Bose systems in spatially random or time-varying potentials

Bose systems, subject to the action of external random potentials, are considered. For describing the system properties, under the action of spatially random potentials of arbitrary strength, the stochastic mean-field approximation is employed. When the strength of disorder increases, the extended Bose-Einstein condensate fragments into spatially disconnected regions, forming a granular condensate. Increasing the strength of disorder even more transforms the granular condensate into the normal glass. The influence of time-dependent external potentials is also discussed. Fastly varying temporal potentials, to some extent, imitate the action of spatially random potentials. In particular, strong time-alternating potential can induce the appearance of a nonequilibrium granular condensate.

Solid state NMR as a new approach for the structural characterization of rare-earth doped lead lanthanum zirconate titanate laser ceramics

To facilitate the design of laser host materials with optimized emission properties, detailed structural information at the atomic level is essential, regarding the local bonding environment of the active ions (distribution over distinct lattice sites) and their extent of local clustering as well as their population distribution over separate micro- or nanophases. The present study explores the potential of solid state NMR spectroscopy to provide such understanding for rare-earth doped lead lanthanum zirconate titanate (PLZT) ceramics. As the NMR signals of the paramagnetic dopant species cannot be observed directly, two complementary approaches are utilized: (1) direct observation of diamagnetic mimics using Sc-45 NMR and (2) study of the paramagnetic interaction of the constituent host lattice nuclei with the rare-earth dopant, using Pb-207 NMR lineshape analysis. Sc-45 MAS NMR spectra of scandium-doped PLZT samples unambiguously reveal scandium to be six-coordinated, suggesting that this rare-earth ion substitutes in the B site. Static Pb-207 spin echo NMR spectra of a series of Tm-doped PLZT samples reveal a clear influence of paramagnetic rare-earth dopant concentration on the NMR lineshape. In the latter case high-fidelity spectra can be obtained by spin echo mapping under systematic incrementation of the excitation frequency, benefiting from the signal-to-noise enhancement afforded by spin echo train Fourier transforms. Consistent with XRD data, the Pb-207 NMR lineshape analysis suggests that statistical incorporation into the PLZT lattice occurs at dopant levels of up to 1 wt.% Tm3+, while at higher levels the solubility limit is reached. (C) 2008 Elsevier Masson SAS. All rights reserved.

A WAVELET-BASED SPEAKER VERIFICATION ALGORITHM

This paper presents a study on wavelets and their characteristics for the specific purpose of serving as a feature extraction tool for speaker verification (SV), considering a Radial Basis Function (RBF) classifier, which is a particular type of Artificial Neural Network (ANN). Examining characteristics such as support-size, frequency and phase responses, amongst others, we show how Discrete Wavelet Transforms (DWTs), particularly the ones which derive from Finite Impulse Response (FIR) filters, can be used to extract important features from a speech signal which are useful for SV. Lastly, an SV algorithm based on the concepts presented is described.

On E-functions of semisimple Lie groups

We develop and describe continuous and discrete transforms of class functions on a compact semisimple, but not simple, Lie group G as their expansions into series of special functions that are invariant under the action of the even subgroup of the Weyl group of G. We distinguish two cases of even Weyl groups-one is the direct product of even Weyl groups of simple components of G and the second is the full even Weyl group of G. The problem is rather simple in two dimensions. It is much richer in dimensions greater than two-we describe in detail E-transforms of semisimple Lie groups of rank 3.