Wave-Particle Complementarity and Reciprocity of Gauss Sums on Talbot Effects

Berry and Klein [J. Mod. Opt. 43, 2139-2164 (1997)] showed that the Talbot effects in classical optics are naturally expressed by Gauss sums in number theory. Their result was obtained by a computation of Helmholtz equation. In this article, we calculate the effects using Fresnel integral and show that the result is also represented by Gauss sums. However function forms of these two computational results are apparently different. We show that the reciprocity law of Gauss sums connects these results and both completely agree with. The Helmholtz equation can be regarded as an equation based upon wavy nature in optics whereas the Fresnel integral is defined by a sum over the paths based upon a particle picture in optics. Thus the agreement of these two computational results could be interpreted in terms of the concept of the wave-particle complementarity, though the concept is for quantum mechanical phenomenon. This interpretation leads us to a relation between the reciprocity of Gauss sums in number theory and the wave-particle complementarity in wave physics. We discuss it in detail.     

Mode Amplification in Inhomogeneous QD Semiconductor Optical Amplifiers

We present modelling results investigating the carrier dynamics of an SOA composed of an inhomogeneous array of quantum dots designed to produce broad gain amplification when optically pumped. We use a set of rate equations that describe the QDs inhomogeneity and include an energy dependent occupation factor within each inhomogeneously broadened level and numerically solve them with the propagation equation to investigate the amplification of optical signals in the waveguide. By treating the carrier filling according to the quasi-equilibrium distribution, we are able to investigate the effect of band-filling (BFE) on the gain and refractive index. The linewidth enhancement factor (α) is computed and analysed with respect to optical signal intensity as well as electrical current density.     

Model independent constraints from vacuum and in-medium QCD Sum Rules

We discuss QCD sum rule constraints based on moments of vector meson spectral distributions in the vacuum and in a nuclear medium. Sum rules for the two lowest moments of these spectral distributions do not suffer from uncertainties related to QCD condensates of dimension higher than four. We exemplify these relations for the case of the ω meson and discuss the issue of in-medium mass shifts from this viewpoint. Received: 22 December 1998 / Revised version: 13 January 1999     

Formation and manipulation of regular metallic nanoparticle arrays on bacterial surface layers: an advanced TEM study

The template-directed formation of regular nanoparticle arrays on two-dimensional crystalline protein layers after their treatment with metal salt complexes was studied by transmission electron microscopy. For these investigations, bacterial surface layers (S layers), recrystallized in vitro into sheets and tube-shaped protein crystals with typical dimensions in the micrometer range, were used as the template. As identified by electron holography and scanning force microscopy, the S-layer tubes form alternating double layers when deposited onto a solid substrate surface. Two distinct pathways for the metal particle formation at the templates have been found: the site-specific growth of metal clusters by chemical reduction of the metal salt complexes, and the electron-beam induced growth of nanoparticles in the transmission electron microscope. Both mechanisms lead to regular arrays with particle densities > 6×10¹¹ cm ^-2. Nanoparticle formation by electron exposure takes exclusively place in the flat-lying double-layered protein tubes, where a sufficient amount of metal complexes can be accumulated during sample preparation. Received 6 December 2000     

Optical absorption and energy-loss spectra of aligned carbon nanotubes

Optical-absorption cross-sections and energy-loss spectra of aligned multishell carbon nanotubes are investigated, on the basis of photonic band-structure calculations. A local graphite-like dielectric tensor is assigned to every point of the tubules, and the effective transverse dielectric function of the composite is computed by solving Maxwell's equations in media with tensor-like dielectric functions. A Maxwell-Garnett-like approach appropriate to the case of infinitely long anisotropic tubules is also developed. Our full calculations indicate that the experimentally measured macroscopic dielectric function of carbon nanotube materials is the result of a strong electromagnetic coupling between the tubes. An analysis of the electric-field pattern associated with this coupling is presented, showing that in the close-packed regime the incident radiation excites a very localized tangential surface plasmon. Received 18 January 2001     

