First-principles quantum simulations of dissociation of molecular condensates: Atom correlations in momentum space

We investigate the quantum many-body dynamics of dissociation of a Bose-Einstein condensate of molecular dimers into pairs of constituent bosonic atoms and analyze the resulting atom-atom correlations. The quantum fields of both the molecules and atoms are simulated from first principles in three dimensions using the positive-P representation method. This allows us to provide an exact treatment of the molecular field depletion and s-wave scattering interactions between the particles, as well as to extend the analysis to nonuniform systems. In the simplest uniform case, we find that the major source of atom-atom decorrelation is atom-atom recombination which produces molecules outside the initially occupied condensate mode. The unwanted molecules are formed from dissociated atom pairs with nonopposite momenta. The net effect of this process-which becomes increasingly significant for dissociation durations corresponding to more than about 40% conversion-is to reduce the atom-atom correlations. In addition, for nonuniform systems we find that mode mixing due to inhomogeneity can result in further degradation of the correlation signal. We characterize the correlation strength via the degree of squeezing of particle number-difference fluctuations in a certain momentum-space volume and show that the correlation strength can be increased if the signals are binned into larger counting volumes.

A total electron content space weather study of the Nighttime Weddell Sea Anomaly of 1996/97 southern summer with TOPEX/Poseidon radar altimetry

This paper reports on a total electron content space weather study of the nighttime Weddell Sea Anomaly, overlooked by previously published TOPEX/Poseidon climate studies, and of the nighttime ionosphere during the 1996/1997 southern summer. To ascertain the morphology of spatial TEC distribution over the oceans in terms of hourly, geomagnetic, longitudinal and summer-winter variations, the TOPEX TEC, magnetic, and published neutral wind velocity data are utilized. To understand the underlying physical processes, the TEC results are combined with inclination and declination data plus global magnetic field-line maps. To investigate spatial and temporal TEC variations, geographic/magnetic latitudes and local times are computed. As results show, the nighttime Weddell Sea Anomaly is a large (∼1,600(°)2; ∼22 million km2 estimated for a steady ionosphere) space weather feature. Extending between 200°E and 300°E (geographic), it is an ionization enhancement peaking at 50°S–60°S/250°E–270°E and continuing beyond 66°S. It develops where the spacing between the magnetic field lines is wide/medium, easterly declination is large-medium (20°–50°), and inclination is optimum (∼55°S). Its development and hourly variations are closely correlated with wind speed variations. There is a noticeable (∼43%) reduction in its average area during the high magnetic activity period investigated. Southern summer nighttime TECs follow closely the variations of declination and field-line configuration and therefore introduce a longitudinal division of four (Indian, western/eastern Pacific, Atlantic). Northern winter nighttime TECs measured over a limited area are rather uniform longitudinally because of the small declination variation. TOPEX maps depict the expected strong asymmetry in TEC distribution about the magnetic dip equator.

Space efficient quantile summary for constrained sliding windows on a data stream

In many online applications, we need to maintain quantile statistics for a sliding window on a data stream. The sliding windows in natural form are defined as the most recent N data items. In this paper, we study the problem of estimating quantiles over other types of sliding windows. We present a uniform framework to process quantile queries for time constrained and filter based sliding windows. Our algorithm makes one pass on the data stream and maintains an E-approximate summary. It uses O((1)/(epsilon2) log(2) epsilonN) space where N is the number of data items in the window. We extend this framework to further process generalized constrained sliding window queries and proved that our technique is applicable for flexible window settings. Our performance study indicates that the space required in practice is much less than the given theoretical bound and the algorithm supports high speed data streams.

Genetic algorithm based distance spectrum technique for performance union bound of space-time trellis coded OFDM

This paper derives the performance union bound of space-time trellis codes in orthogonal frequency division multiplexing system (STTC-OFDM) over quasi-static frequency selective fading channels based on the distance spectrum technique. The distance spectrum is the enumeration of the codeword difference measures and their multiplicities by exhausted searching through all the possible error event paths. Exhaustive search approach can be used for low memory order STTC with small frame size. However with moderate memory order STTC and moderate frame size the computational cost of exhaustive search increases exponentially, and may become impractical for high memory order STTCs. This requires advanced computational techniques such as Genetic Algorithms (GAS). In this paper, a GA with sharing function method is used to locate the multiple solutions of the distance spectrum for high memory order STTCs. Simulation evaluates the performance union bound and the complexity comparison of non-GA aided and GA aided distance spectrum techniques. It shows that the union bound give a close performance measure at high signal-to-noise ratio (SNR). It also shows that GA sharing function method based distance spectrum technique requires much less computational time as compared with exhaustive search approach but with satisfactory accuracy.

