Survey of roughness by stochastic oscillations

In this paper, connections between surface roughness and directed polymers in random medium are studied, when the surface is considered as a directed line undergoing stochastic oscillations. This is performed by studying the influence of a stochastic elastic forcing term $-\kappa y+\eta(s)$, on a particle moving along a rough surface. Two models are proposed and analysed in this way: the random-walk process (RW) in its discrete and continuous form, and a Markovian process via the Ornstein-Uhlenbeck (O-U) process. It is shown that the continuous RW leads to an oscillator equation, via an effective action obeying a KPZ equation which is solved analytically. The O-U process allows to obtain information on the profile of surface for a long size substrate. The analogy with the roughness is achieved by introducing a quantity suited to directed line formalism: the height velocity variation $\partial h/\partial s$.Comment: 8 pages, 4 figure

Connection between the Burgers equation with an elastic forcing term and a stochastic process

We present a complete analytical resolution of the one dimensional Burgers equation with the elastic forcing term $-\kappa^{2} x+f(t)$, $\kappa\in\mathbb{R}$. Two methods existing for the case $\kappa=0$ are adapted and generalized using variable and function transformations, valid for all values of space an time. The emergence of a Fokker-Planck equation in the method allows to connect a fluid model, depicted by the Burgers equation, with an Ornstein-Uhlenbeck process

Optimising the signal-to-noise ratio in measurement of photon pairs with detector arrays

To evidence multimode spatial entanglement of spontaneous down-conversion, detector arrays allow a full field measurement, without any a priori selection of the paired photons. We show by comparing results of the recent literature that electron-multiplying CCD (EMCCD) cameras allow, in the present state of technology, the detection of quantum correlations with the best signal-to-noise ratio (SNR), while intensified CCD (ICCD) cameras allow at best to identify pairs. The SNR appears to be proportional to the square root of the number of coherence cells in each image, or Schmidt number. Then, corrected estimates are derived for extended coherence cells and not very low and not space-stationary photon fluxes. Finally, experimental measurements of the SNR confirm our model

Einstein-Podolsky-Rosen paradox in twin images

Spatially entangled twin photons provide both promising resources for modern quantum information protocols, because of the high dimensionality of transverse entanglement, and a test of the Einstein-Podolsky-Rosen(EPR) paradox in its original form of position versus impulsion. Usually, photons in temporal coincidence are selected and their positions recorded, resulting in a priori assumptions on their spatio-temporal behavior. Here, we record on two separate electron-multiplying charge coupled devices (EMCCD) cameras twin images of the entire flux of spontaneous down-conversion. This ensures a strict equivalence between the subsystems corresponding to the detection of either position (image or near-field plane) or momentum (Fourier or far-field plane). We report then highest degree of paradox ever reported and show that this degree corresponds to the number of independent degrees of freedom or resolution cells, of the images

Temporal ghost imaging with twin photons

We use twin photons generated by spontaneous parametric down conversion to perform temporal ghost imaging of a single time signal. The retrieval of a binary signal containing eight bits is performed with an error rate below 1%

The Electronic Ground State Energy Problem: a New Reduced Density Matrix Approach

We present here a formulation of the electronic ground-state energy in terms of the second order reduced density matrix, using a duality argument. It is shown that the computation of the ground-state energy reduces to the search of the projection of some two-electron reduced Hamiltonian on the dual cone of $N$-representability conditions. Some numerical results validate the approach, both for equilibrium geometries and for the dissociation curve of N$_2$

Computational temporal ghost imaging

Ghost imaging is a fascinating process, where light interacting with an object is recorded without resolution, but the shape of the object is nevertheless retrieved, thanks to quantum or classical correlations of this interacting light with either a computed or detected random signal. Recently, ghost imaging has been extended to a time object, by using several thousands copies of this periodic object. Here, we present a very simple device, inspired by computational ghost imaging, that allows the retrieval of a single non-reproducible, periodic or non-periodic, temporal signal. The reconstruction is performed by a single shot, spatially multiplexed, measurement of the spatial intensity correlations between computer-generated random images and the images, modulated by a temporal signal, recorded and summed on a chip CMOS camera used with no temporal resolution. Our device allows the reconstruction of either a single temporal signal with monochrome images or wavelength-multiplexed signals with color images

Generalized identifiability conditions for blind convolutive MIMO separation

International audienceThis paper deals with the problem of source separation in the case where the output of a multivariate convolutive mixture is observed: we propose novel and generalized conditions for the blind identifiability of a separating system. The results are based on higher-order statistics and are valid in the case of stationary but not necessarily i.i.d. signals. In particular, we extend recent results based on second-order statistics only. The approach relies on the use of so called reference signals. Our new results also show that only weak conditions are required on the reference signals: this is illustrated by simulations and opens up the possibility of developing new methods

New kurtosis optimization schemes for MISO equalization

International audienceThis paper deals with efficient optimization of cumulant based contrast functions. Such a problem occurs in the blind source separation framework, where contrast functions are criteria to be maximized in order to retrieve the sources. More precisely, we focus on the extraction of one source signal and our method applies in deflation approaches, where the sources are extracted one by one. We propose new methods to maximize the kurtosis contrast function. These methods are intermediate between a gradient and an iterative "fixed-point" optimization of so-called reference contrasts. They rely on iterative updates of the parameters which monotonically increase the contrast function value: we point out the strong similarity with the Expectation-Maximization (EM) method and with recent generalizations referred to as Minimization-Maximization (MM). We also prove the global convergence of the algorithm to a stationary point. Simulations confirm the convergence of our methods to a separating solution. They also show experimentally that our methods have a much lower computational cost than former classical optimization methods. Finally, simulations suggest that the methods remain valid under weaker conditions than those required for proving convergence