Multiplexing encryption technique by combining random amplitude and phase masks

We propose and demonstrate an encryption-selectable undercover multiplexing. We encrypt and multiplex images for storage by means of a random phase mask common to every image, covered with random amplitude masks different for each image. In order to get a correct decryption of the encoded information, we have to use the appropriate random amplitude mask; otherwise fake information is recovered. We employ a phase conjugation scheme to generate the recovering wavefronts. We analyze and compare the different alternatives and degrees of complexity this combination of masks brings to enhance the security of optical encrypting techniques. We also include an analysis on the advantages and disadvantages this undercover multiplexing protocol offers. We present digital simulations to demonstrate the soundness of the proposal.     

Diffusion controlled multiplicative process: typical versus average behaviour

We investigate the dynamics of the number of particles diffusing in a multiplicative medium. We show that the typical behaviour of the growth process is different from the average. We develop a new formalism to study the average growth process and extend it to the calculation of higher moments and finally of the probability distribution. We show that the fluctuations of the growth process increase exponentially with time. We describe the interesting features of the distribution.     

Resistive Plates Carrying a Steady Current: Electric Potential and Surface Charges Close to the Battery

We treat the problem of two resistive plates carrying a steady current in the same direction. We consider a linear battery orthogonal to the direction of the current in the middle of the plates. We study the behavior of the surface charges close to the battery. We calculate the potential and electric field in the space outside the plates. We also consider the case of a single resistive plate carrying a steady current.     

The Renormalization Group and Its Finite Lattice Approximations

We investigate finite lattice approximations to the Wilson renormalization group in models of unconstrained spins. We discuss first the properties of the renormalization group transformation (RGT) that control the accuracy of this type of approximation and explain different methods and techniques to practically identify them. We also discuss how to determine the anomalous dimension of the field. We apply our considerations to a linear sigma model in two dimensions in the domain of attraction of the Ising fixed point using a Bell–Wilson RGT. We are able to identify optimal RGTs which allow accurate computations of quantities such as critical exponents, fixed-point couplings and eigenvectors with modest statistics. We finally discuss the advantages and limitations of this type of approach.     

Experimental study of cracking induced by desiccation in 1-dimensional systems

We designed a simple experiment to study both the dynamical and statistical properties of cracking that occurs in a one-dimensional system composed of wet clay (or similar material) exposed to shrinkage induced by desiccation. We study both the dynamical formation of cracks and the statistical characteristics of the final cracks pattern. We observe that the drying rate has a strong influence on the way cracks appear and grow. We find that the final crack width is related to the order of apparition of the cracks. We discuss the statistical distributions of cracks width and separation between two adjacent cracks. We also study the correlations between these two quantities. Our results are compared to the predictions of existing models. Finally, a comparison with another kind of clay is made. Received 6 May 2002 and Received in final form 5 July 2002     

Effect of gravitational force upon traffic flow with gradients

We study the effect of gravitational force upon traffic flow on a highway with sag, uphill, and downhill. We extend the optimal velocity model to take into account the gravitational force which acts on vehicles as an external force. We study the traffic states and jamming transitions induced by the slope of highway. We derive the fundamental diagrams (flow-density diagrams) for the traffic flow on the sag, the uphill, and downhill by using the extended optimal velocity model. We clarify where and when traffic jams occur on a highway with gradients. We show the relationship between densities before and after the jam. We derive the dependence of the fundamental diagram on the slope of gradients.     

Abelian Higgs model with a Chern-Simons term in 3-dimensional gravitation

We consider the Abelian Higgs model with a Chern-Simons term coupled to the Einstein theory of gravitation in 3-dimensional space-time. We seek a finite solution, regular everywhere, having a stationary, cylindrically symmetric metric. We analyze these field equations and we suggest that such a solution exists. We find that the asymptotic metric of this solution corresponds to that which describes gravitationally a massive particle with spin. We obtain explicitly the expression of the spin. We give only the expression of the mass in the first order with respect to the gravitational coupling constant.     

Quantum information and entanglement transfer for qutrits

We propose a scheme for the transfer of quantum information among distant qutrits. We apply this scheme to the distribution of entanglement of qutrits states among distant nodes and to the generation of multipartite antisymmetric states. We also discuss applications to quantum secret sharing.     

Quantum phase analysis of 1D superconducting quantum dot lattice using extended Bose-Hubbard model

We have obtained the quantum phase diagram of a one-dimensional superconducting quantum dot lattice using the extended Bose-Hubbard model for different commensurabilities. We describe the nature of different quantum phases at the charge degeneracy point. We find a direct phase transition from the Mott insulating phase to the superconducting phase for integer band fillings of Cooper pairs. We predict explicitly the presence of two kinds of repulsive Luttinger liquid phases, besides the charge density wave and superconducting phases for half-integer band fillings. We also predict that extended range interactions are necessary to obtain the correct phase boundary of a one-dimensional interacting Cooper system. We have used the density matrix renormalization group method and Abelian bosonization to study our system.     