Optical functions of InGaP/GaAs epitaxial layers from 0.01 to 5.5 eV

In_0.49Ga_0.51P films, both undoped and doped n- and p-type (up to 10¹⁸ cm^-3), were grown lattice matched on GaAs substrates, with different miscut angles, by Metal-Organic Vapour Phase Epitaxy (MOVPE) at different temperatures. The shift of the fundamental gap E₀, caused by “ordering effect” was measured as a function of temperature by photoluminescence. The complex refractive index = n + ik and the dielectric function = ɛ ₁ + iɛ ₂ at room temperature were determined from 0.01 to 5.5 eV by using complementary data from fast-Fourier-transform far-infrared (FFT-FIR), dispersive, and ellipsometric spectroscopies. The effect of the native oxide was accounted for and the self-consistency of the optical functions was checked in the framework of the Kramers-Kronig causality relations. In the restrahlen region the dielectric function was well fitted by classical Lorentz oscillators; in the transparent region below E₀, the refractive index was modelled by a Sellmeier dispersion relation; in the interband region the dielectric function was well reproduced by analytical lineshapes associated to seven critical points. Thus parametrized analytical expressions were obtained for the optical functions all over the spectral range, without discontinuities, to be used in the modelling and characterization of multi-layer structures, also on opaque substrates. Received 13 December 2001 Published online 25 June 2002     

Optical measurements of the superconducting gap in MgB 2

Far-infrared reflectivity studies on the polycrystalline intermetallic compound MgB₂ with a superconducting transition temperature T _c = 39 K were performed at temperatures 20 K to 300 K. We observe a significant raise of the superconducting-to-normal state reflectivity ratio below 70 cm ^-1 , with a maximum at about 25-30 cm ^-1 , which gives a lower estimate of the superconducting gap of 2Δ(0) ≈ 3-4 meV. Received 7 March 2001 and Received in final form 18 April 2001     

Multiscaling and multifractality in an one-dimensional Ising model

Scaling properties of the Gibbs distribution of a finite-size one-dimensional Ising model are investigated as the thermodynamic limit is approached. It is shown that, for each nonzero temperature, coarse-grained probabilities of the appearance of particular energy levels display multiscaling with the scaling length ℓ = 1/M _n, where n denotes the number of spins and M_n is the total number of energy levels. Using the multifractal formalism, the probabilities are argued to reveal also multifractal properties. Received 10 July 2000 and Received in final form 6 November 2000     

Skyrmions on an elastic cylinder

For a spin-polarized electron gas on an elastic cylinder in an external axial magnetic field and an axial electric field we find that the corresponding Euler-Lagrange equation is the double sine-Gordon (DSG) equation with an exact 2π-skyrmion solution. The DSG skyrmion is stabilized, without Coulomb repulsion, by the curvature of the cylinder. It adopts a characteristic length ξ which is smaller than the radius of the cylinder. For an elastic cylinder this mismatch of length scales causes a deformation of the cylinder in the region of the skyrmion. Received 23 October 2001 / Received in final form 8 March 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: rossen.dandoloff@ptm.u-cergy.fr     

Ginzburg-Landau theory and effects of pressure on a two-band superconductor: application to MgB <Emphasis Type="Bold">2</Emphasis>

We present a model of pressure effects of a two-band superconductor based on a Ginzburg-Landau free energy with two order parameters. The parameters of the theory are pressure as well as temperature dependent. New pressure effects emerge as a result of the competition between the two bands. The theory then is applied to MgB₂. We identify two possible scenaria regarding the fate of the two σ subbands under pressure, depending on whether or not both subbands are above the Fermi energy at ambient pressure. The splitting of the two subbands is probably caused by the E_2g distortion. If only one subband is above the Fermi energy at ambient pressure (scenario I), application of pressure diminishes the splitting and it is possible that the lower subband participates in the superconductivity. The corresponding crossover pressure and Gr neisen parameter are estimated. In the second scenario both bands start above the Fermi energy and they move below it, either by pressure or via the substitution of Mg by Al. In both scenaria, the possibility of electronical topological transition is emphasized. Experimental signatures of both scenaria are presented and existing experiments are discussed in the light of the different physical pictures. Received 3 September 2002 / Received in final form 16 December 2002 Published online 14 February 2003 RID="a" ID="a"e-mail: joseph.betouras@ua.ac.be RID="b" ID="b"On leave from N.S. Kurnakov Institute of General and Inorganic Chemistry of the Russian Academy of Sciences, 31 Leninskii prospekt, 117915, Moscow, Russia     

