On two 10th order mock theta identities

We give short proofs of conjectural identities due to Gordon and McIntosh involving two 10th order mock theta functions.Comment: 5 pages, to appear in the Ramanujan Journa

Theory and applications of an atoms in molecules approach to the Xα -SCF method

We have studied the Xα -SCF problem with an atoms in molecules approach. LCAO-molecular orbitals are used and the molecular charge and exchange densities are built up from atomic contributions. We have applied our method to CH3F with subsequent comparison to ab initio calculations. The Xα -SCF dipole moment of CH3F is 1.76 D compared with an experimental value of 1.79 D. We also give calculations of TCNQ and TTF with comparisons to recent Xα calculations using the overlapping sphere modification of a muffin-tin potential. Quadrupole moments for TCNQ and TTF have also been determined. The Journal of Chemical Physics is copyrighted by The American Institute of Physics

Low Timing Jitter Detector for Gigahertz Quantum Key Distribution

A superconducting single-photon detector based on a niobium nitride nanowire is demonstrated in an optical-fibre-based quantum key distribution test bed operating at a clock rate of 3.3 GHz and a transmission wavelength of 850 nm. The low jitter of the detector leads to significant reduction in the estimated quantum bit error rate and a resultant improvement in the secrecy efficiency compared to previous estimates made by use of silicon single-photon avalanche detectors.Comment: 11 pages, including 2 figure

Bistability and macroscopic quantum coherence in a BEC of ^7Li

We consider a Bose-Einstein condensate (BEC) of $^7Li$ in a situation where the density undergoes a symmetry breaking in real space. This occurs for a suitable number of condensed atoms in a double well potential, obtained by adding a standing wave light field to the trap potential. Evidence of bistability results from the solution of the Gross-Pitaevskii equation. By second quantization, we show that the classical bistable situation is in fact a Schr\"odinger cat (SC) and evaluate the tunneling rate between the two SC states. The oscillation between the two states is called MQC (macroscopic quantum coherence); we study the effects of losses on MQC.Comment: 8 pages, 11 figures. e-mail: [email protected]

K-string tensions at finite temperature and integrable models

It has recently been pointed out that simple scaling properties of Polyakov correlation functions of gauge systems in the confining phase suggest that the ratios of k-string tensions in the low temperature region is constant up to terms of order T^3. Here we argue that, at least in a three-dimensional Z_4 gauge model, the above ratios are constant in the whole confining phase. This result is obtained by combining numerical experiments with known exact results on the mass spectrum of an integrable two-dimensional spin model describing the infrared behaviour of the gauge system near the deconfining transition.Comment: 22 pages, 7 figures, 1 tabl

State-space modelling of the drivers of movement behaviour in sympatric species

Understanding animal movement behaviour is key to furthering our knowledge on intra- and inter-specific competition, group cohesion, energy expenditure, habitat use, the spread of zoonotic diseases or species management. We used a radial basis function surface approximation subject to minimum description length constraint to uncover the state-space dynamical systems from time series data. This approximation allowed us to infer structure from a mathematical model of the movement behaviour of sheep and red deer, and the effect of density, thermal stress and vegetation type. Animal movement was recorded using GPS collars deployed in sheep and deer grazing a large experimental plot in winter and summer. Information on the thermal stress to which animals were exposed was estimated using the power consumption of mechanical heated models and meteorological records of a network of stations in the plot. Thermal stress was higher in deer than in sheep, with less differences between species in summer. Deer travelled more distance than sheep, and both species travelled more in summer than in winter; deer travel distance showed less seasonal differences than sheep. Animal movement was better predicted in deer than in sheep and in winter than in summer; both species showed a swarming behaviour in group cohesion, stronger in deer. At shorter separation distances swarming repulsion was stronger between species than within species. At longer separation distances inter-specific attraction was weaker than intra-specific; there was a positive density-dependent effect on swarming, and stronger in deer than in sheep. There was not clear evidence which species attracted or repelled the other; attraction between deer at long separation distances was stronger when the model accounted for thermal stress, but in general the dynamic movement behaviour was hardly affected by the thermal stress. Vegetation type affected intra-species interactions but had little effect on inter-species interactions. Our modelling approach is useful in interpreting animal interactions, in order to unravel complex cooperative or competitive behaviours, and to the best of our knowledge is the first modelling attempt to make predictions of multi-species animal movement under different habitat mosaics and abiotic environmental conditions

Are braneworlds born isotropic?

It has recently been suggested that an isotropic singularity may be a generic feature of brane cosmologies, even in the inhomogeneous case. Using the covariant and gauge-invariant approach we present a detailed analysis of linear perturbations of the isotropic model ${\cal F}_b$ which is a past attractor in the phase space of homogeneous Bianchi models on the brane. We find that for matter with an equation of state parameter $\gamma > 1$, the dimensionless variables representing generic anisotropic and inhomogeneous perturbations decay as $t\to 0$, showing that the model ${\cal F}_b$ is asymptotically stable in the past. We conclude that brane universes are born with isotropy naturally built-in, contrary to standard cosmology. The observed large-scale homogeneity and isotropy of the universe can therefore be explained as a consequence of the initial conditions if the brane-world paradigm represents a description of the very early universe.Comment: Changed to match published versio

A comparison principle for functions of a uniformly random subspace

This note demonstrates that it is possible to bound the expectation of an arbitrary norm of a random matrix drawn from the Stiefel manifold in terms of the expected norm of a standard Gaussian matrix with the same dimensions. A related comparison holds for any convex function of a random matrix drawn from the Stiefel manifold. For certain norms, a reversed inequality is also valid.Comment: 8 page

Atom loss and the formation of a molecular Bose-Einstein condensate by Feshbach resonance

In experiments conducted recently at MIT on Na Bose-Einstein condensates [S. Inouye et al, Nature 392, 151 (1998); J. Stenger et al, Phys. Rev. Lett. 82, 2422 (1999)], large loss rates were observed when a time-varying magnetic field was used to tune a molecular Feshbach resonance state near the state of a pair of atoms in the condensate. A collisional deactivation mechanism affecting a temporarily formed molecular condensate [see V. A. Yurovsky, A. Ben-Reuven, P. S. Julienne and C. J. Williams, Phys. Rev. A 60, R765 (1999)], studied here in more detail, accounts for the results of the slow-sweep experiments. A best fit to the MIT data yields a rate coefficient for deactivating atom-molecule collisions of 1.6e-10 cm**3/s. In the case of the fast sweep experiment, a study is carried out of the combined effect of two competing mechanisms, the three-atom (atom-molecule) or four-atom (molecule-molecule) collisional deactivation vs. a process of two-atom trap-state excitation by curve crossing [F. H. Mies, P. S. Julienne, and E. Tiesinga, Phys. Rev. A 61, 022721 (2000)]. It is shown that both mechanisms contribute to the loss comparably and nonadditively.Comment: LaTeX, 14 pages, 12 PostScript figures, uses REVTeX and psfig, submitted to Physical Review