Molecular phase space transport in water:non-stationary random walk model

Molecular transport in phase space is crucial for chemical reactions because it defines how pre-reactive molecular configurations are found during the time evolution of the system. Using Molecular Dynamics (MD) simulated atomistic trajectories we test the assumption of the normal diffusion in the phase space for bulk water at ambient conditions by checking the equivalence of the transport to the random walk model. Contrary to common expectations we have found that some statistical features of the transport in the phase space differ from those of the normal diffusion models. This implies a non-random character of the path search process by the reacting complexes in water solutions. Our further numerical experiments show that a significant long period of non-stationarity in the transition probabilities of the segments of molecular trajectories can account for the observed non-uniform filling of the phase space. Surprisingly, the characteristic periods in the model non-stationarity constitute hundreds of nanoseconds, that is much longer time scales compared to typical lifetime of known liquid water molecular structures (several picoseconds).

Contrast summation across eyes and space is revealed along the entire dipper function by a "Swiss cheese" stimulus.

Previous contrast discrimination experiments have shown that luminance contrast is summed across ocular (T. S. Meese, M. A. Georgeson, & D. H. Baker, 2006) and spatial (T. S. Meese & R. J. Summers, 2007) dimensions at threshold and above. However, is this process sufficiently general to operate across the conjunction of eyes and space? Here we used a "Swiss cheese" stimulus where the blurred "holes" in sine-wave carriers were of equal area to the blurred target ("cheese") regions. The locations of the target regions in the monocular image pairs were interdigitated across eyes such that their binocular sum was a uniform grating. When pedestal contrasts were above threshold, the monocular neural images contained strong evidence that the high-contrast regions in the two eyes did not overlap. Nevertheless, sensitivity to dual contrast increments (i.e., to contrast increments in different locations in the two eyes) was a factor of ∼1.7 greater than to single increments (i.e., increments in a single eye), comparable with conventional binocular summation. This provides evidence for a contiguous area summation process that operates at all contrasts and is influenced little, if at all, by eye of origin. A three-stage model of contrast gain control fitted the results and possessed the properties of ocularity invariance and area invariance owing to its cascade of normalization stages. The implications for a population code for pattern size are discussed.

Design of a flat-top fiber Bragg filter via quasi-random modulation of the refractive index

The statistics of the reflection spectrum of a short-correlated disordered fiber Bragg grating are studied. The averaged spectrum appears to be flat inside the bandgap and has significantly suppressed sidelobes compared to the uniform grating of the same bandwidth. This is due to the Anderson localization of the modes of a disordered grating. This observation prompts a new algorithm for designing passband reflection gratings. Using the stochastic invariant imbedding approach it is possible to obtain the probability distribution function for the random reflection coefficient inside the bandgap and obtain both the variance of the averaged reflectivity as well as the distribution of the time delay of the grating.

Sparse signal representation by adaptive non-uniform B-spline dictionaries on a compact interval

Non-uniform B-spline dictionaries on a compact interval are discussed in the context of sparse signal representation. For each given partition, dictionaries of B-spline functions for the corresponding spline space are built up by dividing the partition into subpartitions and joining together the bases for the concomitant subspaces. The resulting slightly redundant dictionaries are composed of B-spline functions of broader support than those corresponding to the B-spline basis for the identical space. Such dictionaries are meant to assist in the construction of adaptive sparse signal representation through a combination of stepwise optimal greedy techniques.

On the Uniform Decay of the Local Energy

It is proved in [1],[2] that in odd dimensional spaces any uniform decay of the local energy implies that it must decay exponentially. We extend this to even dimensional spaces and to more general perturbations (including the transmission problem) showing that any uniform decay of the local energy implies that it must decay like O(t^(−2n) ), t ≫ 1 being the time and n being the space dimension.

The General Differential Operators Generated by a Quasi-Differential Expressions with their Interior Singular Points

The general ordinary quasi-differential expression M of n-th order with complex coefficients and its formal adjoint M + are considered over a regoin (a, b) on the real line, −∞ ≤ a < b ≤ ∞, on which the operator may have a finite number of singular points. By considering M over various subintervals on which singularities occur only at the ends, restrictions of the maximal operator generated by M in L2|w (a, b) which are regularly solvable with respect to the minimal operators T0 (M ) and T0 (M + ). In addition to direct sums of regularly solvable operators defined on the separate subintervals, there are other regularly solvable restrications of the maximal operator which involve linking the various intervals together in interface like style.

Uniform Eberlein Compacta and Uniformly Gâteaux Smooth Norms

* Supported by grants: AV ĈR 101-95-02, GAĈR 201-94-0069 (Czech Republic) and NSERC 7926 (Canada).

On the Uniform Convergence of Partial Dunkl Integrals in Besov-Dunkl Spaces

2000 Mathematics Subject Classification: 44A15, 44A35, 46E30

A Dichotomy for Ordinary Differential Equations in a Banach Space

A dichotomysimilar property for a class of homogeneous differential equations in an arbitrary Banach space is introduced. By help of them, existence of quasi bounded solutions of the appropriate nonhomogeneous equation is proved.

A Generalized Quasi-Likelihood Estimator for Nonstationary Stochastic Processes−Asymptotic Properties and Examples

2010 Mathematics Subject Classification: 62F12, 62M05, 62M09, 62M10, 60G42.

Existence of Solutions for a Class of Quasi-Linear Singular Integro-Differential Equations

2000 Mathematics Subject Classification: 45F15, 45G10, 46B38.