Ultra-high energy neutrino scattering

Estimates are made of the ultra-high energy neutrino cross sections based on an extrapolation to very small Bjorken x of the logarithmic Froissart dependence in x shown previously to provide an excellent fit to the measured proton structure function F_2^p(x,Q^2) over a broad range of the virtuality Q^2. Expressions are obtained for both the neutral current and the charged current cross sections. Comparison with an extrapolation based on perturbative QCD shows good agreement for energies where both fit data, but our rates are as much as a factor of 10 smaller for neutrino energies above 10^9 GeV, with important implications for experiments searching for extra-galactic neutrinos.Comment: 4 pages, 1 figure, 1 table; Title, abstract and text changed, conclusions unchanged. Version accepted for publication in Physical Review

Spectra of sparse non-Hermitian random matrices: an analytical solution

We present the exact analytical expression for the spectrum of a sparse non-Hermitian random matrix ensemble, generalizing two classical results in random-matrix theory: this analytical expression forms a non-Hermitian version of the Kesten-Mckay law as well as a sparse realization of Girko's elliptic law. Our exact result opens new perspectives in the study of several physical problems modelled on sparse random graphs. In this context, we show analytically that the convergence rate of a transport process on a very sparse graph depends upon the degree of symmetry of the edges in a non-monotonous way.Comment: 5 pages, 5 figures, 12 pages supplemental materia

All Teleportation and Dense Coding Schemes

We establish a one-to-one correspondence between (1) quantum teleportation schemes, (2) dense coding schemes, (3) orthonormal bases of maximally entangled vectors, (4) orthonormal bases of unitary operators with respect to the Hilbert-Schmidt scalar product, and (5) depolarizing operations, whose Kraus operators can be chosen to be unitary. The teleportation and dense coding schemes are assumed to be ``tight'' in the sense that all Hilbert spaces involved have the same finite dimension d, and the classical channel involved distinguishes d^2 signals. A general construction procedure for orthonormal bases of unitaries, involving Latin Squares and complex Hadamard Matrices is also presented.Comment: 21 pages, LaTe

An exploration of ebook selection behavior in academic library collections

Academic libraries have offered ebooks for some time, however little is known about how readers interact with them while making relevance decisions. In this paper we seek to address that gap by analyzing ebook transaction logs for books in a university library

Neutrino-Induced Giant Air Showers in Large Extra Dimension Models

In models based on large extra dimensions where massive spin 2 exchange can dominate at high energies, the neutrino-proton cross section can rise to typical hadronic values at energies above 10^20 eV. The neutrino then becomes a candidate for the primary that initiates the highest energy cosmic ray showers. We investigate characteristics of neutrino-induced showers compared to proton-induced showers. The comparison includes study of starting depth, profile with depth, lateral particle distribution at ground and muon lateral distribution at ground level. We find that for cross sections above 20 mb there are regions of parameter space where the two types of showers are essentially indistinguishable. We conclude that the neutrino candidate hypothesis cannot be ruled out on the basis of shower characteristics.Comment: 24 pages, latex, 19 figures; text discussion and references added, typos corrected; figures and conclusions unchange

Study of Quark Propagator Solutions to the Dyson--Schwinger Equation in a Confining Model

We solve the Dyson--Schwinger equation for the quark propagator in a model with singular infrared behavior for the gluon propagator. We require that the solutions, easily found in configuration space, be tempered distributions and thus have Fourier transforms. This severely limits the boundary conditions that the solutions may satisify. The sign of the dimensionful parameter that characterizes the model gluon propagator can be either positive or negative. If the sign is negative, we find a unique solution. It is singular at the origin in momentum space, falls off like $1/p^2$ as $p^2\rightarrow +/-\infty$, and it is truly nonperturbative in that it is singular in the limit that the gluon--quark interaction approaches zero. If the sign of the gluon propagator coefficient is positive, we find solutions that are, in a sense that we exhibit, unconstrained linear combinations of advanced and retarded propagators. These solutions are singular at the origin in momentum space, fall off like $1/p^2$ asympotically, exhibit ``resonant--like" behavior at the position of the bare mass of the quark when the mass is large compared to the dimensionful interaction parameter in the gluon propagator model, and smoothly approach a linear combination of free--quark, advanced and retarded two--point functions in the limit that the interaction approaches zero. In this sense, these solutions behave in an increasingly ``particle--like" manner as the quark becomes heavy. The Feynman propagator and the Wightman function are not tempered distributions and therefore are not acceptable solutions to the Schwinger--Dyson equation in our model. On this basis we advance several arguments to show that the Fourier--transformable solutions we find are consistent with quark confinement, even though they have singularities on th

The rings of n-dimensional polytopes

Points of an orbit of a finite Coxeter group G, generated by n reflections starting from a single seed point, are considered as vertices of a polytope (G-polytope) centered at the origin of a real n-dimensional Euclidean space. A general efficient method is recalled for the geometric description of G- polytopes, their faces of all dimensions and their adjacencies. Products and symmetrized powers of G-polytopes are introduced and their decomposition into the sums of G-polytopes is described. Several invariants of G-polytopes are found, namely the analogs of Dynkin indices of degrees 2 and 4, anomaly numbers and congruence classes of the polytopes. The definitions apply to crystallographic and non-crystallographic Coxeter groups. Examples and applications are shown.Comment: 24 page

Discovery of Five Binary Radio Pulsars

We report on five binary pulsars discovered in the Parkes multibeam Galactic plane survey. All of the pulsars are old, with characteristic ages 1-11 Gyr, and have relatively small inferred magnetic fields, 5-90e8 G. The orbital periods range from 1.3 to 15 days. As a group these objects differ from the usual low-mass binary pulsars (LMBPs): their spin periods of 9-88 ms are relatively long; their companion masses, 0.2-1.1 Msun, are, in at least some cases, suggestive of CO or more massive white dwarfs; and some of the orbital eccentricities, 1e-5 < e < 0.002, are unexpectedly large. We argue that these observed characteristics reflect binary evolution that is significantly different from that of LMBPs. We also note that intermediate-mass binary pulsars apparently have a smaller scale-height than LMBPs.Comment: 5 pages, 4 embedded EPS figs, accepted for publication by ApJ Letter

Neutron spin echo is a "quantum tale of two paths''

We describe an experiment that strongly supports a two-path interferometric model in which the spin-up and spin-down components of each neutron propagate coherently along spatially separated parallel paths in a typical neutron spin echo small angle scattering (SESANS) experiment. Specifically, we show that the usual semi-classical, single-path treatment of the Larmor precession of a polarized neutron in an external magnetic field predicts a damping as a function of the spin-echo length of the SESANS signal obtained with a periodic phase grating when the transverse width of the neutron wave packet is finite. However, no such damping is observed experimentally, implying either that the Larmor model is incorrect or that the transverse extent of the wave packet is very large. In contrast, we demonstrate theoretically that a quantum-mechanical interferometric model in which the two mode-entangled (i.e. intraparticle entangled) spin states of a single neutron are separated in space when they interact with the grating accurately predicts the measured SESANS signal, which is independent of the wave packet width