The mitotic chromosomes of a macropod hybrid

In a yard at Hermitage Research Station, Warwick, a male agile wallaby (Wallabia agilis (Gould)) was observed mating with two female red kangaroos (Megaleia rufa (Desmarest)) and by late 1970 these females were carrying furred pouch young of phenotypic appearance intermediate between the species. A mitotic chromosome count of 2n = 18 was obtained for both progeny, male and female, of Wallabia agilis (Gould), (2n = 16) x Megaleia rufa (Desmarest), (2n = 20)

The vector-valued big q-Jacobi transform

Big $q$-Jacobi functions are eigenfunctions of a second order $q$-difference operator $L$. We study $L$ as an unbounded self-adjoint operator on an $L^2$-space of functions on $\mathbb R$ with a discrete measure. We describe explicitly the spectral decomposition of $L$ using an integral transform $\mathcal F$ with two different big $q$-Jacobi functions as a kernel, and we construct the inverse of $\mathcal F$.Comment: 35 pages, corrected an error and typo

Pentaquark as Kaon-Nucleon Resonance

Several recent experiments have reported evidence for a narrow feature in the K(+)-neutron system, an apparent resonant state ~ 100 MeV above threshold and with a width < 25 MeV. This state has been labelled as Theta(+) (previously as Z(*)), and because of the implied inclusion of a anti-strange quark, is referred to as a pentaquark, that is, five quarks within a single bag. We present an alternative explanation for such a structure, as a higher angular momentum resonance in the isospin zero K(+) -N system. One might call this an exit channel or a molecular resonance. In a non-relativistic potential model we find a possible candidate for the kaon-nucleon system with relative angular momentum L=3, while L=1 and 2 states possess centrifugal barriers too low to confine the kaon and nucleon in a narrow state at an energy so high above threshold. A rather strong state-dependence in the potential is essential, however, for eliminating an observable L=2 resonance at lower energies.Comment: 4 page

Conserving and Gapless Approximations for an Inhomogeneous Bose Gas at Finite Temperatures

We derive and discuss the equations of motion for the condensate and its fluctuations for a dilute, weakly interacting Bose gas in an external potential within the self--consistent Hartree--Fock--Bogoliubov (HFB) approximation. Account is taken of the depletion of the condensate and the anomalous Bose correlations, which are important at finite temperatures. We give a critical analysis of the self-consistent HFB approximation in terms of the Hohenberg--Martin classification of approximations (conserving vs gapless) and point out that the Popov approximation to the full HFB gives a gapless single-particle spectrum at all temperatures. The Beliaev second-order approximation is discussed as the spectrum generated by functional differentiation of the HFB single--particle Green's function. We emphasize that the problem of determining the excitation spectrum of a Bose-condensed gas (homogeneous or inhomogeneous) is difficult because of the need to satisfy several different constraints.Comment: plain tex, 19 page

Time dependent solitons of noncommutative Chern-Simons theory coupled to scalar fields

We study one- and two-soliton solutions of noncommutative Chern-Simons theory coupled to a nonrelativistic or a relativistic scalar field. In the nonrelativistic case, we find a tower of new stationary time-dependent solutions, all with the same charge density, but with increasing energies. The dynamics of these solitons cannot be studied using traditional moduli space techniques, but we do find a nontrivial symplectic form on the phase space indicating that the moduli space is not flat. In the relativistic case we find the metric on the two soliton moduli space.Comment: 22 pages, 2 figures, JHEP3 style. v2: This paper is a thoroughly revised version. We thank P.A. Horvathy, L. Martina and P.C. Stichel for illuminating comments that led us to reconsider some of our previously reported results; see note added at the end of the paper. v3: Acknowledgements adde

A nonlinear hydrodynamical approach to granular materials

We propose a nonlinear hydrodynamical model of granular materials. We show how this model describes the formation of a sand pile from a homogeneous distribution of material under gravity, and then discuss a simulation of a rotating sandpile which shows, in qualitative agreement with experiment, a static and dynamic angle of repose.Comment: 17 pages, 14 figures, RevTeX4; minor changes to wording and some additional discussion. Accepted by Phys. Rev.

Photo--assisted current and shot noise in the fractional quantum Hall effect

The effect of an AC perturbation on the shot noise of a fractional quantum Hall fluid is studied both in the weak and the strong backscattering regimes. It is known that the zero-frequency current is linear in the bias voltage, while the noise derivative exhibits steps as a function of bias. In contrast, at Laughlin fractions, the backscattering current and the backscattering noise both exhibit evenly spaced singularities, which are reminiscent of the tunneling density of states singularities for quasiparticles. The spacing is determined by the quasiparticle charge $\nu e$ and the ratio of the DC bias with respect to the drive frequency. Photo--assisted transport can thus be considered as a probe for effective charges at such filling factors, and could be used in the study of more complicated fractions of the Hall effect. A non-perturbative method for studying photo--assisted transport at $\nu=1/2$ is developed, using a refermionization procedure.Comment: 14 pages, 6 figure

Carbon clusters near the crossover to fullerene stability

The thermodynamic stability of structural isomers of $\mathrm{C}_{24}$, $\mathrm{C}_{26}$, $\mathrm{C}_{28}$ and $\mathrm{C}_{32}$, including fullerenes, is studied using density functional and quantum Monte Carlo methods. The energetic ordering of the different isomers depends sensitively on the treatment of electron correlation. Fixed-node diffusion quantum Monte Carlo calculations predict that a $\mathrm{C}_{24}$ isomer is the smallest stable graphitic fragment and that the smallest stable fullerenes are the $\mathrm{C}_{26}$ and $\mathrm{C}_{28}$ clusters with $\mathrm{C}_{2v}$ and $\mathrm{T}_{d}$ symmetry, respectively. These results support proposals that a $\mathrm{C}_{28}$ solid could be synthesized by cluster deposition.Comment: 4 pages, includes 4 figures. For additional graphics, online paper and related information see http://www.tcm.phy.cam.ac.uk/~prck

Expanded Vandermonde powers and sum rules for the two-dimensional one-component plasma

The two-dimensional one-component plasma (2dOCP) is a system of $N$ mobile particles of the same charge $q$ on a surface with a neutralising background. The Boltzmann factor of the 2dOCP at temperature $T$ can be expressed as a Vandermonde determinant to the power $\Gamma=q^{2}/(k_B T)$. Recent advances in the theory of symmetric and anti-symmetric Jack polymonials provide an efficient way to expand this power of the Vandermonde in their monomial basis, allowing the computation of several thermodynamic and structural properties of the 2dOCP for $N$ values up to 14 and $\Gamma$ equal to 4, 6 and 8. In this work, we explore two applications of this formalism to study the moments of the pair correlation function of the 2dOCP on a sphere, and the distribution of radial linear statistics of the 2dOCP in the plane