Fano resonances in a three-terminal nanodevice

The electron transport through a quantum sphere with three one-dimensional wires attached to it is investigated. An explicit form for the transmission coefficient as a function of the electron energy is found from the first principles. The asymmetric Fano resonances are detected in transmission of the system. The collapse of the resonances is shown to appear under certain conditions. A two-terminal nanodevice with an additional gate lead is studied using the developed approach. Additional resonances and minima of transmission are indicated in the device.Comment: 11 pages, 5 figures, 2 equations are added, misprints in 5 equations are removed, published in Journal of Physics: Condensed Matte

Property (T) and rigidity for actions on Banach spaces

We study property (T) and the fixed point property for actions on $L^p$ and other Banach spaces. We show that property (T) holds when $L^2$ is replaced by $L^p$ (and even a subspace/quotient of $L^p$), and that in fact it is independent of $1\leq p<\infty$. We show that the fixed point property for $L^p$ follows from property (T) when 1. For simple Lie groups and their lattices, we prove that the fixed point property for $L^p$ holds for any $1< p<\infty$ if and only if the rank is at least two. Finally, we obtain a superrigidity result for actions of irreducible lattices in products of general groups on superreflexive Banach spaces.Comment: Many minor improvement

Chaotic maps and flows: Exact Riemann-Siegel lookalike for spectral fluctuations

To treat the spectral statistics of quantum maps and flows that are fully chaotic classically, we use the rigorous Riemann-Siegel lookalike available for the spectral determinant of unitary time evolution operators $F$. Concentrating on dynamics without time reversal invariance we get the exact two-point correlator of the spectral density for finite dimension $N$ of the matrix representative of $F$, as phenomenologically given by random matrix theory. In the limit $N\to\infty$ the correlator of the Gaussian unitary ensemble is recovered. Previously conjectured cancellations of contributions of pseudo-orbits with periods beyond half the Heisenberg time are shown to be implied by the Riemann-Siegel lookalike

Probabilistic models of information retrieval based on measuring the divergence from randomness

We introduce and create a framework for deriving probabilistic models of Information Retrieval. The models are nonparametric models of IR obtained in the language model approach. We derive term-weighting models by measuring the divergence of the actual term distribution from that obtained under a random process. Among the random processes we study the binomial distribution and Bose--Einstein statistics. We define two types of term frequency normalization for tuning term weights in the document--query matching process. The first normalization assumes that documents have the same length and measures the information gain with the observed term once it has been accepted as a good descriptor of the observed document. The second normalization is related to the document length and to other statistics. These two normalization methods are applied to the basic models in succession to obtain weighting formulae. Results show that our framework produces different nonparametric models forming baseline alternatives to the standard tf-idf model

On multiplicities in length spectra of arithmetic hyperbolic three-orbifolds

Asymptotic laws for mean multiplicities of lengths of closed geodesics in arithmetic hyperbolic three-orbifolds are derived. The sharpest results are obtained for non-compact orbifolds associated with the Bianchi groups SL(2,o) and some congruence subgroups. Similar results hold for cocompact arithmetic quaternion groups, if a conjecture on the number of gaps in their length spectra is true. The results related to the groups above give asymptotic lower bounds for the mean multiplicities in length spectra of arbitrary arithmetic hyperbolic three-orbifolds. The investigation of these multiplicities is motivated by their sensitive effect on the eigenvalue spectrum of the Laplace-Beltrami operator on a hyperbolic orbifold, which may be interpreted as the Hamiltonian of a three-dimensional quantum system being strongly chaotic in the classical limit.Comment: 29 pages, uuencoded ps. Revised version, to appear in NONLINEARIT

Numerical Study of Length Spectra and Low-lying Eigenvalue Spectra of Compact Hyperbolic 3-manifolds

In this paper, we numerically investigate the length spectra and the low-lying eigenvalue spectra of the Laplace-Beltrami operator for a large number of small compact(closed) hyperbolic (CH) 3-manifolds. The first non-zero eigenvalues have been successfully computed using the periodic orbit sum method, which are compared with various geometric quantities such as volume, diameter and length of the shortest periodic geodesic of the manifolds. The deviation of low-lying eigenvalue spectra of manifolds converging to a cusped hyperbolic manifold from the asymptotic distribution has been measured by $\zeta-$ function and spectral distance.Comment: 19 pages, 18 EPS figures and 2 GIF figures (fig.10) Description of cusped manifolds in section 2 is correcte

Differential criterion of a bubble collapse in viscous liquids

The present work is devoted to a model of bubble collapse in a Newtonian viscous liquid caused by an initial bubble wall motion. The obtained bubble dynamics described by an analytic solution significantly depends on the liquid and bubble parameters. The theory gives two types of bubble behavior: collapse and viscous damping. This results in a general collapse condition proposed as the sufficient differential criterion. The suggested criterion is discussed and successfully applied to the analysis of the void and gas bubble collapses.Comment: 5 pages, 3 figure

The structure of molecular gas associated with NGC2264: wide-field 12CO and H2 imaging

We present wide-field, high-resolution imaging observations in 12CO 3-2 and H2 1-0 S(1) towards a ~1 square degree region of NGC2264. We identify 46 H2 emission objects, of which 35 are new discoveries. We characterize several cores as protostellar, reducing the previously observed ratio of prestellar/protostellar cores in the NGC2264 clusters. The length of H2 jets increases the previously reported spatial extent of the clusters. In each cluster, <0.5% of cloud material has been perturbed by outflow activity. A principal component analysis of the 12CO data suggests that turbulence is driven on scales >2.6 pc, which is larger than the extent of the outflows. We obtain an exponent alpha=0.74 for the size-linewidth relation, possibly due to the high surface density of NGC2264. In this very active, mixed-mass star forming region, our observations suggest that protostellar outflow activity is not injecting energy and momentum on a large enough scale to be the dominant source of turbulence.Comment: MNRAS accepte

Blood ties: ABO is a trans-species polymorphism in primates

The ABO histo-blood group, the critical determinant of transfusion incompatibility, was the first genetic polymorphism discovered in humans. Remarkably, ABO antigens are also polymorphic in many other primates, with the same two amino acid changes responsible for A and B specificity in all species sequenced to date. Whether this recurrence of A and B antigens is the result of an ancient polymorphism maintained across species or due to numerous, more recent instances of convergent evolution has been debated for decades, with a current consensus in support of convergent evolution. We show instead that genetic variation data in humans and gibbons as well as in Old World Monkeys are inconsistent with a model of convergent evolution and support the hypothesis of an ancient, multi-allelic polymorphism of which some alleles are shared by descent among species. These results demonstrate that the ABO polymorphism is a trans-species polymorphism among distantly related species and has remained under balancing selection for tens of millions of years, to date, the only such example in Hominoids and Old World Monkeys outside of the Major Histocompatibility Complex.Comment: 45 pages, 4 Figures, 4 Supplementary Figures, 5 Supplementary Table