The Strong Levinson Theorem for the Dirac Equation

We consider the Dirac equation in one space dimension in the presence of a symmetric potential well. We connect the scattering phase shifts at E=+m and E=-m to the number of states that have left the positive energy continuum or joined the negative energy continuum respectively as the potential is turned on from zero.Comment: Submitted to Physical Review Letter

Regards sociologiques croisés sur les processus de création au théâtre

International audienc

Ising model in small-world networks

The Ising model in small-world networks generated from two- and three-dimensional regular lattices has been studied. Monte Carlo simulations were carried out to characterize the ferromagnetic transition appearing in these systems. In the thermodynamic limit, the phase transition has a mean-field character for any finite value of the rewiring probability p, which measures the disorder strength of a given network. For small values of p, both the transition temperature and critical energy change with p as a power law. In the limit p -> 0, the heat capacity at the transition temperature diverges logarithmically in two-dimensional (2D) networks and as a power law in 3D.Comment: 6 pages, 7 figure

Synthesis process and hydrodynamic behavior of a new filtration material for passive wastewater dephosphatation

International audienceThe preparation optimization of a filter material intended to be used as a phosphate sorbent in flow-through conditions is investigated. The mixing of ferrihydrite (Fh) and pozzolana (Pz) using a “dry contact method” is found to be the most efficient and leads to the formation of a micrometric thick Fh coating deposited into the honeycombed structure of Pz. The maximal Fh content of ~ 8.5 wt.% is significantly higher than the quantity deposited on other classical substrates such as sand. The phosphate sorption kinetics and isotherms, under dynamic conditions in batch experiments, are best described by pseudo-second-order and Freundlich models respectively. Moreover, under static conditions, sorption kinetics reveals intra-aggregate diffusion process. Phosphate ion retention in packed columns, and especially the breakthrough point, can be adequately predicted when coupling the classical convection dispersion equation and the surface complexation model. Breakthrough curves of phosphate ions are strongly dependent on flow rate; which is important for future industrial applications. Finally, and unexpectedly, a high value of phosphate adsorption capacity (80 mg PO4 g− 1) is observed when phosphate-containing wastewater is used as feed solution. This is mostly explained by soluble calcium ions, which favors the phosphate fixation onto the filter material surfac

Quantized conductance in a one-dimensional ballistic oxide nanodevice

Electric-field effect control of two-dimensional electron gases (2-DEG) has enabled the exploration of nanoscale electron quantum transport in semiconductors. Beyond these classical materials, transition metal-oxide-based structures have d-electronic states favoring the emergence of novel quantum orders absent in conventional semiconductors. In this context, the LaAlO3/SrTiO3 interface that combines gate-tunable superconductivity and sizeable spin-orbit coupling is emerging as a promising platform to realize topological superconductivity. However, the fabrication of nanodevices in which the electronic properties of this oxide interface can be controlled at the nanoscale by field-effect remains a scientific and technological challenge. Here, we demonstrate the quantization of conductance in a ballistic quantum point contact (QPC), formed by electrostatic confinement of the LaAlO3/SrTiO3 2-DEG with a split-gate. Through finite source-drain voltage, we perform a comprehensive spectroscopic investigation of the 3d energy levels inside the QPC, which can be regarded as a spectrometer able to probe Majorana states in an oxide 2-DEG

Mean-field solution of the small-world network model

The small-world network model is a simple model of the structure of social networks, which simultaneously possesses characteristics of both regular lattices and random graphs. The model consists of a one-dimensional lattice with a low density of shortcuts added between randomly selected pairs of points. These shortcuts greatly reduce the typical path length between any two points on the lattice. We present a mean-field solution for the average path length and for the distribution of path lengths in the model. This solution is exact in the limit of large system size and either large or small number of shortcuts.Comment: 14 pages, 2 postscript figure

Les compléments neurophysiologiques du diagnostic

Neurophysiological complements of autism diagnosis Research presented show relationships between behavioral and cognitive disorders and underlying cerebral functional abnormalities, on the basis of non invasive electrophysiological investigations (electroencephalography, cortical evoked potentials). Three types of disturbances are studied: sleep problems, intolerance to change and atypical visual processing of human faces. The complementarity of clinical and neurophysiological approaches is crucial at the levels of functional diagnosis, therapeutic and educative interventions

Competition between electron pairing and phase coherence in superconducting interfaces

In LaAlO3/SrTiO3 heterostructures, a gate tunable superconducting electron gas is confined in a quantum well at the interface between two insulating oxides. Remarkably, the gas coexists with both magnetism and strong Rashba spin–orbit coupling. However, both the origin of superconductivity and the nature of the transition to the normal state over the whole doping range remain elusive. Here we use resonant microwave transport to extract the superfluid stiffness and the superconducting gap energy of the LaAlO3/SrTiO3 interface as a function of carrier density. We show that the superconducting phase diagram of this system is controlled by the competition between electron pairing and phase coherence. The analysis of the superfluid density reveals that only a very small fraction of the electrons condenses into the superconducting state. We propose that this corresponds to the weak filling of high- energy dxz/dyz bands in the quantum well, more apt to host superconductivity

Spatiotemporal Characterization of Supercontinuum Extending from the Visible to the Mid-Infrared in Multimode Graded-Index Optical Fiber

We experimentally demonstrate that pumping a graded-index multimode fiber with sub-ns pulses from a microchip Nd:YAG laser leads to spectrally flat supercontinuum generation with a uniform bell-shaped spatial beam profile extending from the visible to the mid-infrared at 2500\,nm. We study the development of the supercontinuum along the multimode fiber by the cut-back method, which permits us to analyze the competition between the Kerr-induced geometric parametric instability and stimulated Raman scattering. We also performed a spectrally resolved temporal analysis of the supercontinuum emission.Comment: 5 pages 7 figure