Spectral fluctuation and 1/f(alpha) noise in the energy level statistics of interacting trapped bosons

It has been recently shown numerically that the transition from integrability to chaos in quantum systems and the corresponding spectral fluctuations are characterized by 1/f(alpha) noise with 1 <= alpha <= 2. The system of interacting trapped bosons is inhomogeneous and complex. The presence of an external harmonic trap makes it more interesting as, in the atomic trap, the bosons occupy partly degenerate single-particle states. Earlier theoretical and experimental results show that at zero temperature the low-lying levels are of a collective nature and high-lying excitations are of a single-particle nature. We observe that for few bosons, the P(s) distribution shows the Shnirelman peak, which exhibits a large number of quasidegenerate states. For a large number of bosons the low-lying levels are strongly affected by the interatomic interaction, and the corresponding level fluctuation shows a transition to a Wigner distribution with an increase in particle number. It does not follow Gaussian orthogonal ensemble random matrix predictions. For high-lying levels we observe the uncorrelated Poisson distribution. Thus it may be a very realistic system to prove that 1/f(alpha) noise is ubiquitous in nature.

Describing some of the Dimensions that comprise the Profile of the Faculty Staff of Statistics Departments in Brazil

Statistics is a required course in virtually all undergraduate programs in Brazilian universities. In addition, undergraduate programs in Statistics are offered in many public universities. However, despite the importance of this science, there are no systematic studies in the national literature regarding the characterization of the faculty staff, which is responsible for the teaching of statistics in the country. In this context, this paper presents a description of the faculty members of undergraduate courses in Statistics. This description was based on a descriptive sample, related to aspects of their education and scientific production. A prediction of future demand for PhDs in Statistics to fill the vacancies is also provided based on the retirement of faculty members in undergraduate courses in Statistics in the country.

Energy-level statistics of interacting trapped bosons

It is a well-established fact that statistical properties of energy-level spectra are the most efficient tool to characterize nonintegrable quantum systems. The statistical behavior of different systems such as complex atoms, atomic nuclei, two-dimensional Hamiltonians, quantum billiards, and noninteracting many bosons has been studied. The study of statistical properties and spectral fluctuations in interacting many-boson systems has developed interest in this direction. We are especially interested in weakly interacting trapped bosons in the context of Bose-Einstein condensation (BEC) as the energy spectrum shows a transition from a collective nature to a single-particle nature with an increase in the number of levels. However this has received less attention as it is believed that the system may exhibit Poisson-like fluctuations due to the existence of an external harmonic trap. Here we compute numerically the energy levels of the zero-temperature many-boson systems which are weakly interacting through the van der Waals potential and are confined in the three-dimensional harmonic potential. We study the nearest-neighbor spacing distribution and the spectral rigidity by unfolding the spectrum. It is found that an increase in the number of energy levels for repulsive BEC induces a transition from a Wigner-like form displaying level repulsion to the Poisson distribution for P(s). It does not follow the Gaussian orthogonal ensemble prediction. For repulsive interaction, the lower levels are correlated and manifest level-repulsion. For intermediate levels P(s) shows mixed statistics, which clearly signifies the existence of two energy scales: external trap and interatomic interaction, whereas for very high levels the trapping potential dominates, generating a Poisson distribution. Comparison with mean-field results for lower levels are also presented. For attractive BEC near the critical point we observe the Shnirelman-like peak near s = 0, which signifies the presence of a large number of quasidegenerate states.

PXRF and multivariate statistics analysis of pre-colonial pottery from northeast of Brazil

Portable system of energy dispersive X-ray fluorescence was used to determine the elemental composition of 68 pottery fragments from Sambaqui do Bacanga, an archeological site in Sao Luis, Maranhao, Brazil. This site was occupied from 6600 BP until 900 BP. By determining the element chemical composition of those fragments, it was possible to verify the existence of engobe in 43 pottery fragments. Obtained from two-dimensional graphs and hierarchical cluster analysis performed in fragments of stratigraphies from surface and 113-cm level, and 10 to 20, 132 and 144-cm level, it was possible to group these fragments in five distinct groups, according to their stratigraphies. The results of data grouping (two-dimensional graphics) are in agreement with hierarchical cluster analysis by Ward method. Copyright (C) 2011 John Wiley & Sons, Ltd.