In the situation encountered here, with dominant regenerated production, a decrease of fluxes was noticed during windy periods (possibly through reduction of grazing). But fluxes increased as soon as calm conditions settle

Standard and Generalized Newtonian Gravities as ``Gauge'' Theories of the Extended Galilei Group - I: The Standard Theory

Newton's standard theory of gravitation is reformulated as a {\it gauge} theory of the {\it extended} Galilei Group. The Action principle is obtained by matching the {\it gauge} technique and a suitable limiting procedure from the ADM-De Witt action of general relativity coupled to a relativistic mass-point.Comment: 51 pages , compress, uuencode LaTex fil

On the Relationship of Quantum Mechanics to Classical Electromagnetism and Classical Relativistic Mechanics

Some connections between quantum mechanics and classical physics are explored. The Planck-Einstein and De Broglie relations, the wavefunction and its probabilistic interpretation, the Canonical Commutation Relations and the Maxwell--Lorentz Equation may be understood in a simple way by comparing classical electromagnetism and the photonic description of light provided by classical relativistic kinematics. The method used may be described as `inverse correspondence' since quantum phenomena become apparent on considering the low photon number density limit of classical electromagnetism. Generalisation to massive particles leads to the Klein--Gordon and Schr\"{o}dinger Equations. The difference between the quantum wavefunction of the photon and a classical electromagnetic wave is discussed in some detail.Comment: 14 pages, no figures, no table

Scalar Kaluza-Klein modes in a multiply warped braneworld

The Kaluza-Klein (KK) modes of a massive scalar field on a 3-brane embedded in six dimensional multiply warped spacetime are determined. Due to the presence of warping along both the extra dimensions the KK mass spectrum splits into two closely spaced branches which is a distinct feature of this model compared to the five dimensional Randall-Sundrum model. This new cluster of the KK mode spectrum is expected to have interesting phenomenological implications for the upcoming collider experiments. Such a scenario may also be extended for even larger number of orbifolded extra dimensions.Comment: 10 pages, Revte

Dynamics of semiclassical Bloch wave - packets

The semiclassical approximation for electron wave-packets in crystals leads to equations which can be derived from a Lagrangian or, under suitable regularity conditions, in a Hamiltonian framework. In the plane, these issues are studied %in presence of external fields using the method of the coadjoint orbit applied to the ``enlarged'' Galilei group.Comment: 15 pages, Talk given at Nonlinear Physics. Theory and Experiment. IV,Gallipoli (Lecce), Italy - June 22 - July 1, 200

Celestial Mechanics, Conformal Structures, and Gravitational Waves

The equations of motion for $N$ non-relativistic particles attracting according to Newton's law are shown to correspond to the equations for null geodesics in a $(3N+2)$-dimensional Lorentzian, Ricci-flat, spacetime with a covariantly constant null vector. Such a spacetime admits a Bargmann structure and corresponds physically to a generalized pp-wave. Bargmann electromagnetism in five dimensions comprises the two Galilean electro-magnetic theories (Le Bellac and L\'evy-Leblond). At the quantum level, the $N$-body Schr\"odinger equation retains the form of a massless wave equation. We exploit the conformal symmetries of such spacetimes to discuss some properties of the Newtonian $N$-body problem: homographic solutions, the virial theorem, Kepler's third law, the Lagrange-Laplace-Runge-Lenz vector arising from three conformal Killing 2-tensors, and motions under inverse square law forces with a gravitational constant $G(t)$ varying inversely as time (Dirac). The latter problem is reduced to one with time independent forces for a rescaled position vector and a new time variable; this transformation (Vinti and Lynden-Bell) arises from a conformal transformation preserving the Ricci-flatness (Brinkmann). A Ricci-flat metric representing $N$ non-relativistic gravitational dyons is also pointed out. Our results for general time-dependent $G(t)$ are applicable to the motion of point particles in an expanding universe. Finally we extend these results to the quantum regime.Comment: 26 pages, LaTe