The Elliptic Billiard: Subtleties of Separability

Some of the subtleties of the integrability of the elliptic quantum billiard are discussed. A well known classical constant of the motion has in the quantum case an ill-defined commutator with the Hamiltonian. It is shown how this problem can be solved. A geometric picture is given revealing why levels of a separable system cross. It is shown that the repulsions found by Ayant and Arvieu are computational effects and that the method used by Traiber et al. is related to the present picture which explains the crossings they find. An asymptotic formula for the energy-levels is derived and it is found that the statistical quantities of the spectrum P(s) and \Delta(L) have the form expected for an integrable system.Comment: 10 pages, LaTeX, 3 Figures (postscript). Submitted to European Journal of Physic

Second moment of the Husimi distribution as a measure of complexity of quantum states

We propose the second moment of the Husimi distribution as a measure of complexity of quantum states. The inverse of this quantity represents the effective volume in phase space occupied by the Husimi distribution, and has a good correspondence with chaoticity of classical system. Its properties are similar to the classical entropy proposed by Wehrl, but it is much easier to calculate numerically. We calculate this quantity in the quartic oscillator model, and show that it works well as a measure of chaoticity of quantum states.Comment: 25 pages, 10 figures. to appear in PR

Observation of Nonspreading Wave Packets in an Imaginary Potential

We propose and experimentally demonstrate a method to prepare a nonspreading atomic wave packet. Our technique relies on a spatially modulated absorption constantly chiseling away from an initially broad de Broglie wave. The resulting contraction is balanced by dispersion due to Heisenberg's uncertainty principle. This quantum evolution results in the formation of a nonspreading wave packet of Gaussian form with a spatially quadratic phase. Experimentally, we confirm these predictions by observing the evolution of the momentum distribution. Moreover, by employing interferometric techniques, we measure the predicted quadratic phase across the wave packet. Nonspreading wave packets of this kind also exist in two space dimensions and we can control their amplitude and phase using optical elements.Comment: 4 figure

Jacobi Polynomials as su(2, 2) Unitary Irreducible Representation

Ver abstrac

Quantum walk on distinguishable non-interacting many-particles and indistinguishable two-particle

We present an investigation of many-particle quantum walks in systems of non-interacting distinguishable particles. Along with a redistribution of the many-particle density profile we show that the collective evolution of the many-particle system resembles the single-particle quantum walk evolution when the number of steps is greater than the number of particles in the system. For non-uniform initial states we show that the quantum walks can be effectively used to separate the basis states of the particle in position space and grouping like state together. We also discuss a two-particle quantum walk on a two- dimensional lattice and demonstrate an evolution leading to the localization of both particles at the center of the lattice. Finally we discuss the outcome of a quantum walk of two indistinguishable particles interacting at some point during the evolution.Comment: 8 pages, 7 figures, To appear in special issue: "quantum walks" to be published in Quantum Information Processin

Statistics of electromagnetic transitions as a signature of chaos in many-electron atoms

Using a configuration interaction approach we study statistics of the dipole matrix elements (E1 amplitudes) between the 14 lower odd states with J=4 and 21st to 100th even states with J=4 in the Ce atom (1120 lines). We show that the distribution of the matrix elements is close to Gaussian, although the width of the Gaussian distribution, i.e. the root-mean-square matrix element, changes with the excitation energy. The corresponding line strengths are distributed according to the Porter-Thomas law which describes statistics of transition strengths between chaotic states in compound nuclei. We also show how to use a statistical theory to calculate mean squared values of the matrix elements or transition amplitudes between chaotic many-body states. We draw some support for our conclusions from the analysis of the 228 experimental line strengths in Ce [J. Opt. Soc. Am. v. 8, p. 1545 (1991)], although direct comparison with the calculations is impeded by incompleteness of the experimental data. Nevertheless, the statistics observed evidence that highly excited many-electron states in atoms are indeed chaotic.Comment: 16 pages, REVTEX, 4 PostScript figures (submitted to Phys Rev A

Random Operator Approach for Word Enumeration in Braid Groups

We investigate analytically the problem of enumeration of nonequivalent primitive words in the braid group B_n for n >> 1 by analysing the random word statistics and the target space on the basis of the locally free group approximation. We develop a "symbolic dynamics" method for exact word enumeration in locally free groups and bring arguments in support of the conjecture that the number of very long primitive words in the braid group is not sensitive to the precise local commutation relations. We consider the connection of these problems with the conventional random operator theory, localization phenomena and statistics of systems with quenched disorder. Also we discuss the relation of the particular problems of random operator theory to the theory of modular functionsComment: 36 pages, LaTeX, 4 separated Postscript figures, submitted to Nucl. Phys. B [PM

Discovery of long-period variable stars in the very-metal-poor globular cluster M15

We present a search for long-period variable (LPV) stars among giant branch stars in M15 which, at [Fe/H] ~ -2.3, is one of the most metal-poor Galactic globular clusters. We use multi-colour optical photometry from the 0.6-m Keele Thornton and 2-m Liverpool Telescopes. Variability of delta-V ~ 0.15 mag is detected in K757 and K825 over unusually-long timescales of nearly a year, making them the most metal-poor LPVs found in a Galactic globular cluster. K825 is placed on the long secondary period sequence, identified for metal-rich LPVs, though no primary period is detectable. We discuss this variability in the context of dust production and stellar evolution at low metallicity, using additional spectra from the 6.5-m Magellan (Las Campanas) telescope. A lack of dust production, despite the presence of gaseous mass loss raises questions about the production of dust and the intra-cluster medium of this cluster.Comment: 13 pages, 9 figures, accepted by MNRA

Use of partial least squares regression to impute SNP genotypes in Italian Cattle breeds

Background The objective of the present study was to test the ability of the partial least squares regression technique to impute genotypes from low density single nucleotide polymorphisms (SNP) panels i.e. 3K or 7K to a high density panel with 50K SNP. No pedigree information was used. Methods Data consisted of 2093 Holstein, 749 Brown Swiss and 479 Simmental bulls genotyped with the Illumina 50K Beadchip. First, a single-breed approach was applied by using only data from Holstein animals. Then, to enlarge the training population, data from the three breeds were combined and a multi-breed analysis was performed. Accuracies of genotypes imputed using the partial least squares regression method were compared with those obtained by using the Beagle software. The impact of genotype imputation on breeding value prediction was evaluated for milk yield, fat content and protein content. Results In the single-breed approach, the accuracy of imputation using partial least squares regression was around 90 and 94% for the 3K and 7K platforms, respectively; corresponding accuracies obtained with Beagle were around 85% and 90%. Moreover, computing time required by the partial least squares regression method was on average around 10 times lower than computing time required by Beagle. Using the partial least squares regression method in the multi-breed resulted in lower imputation accuracies than using single-breed data. The impact of the SNP-genotype imputation on the accuracy of direct genomic breeding values was small. The correlation between estimates of genetic merit obtained by using imputed versus actual genotypes was around 0.96 for the 7K chip. Conclusions Results of the present work suggested that the partial least squares regression imputation method could be useful to impute SNP genotypes when pedigree information is not available