L^{2}-restriction bounds for eigenfunctions along curves in the quantum completely integrable case

We show that for a quantum completely integrable system in two dimensions,the $L^{2}$-normalized joint eigenfunctions of the commuting semiclassical pseudodifferential operators satisfy restriction bounds ofthe form $\int_{\gamma} |\phi_{j}^{\hbar}|^2 ds = {\mathcal O}(|\log \hbar|)$ for generic curves $\gamma$ on the surface. We also prove that the maximal restriction bounds of Burq-Gerard-Tzvetkov are always attained for certain exceptional subsequences of eigenfunctions.Comment: Correct some typos and added some more detail in section

Theory of correlations between ultra-cold bosons released from an optical lattice

In this paper we develop a theoretical description of the correlations between ultra-cold bosons after free expansion from confinement in an optical lattice. We consider the system evolution during expansion and give criteria for a far field regime. We develop expressions for first and second order two-point correlations based on a variety of commonly used approximations to the many-body state of the system including Bogoliubov, meanfield decoupling, and particle-hole perturbative solution about the perfect Mott-insulator state. Using these approaches we examine the effects of quantum depletion and pairing on the system correlations. Comparison with the directly calculated correlation functions is used to justify a Gaussian form of our theory from which we develop a general three-dimensional formalism for inhomogeneous lattice systems suitable for numerical calculations of realistic experimental regimes.Comment: 18 pages, 11 figures. To appear in Phys. Rev. A. (few minor changes made and typos fixed

Two point correlations of a trapped interacting Bose gas at finite temperature

We develop a computationally tractable method for calculating correlation functions of the finite temperature trapped Bose gas that includes the effects of s-wave interactions. Our approach uses a classical field method to model the low energy modes and treats the high energy modes using a Hartree-Fock description. We present results of first and second order correlation functions, in position and momentum space, for an experimentally realistic system in the temperature range of $0.6T_c$ to $1.0T_c$. We also characterize the spatial coherence length of the system. Our theory should be applicable in the critical region where experiments are now able to measure first and second order correlations.Comment: 9 pages, 4 figure

Neural networks and non-parametric methods for improving real-time flood forecasting through conceptual hydrological models

International audienceTime-series analysis techniques for improving the real-time flood forecasts issued by a deterministic lumped rainfall-runoff model are presented. Such techniques are applied for forecasting the short-term future rainfall to be used as real-time input in a rainfall-runoff model and for updating the discharge predictions provided by the model. Along with traditional linear stochastic models, both stationary (ARMA) and non-stationary (ARIMA), the application of non-linear time-series models is proposed such as Artificial Neural Networks (ANNs) and the ?nearest-neighbours' method, which is a non-parametric regression methodology. For both rainfall forecasting and discharge updating, the implementation of each time-series technique is investigated and the forecasting schemes which perform best are identified. The performances of the models are then compared and the improvement in the efficiency of the discharge forecasts achievable is demonstrated when i) short-term rainfall forecasting is performed, ii) the discharge is updated and iii) both rainfall forecasting and discharge updating are performed in cascade. The proposed techniques, especially those based on ANNs, allow a remarkable improvement in the discharge forecast, compared with the use of heuristic rainfall prediction approaches or the not-updated discharge forecasts given by the deterministic rainfall-runoff model alone

Invariance Principle for the Random Lorentz Gas -- Beyond the Boltzmann-Grad Limit

We prove the invariance principle for a \emph{random Lorentz-gas} particle in 3 dimensions under the Boltzmann-Grad limit and simultaneous diffusive scaling. That is, for the trajectory of a point-like particle moving among infinite-mass, hard-core, spherical scatterers of radius r, placed according to a Poisson point process of density ϱ, in the limit ϱ→∞, r→0, ϱr2→1 up to time scales of order T=o(r−2|logr|−2). To our knowledge this represents the first significant progress towards solving rigorously this problem in classical nonequilibrium statistical physics, since the groundbreaking work of Gallavotti (1969), Spohn (1978) and Boldrighini-Bunimovich-Sinai (1983). The novelty is that the diffusive scaling of particle trajectory and the kinetic (Boltzmann-Grad) limit are taken simultaneously. The main ingredients are a coupling of the mechanical trajectory with the Markovian random flight process, and probabilistic and geometric controls on the efficiency of this coupling. Similar results have been earlier obtained for the weak coupling limit of classical and quantum random Lorentz gas, by Komorowski-Ryzhik (2006), respectively, Erd\H os-Salmhofer-Yau (2007). However, the following are substantial differences between our work and these ones: (1) The physical setting is different: low density rather than weak coupling. (2)The method of approach is different: probabilistic coupling rather than analytic/perturbative. (3) Due to (2), the time scale of validity of our diffusive approximation -- expressed in terms of the kinetic time scale -- is much longer and fully explicit

Ion-implantation induced anomalous surface amorphization in silicon

Spectroscopic ellipsometry (SE), high-depth-resolution Rutherford backscattering (RBS) and channeling have been used to examine the surface damage formed by room temperature N and B implantation into silicon. For the analysis of the SE data we used the conventional method of assuming appropriate optical models and fitting the model parameters (layer thicknesses and volume fraction of the amorphous silicon component in the layers) by linear regression. The dependence of the thickness of the surface-damaged silicon layer (beneath the native oxide layer) on the implantation parameters was determined: the higher the dose, the thicker the disordered layer at the surface. The mechanism of the surface amorphization process is explained in relation to the ion beam induced layer-by-layer amorphization. The results demonstrate the applicability of Spectroscopic ellipsometry with a proper optical model. RBS, as an independent cross-checking method supported the constructed optical model