Matter-wave localization in a random potential

By numerical and variational solution of the Gross-Pitaevskii equation, we studied the localization of a noninteracting and weakly-interacting Bose-Einstein condensate (BEC) in a disordered cold atom lattice and a speckle potential. In the case of a single BEC fragment, the variational analysis produced good results. For a weakly disordered potential, the localized BECs are found to have an exponential tail as in weak Anderson localization. We also investigated the expansion of a noninteracting BEC in these potential. We find that the BEC will be locked in an appropriate localized state after an initial expansion and will execute breathing oscillation around a mean shape when a BEC at equilibrium in a harmonic trap is suddenly released into a disorder potential

The inverse problem for the Gross - Pitaevskii equation

Two different methods are proposed for the generation of wide classes of exact solutions to the stationary Gross - Pitaevskii equation (GPE). The first method, suggested by the work by Kondrat'ev and Miller (1966), applies to one-dimensional (1D) GPE. It is based on the similarity between the GPE and the integrable Gardner equation, all solutions of the latter equation (both stationary and nonstationary ones) generating exact solutions to the GPE, with the potential function proportional to the corresponding solutions. The second method is based on the "inverse problem" for the GPE, i.e. construction of a potential function which provides a desirable solution to the equation. Systematic results are presented for 1D and 2D cases. Both methods are illustrated by a variety of localized solutions, including solitary vortices, for both attractive and repulsive nonlinearity in the GPE. The stability of the 1D solutions is tested by direct simulations of the time-dependent GPE

Density of states in an optical speckle potential

We study the single particle density of states of a one-dimensional speckle potential, which is correlated and non-Gaussian. We consider both the repulsive and the attractive cases. The system is controlled by a single dimensionless parameter determined by the mass of the particle, the correlation length and the average intensity of the field. Depending on the value of this parameter, the system exhibits different regimes, characterized by the localization properties of the eigenfunctions. We calculate the corresponding density of states using the statistical properties of the speckle potential. We find good agreement with the results of numerical simulations.Comment: 11 pages, 11 figures, revtex

Collective excitations of a trapped Bose-Einstein condensate in the presence of a 1D optical lattice

We study low-lying collective modes of a horizontally elongated 87Rb condensate produced in a 3D magnetic harmonic trap with the addition of a 1D periodic potential which is provided by a laser standing-wave along the horizontal axis. While the transverse breathing mode results unperturbed, quadrupole and dipole oscillations along the optical lattice are strongly modified. Precise measurements of the collective mode frequencies at different height of the optical barriers provide a stringent test of the theoretical model recently introduced [M.Kraemer et al. Phys. Rev. Lett. 88 180404 (2002)].Comment: 4 pages, 4 figure

Internal combustion engine sensor network analysis using graph modeling

In recent years there has been a rapid development in technologies for smart monitoring applied to many different areas (e.g. building automation, photovoltaic systems, etc.). An intelligent monitoring system employs multiple sensors distributed within a network to extract useful information for decision-making. The management and the analysis of the raw data derived from the sensor network includes a number of specific challenges still unresolved, related to the different communication standards, the heterogeneous structure and the huge volume of data. In this paper we propose to apply a method based on complex network theory, to evaluate the performance of an Internal Combustion Engine. Data are gathered from the OBD sensor subset and from the emission analyzer. The method provides for the graph modeling of the sensor network, where the nodes are represented by the sensors and the edge are evaluated with non-linear statistical correlation functions applied to the time series pairs. The resulting functional graph is then analyzed with the topological metrics of the network, to define characteristic proprieties representing useful indicator for the maintenance and diagnosis

Localization of a matter wave packet in a disordered potential

We theoretically study the Anderson localization of a matter wave packet in a one-dimensional disordered potential. We develop an analytical model which includes the initial phase-space density of the matter wave and the spectral broadening induced by the disorder. Our approach predicts a behavior of the localized density profile significantly more complex than a simple exponential decay. These results are confirmed by large-scale and long-time numerical calculations. They shed new light on recent experiments with ultracold atoms and may impact their analysis

Causality estimates among brain cortical areas by Partial Directed Coherence: simulations and application to real data

The problem of the definition and evaluation of brain connectivity has become a central one in neuroscience during the latest years, as a way to understand the organization and interaction of cortical areas during the execution of cognitive or motor tasks. Among various methods established during the years, the Partial Directed Coherence (PDC) is a frequency-domain approach to this problem, based on a multivariate autoregressive modeling of time series and on the concept of Granger causality. In this paper we propose the use of the PDC method on cortical signals estimated from high resolution EEG recordings, a non invasive method which exhibits a higher spatial resolution than conventional cerebral electromagnetic measures. The principle contributions of this work are the results of a simulation study, testing the performances of PDC, and a statistical analysis (via the ANOVA, analysis of variance) of the influence of different levels of Signal to Noise Ratio and temporal length, as they have been systematically imposed on simulated signals. An application to high resolution EEG recordings during a foot movement is also presented