Optical mode characterization of single photons prepared by means of conditional measurements on a biphoton state

A detailed theoretical analysis of the spatiotemporal mode of a single photon prepared via conditional measurements on a photon pair generated in the process of parametric down-conversion is presented. The maximum efficiency of coupling the photon into a transform-limited classical optical mode is calculated and ways for its optimization are determined. An experimentally feasible technique of generating the optimally matching classical mode is proposed. The theory is applied to a recent experiment on pulsed homodyne tomography of the single-photon Fock state [A.I. Lvovsky et al., Phys. Rev. Lett. 87, 050402 (2001)]. Received 16 July 2001     

Parametrization of the Moduli Space of Flat SL(2, R) Connections on the Torus

The moduli space of flat SL(2, R)-connections modulo gauge transformations on the torus may be described by ordered pairs of commuting SL(2, R) matrices modulo simultaneous conjugation by SL(2, R) matrices. Their spectral properties allow a classification of the equivalence classes, and a unique canonical form is given for each of these. In this way the moduli space becomes explicitly parametrized, and has a simple structure, resembling that of a cell complex, allowing it to be depicted. Finally, a Hausdorff topology based on this classification and parametrization is proposed.     

Measurement and analysis of alpha particle induced reactions on gold

Stacked foil activation technique and Ge(Li) gamma ray spectroscopy have been used for the measurement of excitation functions of¹⁹⁷Au(α,xn) (x=1−3),¹⁹⁷Au(α,2pn) and¹⁹⁷Au(α,αn) reactions up to 50 MeV. The experimental cross-sections were compared with the predictions of pre-equilibrium hybrid model, as well as with the more recent index model. A general agreement was found in all reactions using initial exciton numbern ₀=4(4p0h) except for¹⁹⁷Au(α,n) reaction, where index model gives fairly good agreement withn ₀=5(5p0h).     

Survival of T4 bacteriophage irradiated in suspension by protons at energies between 4.6 and 2.5 MeV. Dependence on linear energy transfer

Summary The mean survival doses of T4 bacteriophage irradiated in suspension by protons were measured at six values of incident energy. Due to the thickness of the target, the beam stopped inside the suspension, so yielding the overall mean dose, averaged from the incident energy to zero. By a suitable analysis of the overall mean doses, measured at different incident energies, the mean doses in narrow intervals of energy, which may be related to definite LET values, were extracted. To speed up publication, the authors of this paper have agreed to not receive the proofs for correction.     

Gaussian Effective Potential and superconductivity

The Gaussian Effective Potential in a fixed transverse unitarity gauge is studied for the static three-dimensional U(1) scalar electrodynamics (Ginzburg-Landau phenomenological theory of superconductivity). In the broken-symmetry phase the mass of the electromagnetic field (inverse penetration depth) and the mass of the scalar field (inverse correlation length) are both determined by solution of the coupled variational equations. At variance with previous calculations, the choice of a fixed unitarity gauge prevents from the occurrence of any unphysical degree of freedom. The theory provides a nice interpolation of the experimental data when approaching the critical region, where the standard mean-field method is doomed to failure. Received 18 November 2002 / Received in final form 26 March 2003 Published online 20 June 2003 RID="a" ID="a"e-mail: giuseppe.angilella@ct.infn.it     

Election results and the Sznajd model on Barabasi network

The network of Barabasi and Albert, a preferential growth model where a new node is linked to the old ones with a probability proportional to their connectivity, is applied to Brazilian election results. The application of the Sznajd rule, that only agreeing pairs of people can convince their neighbours, gives a vote distribution in good agreement with reality Received 19 September 2001 and Received in final form 2 November 2001     

Resonant coupling in the van der Waals interaction between an excited alkali atom and a dielectric surface: an experimental study via stepwise selective reflection spectroscopy

