Models for the integer quantum Hall effect: the network model, the Dirac equation, and a tight-binding Hamiltonian

We consider models for the plateau transition in the integer quantum Hall effect. Starting from the network model, we construct a mapping to the Dirac Hamiltonian in two dimensions. In the general case, the Dirac Hamiltonian has randomness in the mass, the scalar potential, and the vector potential. Separately, we show that the network model can also be associated with a nearest neighbour, tight-binding Hamiltonian.Comment: Revtex, 15 pages, 7 figures; submitted to Phys. Rev.

Spinor Bose Condensates in Optical Traps

In an optical trap, the ground state of spin-1 Bosons such as $^{23}$Na, $^{39}$K, and $^{87}$Rb can be either a ferromagnetic or a "polar" state, depending on the scattering lengths in different angular momentum channel. The collective modes of these states have very different spin character and spatial distributions. While ordinary vortices are stable in the polar state, only those with unit circulation are stable in the ferromagnetic state. The ferromagnetic state also has coreless (or Skyrmion) vortices like those of superfluid $^{3}$He-A. Current estimates of scattering lengths suggest that the ground states of $^{23}$Na and $^{87}$Rb condensate are a polar state and a ferromagnetic state respectively.Comment: 11 pages, no figures. email : [email protected]

Quantum Simulation of the Hubbard Model: The Attractive Route

We study the conditions under which, using a canonical transformation, the phases sought after for the repulsive Hubbard model, namely a Mott insulator in the paramagnetic and anti-ferromagnetic phases, and a putative d-wave superfluid can be deduced from observations in an optical lattice loaded with a spin-imbalanced ultra-cold Fermi gas with attractive interactions, thus realizing the attractive Hubbard model. We show that the Mott insulator and antiferromagnetic phase of the repulsive Hubbard model are in fact more easy to observe as a paired, and superfluid phase respectively, in the attractive Hubbard model. The putative d-wave superfluid phase of the repulsive Hubbard model doped away from half-filling is related to a d-wave antiferromagnetic phase for the attractive Hubbard model. We discuss the advantages of this approach to 'quantum simulate' the Hubbard model in an optical lattice over the approach that attempts to directly simulate the doped Hubbard model in the repulsive regime. We also point out a number of technical difficulties of the proposed approach and, in some cases, suggest possible solutions.Comment: 11 pages, 5 figs. New version as accepted in PRA. We have clarified the models we are discussing in various places, and expanded on the critical number estimate to include both K40 and Li6 in section V. Also added reference

Development of aircraft brake materials

The requirements of brake materials were outlined and a survey made to select materials to meet the needs of high temperature brakes. A number of metals and ceramic materials were selected and evaluated in sliding tests which simulated aircraft braking. Nickel, molybdenum tungsten, Zr02, high temperature cements and carbons were tested. Additives were then incorporated into these materials to optimize their wear or strength behavior with particular emphasis on nickel and molybdenum base materials and a high temperature potassium silicate cement. Optimum materials were developed which improved wear behavior over conventional brake materials in the simulated test. The best materials are a nickel, aluminum oxide, lead tungstate composition containing graphite or molybdenum disulphite; a molybdenum base material containing LPA100 (an intermetallic compound of cobalt, molybdenum, and silicon); and a carbon material (P5)

Deconfinement and cold atoms in optical lattices

Despite the fact that by now one dimensional and three dimensional systems of interacting particles are reasonably well understood, very little is known on how to go from the one dimensional physics to the three dimensional one. This is in particular true in a quasi-one dimensional geometry where the hopping of particles between one dimensional chains or tubes can lead to a dimensional crossover between a Luttinger liquid and more conventional high dimensional states. Such a situation is relevant to many physical systems. Recently cold atoms in optical traps have provided a unique and controllable system in which to investigate this physics. We thus analyze a system made of coupled one dimensional tubes of interacting fermions. We explore the observable consequences, such as the phase diagram for isolated tubes, and the possibility to realize unusual superfluid phases in coupled tubes systems.Comment: Proceedings of the conference on "Quantum Many Body Theories 13", to be published by World Scientifi

Retrospective study of more than 9000 feline cutaneous tumours in the UK: 2006–2013

The aim of the study was to utilise a large database available from a UK-based, commercial veterinary diagnostic laboratory to ascertain the prevalence of different forms of cutaneous neoplasia within the feline population, and to detect any breed, sex or age predilections for the more common tumours

Double Phase Transitions in Magnetized Spinor Bose-Einstein Condensation

It is investigated theoretically that magnetized Bose-Einstein condensation (BEC) with the internal (spin) degrees of freedom exhibits a rich variety of phase transitions, depending on the sign of the interaction in the spin channel. In the antiferromagnetic interaction case there exist always double BEC transitions from single component BEC to multiple component BEC. In the ferromagnetic case BEC becomes always unstable at a lower temperature, leading to a phase separation. The detailed phase diagram for the temperature vs the polarization, the spatial spin structure, the distribution of non-condensates and the excitation spectrum are examined for the harmonically trapped systems.Comment: 6 pages, 7 figures. Submitted to J. Phys. Soc. Jp