Jump diffusion models and the evolution of financial prices

We analyze a stochastic model to describe the evolution of financial prices. We consider the stochastic term as a sum of the Wiener noise and a jump process. We point to the effects of the jumps on the return time evolution, a central concern of the econophysics literature. The presence of jumps suggests that the process can be described by an infinitely divisible characteristic function belonging to the De Finetti class. We then extend the De Finetti functions to a generalized nonlinear model and show the model to be capable of explaining return behavior.     

Non-linear relativistic diffusions

We obtain a non-linear generalization of the relativistic diffusion. We discuss diffusion equations whose non-linearity is a consequence of quantum statistics. We show that the assumptions of the relativistic invariance and an interpretation of the solution as a probability distribution substantially restrict the class of admissible non-linear diffusion equations. We consider relativistic invariant as well as covariant frame-dependent diffusion equations with a drift. In the latter case we show that there can exist stationary solutions of the diffusion equation besides the equilibrium solution corresponding to the quantum or Tsallis distributions. We define the relative entropy as a function of the diffusion probability and prove that it is monotonically decreasing in time when the diffusion tends to equilibrium. We discuss its relation to the thermodynamic behavior of diffusing particles.     

Some unusual electronic patterns on graphite surface

We report on the observation of some unusual electronic patterns on a graphite surface using scanning tunneling spectroscopy (STM). We attribute these patterns to different types of strain near the surface. One such pattern seen on a particular layer comprises of two-dimensional spatially varying super-lattice and one-dimensional fringes. This pattern is present in a finite region of a layer on the surface confined between two carbon fibers. We attribute this spatially varying super-lattice structure to the shear strain generated in the top layer due to the restraining fibers. We have also developed a model with the Moirè rotation hypothesis that gives us a better insight into such largescale spatially varying patterns. We have been able to model the above-observed pattern. We also report another pattern near a defect, which we attribute to the change in density of states due to the physical buckling of the top graphite layer. Part of this buckled layer is found to be buried under another layer and this region shows a reversed contrast and thus supporting our idea of buckling. We also performed tunneling spectroscopy measurements on various regions of these patterns which show significant variations in the density of states.      

On multiple phase transitions for branching Markov chains

We consider branching Markov chains on a countable set. We give a necessary and sufficient condition in terms of the transition kernel of the underlying Markov chain to have two phase transitions. We compute the critical values. We apply this result to prove that asymmetric branching random walks onZ have two phase transitions.     

Atomic fountains and optical clocks at SYRTE: Status and perspectives

In this article, we report on the work done with the LNE–SYRTE atomic clock ensemble during the last 10 years. We cover the progress made in atomic fountains and in their application to timekeeping. We also cover the development of optical lattice clocks based on strontium and on mercury. We report on tests of fundamental physical laws made with these highly accurate atomic clocks. We also report on work relevant to a future possible redefinition of the SI second.     

A Benney-Like Lattice

We propose a new Benney-like lattice and show that the new system of equations can be reduced to Chaplygin gas-like equations as well as the heavenly equation. We construct two infinite sets of conserved charges. The conserved densities are related to Legendre polynomials. We prove that the system is bi-Hamiltonian and that the conserved charges are in involution with respect to either of the Hamiltonian structures. We show that our Lax operator generates a new dispersionless Toda hierarchy.     

Delineating incoherent non-Markovian dynamics using quantum coherence

We introduce a method of characterization of non-Markovianity using coherence of a system interacting with the environment. We show that under the allowed incoherent operations, monotonicity of a valid coherence measure is affected due to non-Markovian features of the system–environment evolution. We also define a measure to quantify non-Markovianity of the underlying dynamics based on the non-monotonic behavior of the coherence measure. We investigate our proposed non-Markovianity marker in the behavior of dephasing and dissipative dynamics for one and two qubit cases. We also show that our proposed measure captures the back-flow of information from the environment to the system and compatible with well known distinguishability criteria of non-Markovianity.     

Flavor changing neutral currents and a Z′

We consider a non-universal Z′ that affects primarily the third generation fermions as an example of new physics associated with the top-quark. We first discuss constraints on the mass and coupling strength of such a Z′. We then turn our attention to the flavor changing neutral currents (FCNC) present in the model. We discuss the experimental constraints and their implications. We propose an ansatz to understand the smallness of the FCNC in terms of the CKM matrix.     

Density,phase and coherence properties of a low dimensional Bose-Einstein systems moving in a disordered potential

We present a detailed numerical study of the dynamics of a disordered one-dimensional Bose-Einstein condensates in position and momentum space. We particularly focus on the region where non-linearity and disorder simultaneously effect the time propagation of the condensate as well as the possible interference between various parts of the matter wave. We report oscillation between spatially extended and localized behavior for the propagating condensate which dies down with increasing non-linearity. We also report intriguing behavior of the phase fluctuation and the coherence properties of the matter wave. We also briefly compare these behavior with that of a two-dimensional condensate. We mention the relevance of our results to the related experiments on Anderson localization and indicate the possibility of future experiments