We present a detailed experimental study of the evaluation of the van der Waals (vW) atom-surface interaction for high-lying excited states of alkali-metal atoms (Cs and Rb), notably when they couple resonantly with a surface-polariton mode of the neighbouring dielectric surface. This report extends our initial observation [Phys. Rev. Lett. 83, 5467 (1999)] of a vW repulsion between Cs(6D_3/2) and a sapphire surface. The experiment is based upon FM selective reflection spectroscopy, on a transition reaching a high-lying state from a resonance level, that has been thermally pumped by an initial one-photon step. Along with a strong vW repulsion fitted with a blue lineshift, -160±25 kHz μm³ for Cs(6D_3/2) in front of a sapphire surface (with a perpendicular c-axis), we demonstrate a weaker vW repulsion (-32±5 kHz μm³) for Cs(6D_3/2) in front of a YAG surface, as due to a similar resonant coupling at 12 μm between a virtual atomic emission (6D_3/2-7P_1/2) and the surface polariton modes. A resonant behaviour of Rb(6D_5/2) in front of a sapphire surface exists also because of analogous decay channels in the 12 μm range. Finally, one demonstrates that fused silica, nonresonant for a virtual transition in the 12 μm range and hence weakly attracting for Cs(6D_3/2), exhibits a resonant behaviour for Cs(9S_1/2) as due to its surface polariton resonance in the 8-9 μm range. The limiting factors that affect both the accuracy of the theoretical prediction, and that of the fitting method applied to the experimental data, are discussed in the conclusion. Received 16 January 2003 / Received in final form 25 March 2003 Published online 5 May 2003     

Thermodynamics and transport in an active Morse ring chain

We investigate the stochastic dynamics of an one-dimensional ring with N self-driven Brownian particles. In this model neighboring particles interact via conservative Morse potentials. The influence of the surrounding heat bath is modeled by Langevin-forces (white noise) and a constant viscous friction coefficient γ. The Brownian particles are provided with internal energy depots which may lead to active motions of the particles. The depots are realized by an additional nonlinearly velocity-dependent friction coefficient γ ₁(v) in the equations of motions. In the first part of the paper we study the partition functions of time averages and thermodynamical quantities (e.g. pressure) characterizing the stationary physical system. Numerically calculated non-equilibrium phase diagrams are represented. The last part is dedicated to transport phenomena by including a homogeneous external force field that breaks the symmetry of the model. Here we find enhanced mobility of the particles at low temperatures. Received 21 July 2001     

The power and beauty of (γ, 2e) experiments

The power and beauty of energy- and angle-resolved two-electron emission in the double photoionization of atoms is demonstrated, concentrating on the particular shapes of the angular correlation patterns of the triple differential cross section. The cases selected are direct double photoionization in helium and neon as well as sequential double photoionization in xenon, both for equal and unequal energies of the emitted electrons.     

Complexes based on ethylene- and propylene-bridged-pentadentate-Fe(III)-units allow interplay between magnetic centers and multistability investigated by Mössbauer spectroscopy

The propylene-based ⁵3,3-L?=?[N,N′-Bis(1-hydroxy-2-benzylidene)-1,7-diamino-4-azaheptane] and ethylene-based pentadentate ligand ⁵2,2-L?=?[N,N′-Bis(1-hydroxy-2-benzylidene)-1,5-diamino-3-azapentane] has been prepared. Complexation with Fe(III) yields high-spin (S?=?5/2) complexes of [Fe^III(⁵2,2-L)Cl] and [Fe^III(⁵3,3-L)Cl]. Such precursors were combined with [M(CN) _x ] ^y? (M?=?W(IV), Mo(IV), Ru(II), Co(III)) and heptanuclear and nonanuclear clusters of [M{(CN-Fe^III(⁵2,2-L)} _x ]Cl _y and [M{(CN-Fe^III(⁵3,3-L)} _x ]Cl _y resulted. Such starshaped hepta- and nonanuclear compounds are high-spin systems at room temperature. On cooling to 20 K in all presented ethylene compounds the iron(III) centers switch to a second high-spin state as proven by Mössbauer spectra with a yield of about 30%, i.e., multiple electronic transitions. The propylene compounds, however, perform a high-spin to low-spin transition. Mössbauer spectra taken during green light irradiation indicate changes in the population of the different electronic states, i.e. concerted inorganic reaction.