Spherical geometry and integrable systems

We prove that the cosine law for spherical triangles and spherical tetrahedra defines integrable systems, both in the sense of multidimensional consistency and in the sense of dynamical systems.Comment: 15 pages, 5 figure

Monte Carlo Hamiltonian of lattice gauge theory

We discuss how the concept of the Monte Carlo Hamiltonian can be applied to lattice gauge theories.Comment: "Non-Perturbative Quantum Field Theory: Lattice and Beyond", Guangzhou, China 200

Evaluating single-sided natural ventilation models against full-scale idealised measurements: impact of wind direction and turbulence

Commonly single-sided natural ventilation is used in temperate climates to provide comfortable and healthy indoor environments. However, within built-up areas it is difficult to predict natural ventilation rates for buildings as they depend on many flow factors and opening type. Here, existing models are evaluated using the nine-month Refresh Cube Campaign (RCC). Pressure-based ventilation rates were determined for a small opening (1% porosity) in a cubical test building (side=6 m). The building was isolated and then sheltered in a limited staggered building array to simulate turbulent flows in dense urban areas. Internal and external flow, temperature and pressure measurements captured a wide range of scales of variability. Although the Warren and Parkins (1985, WP85) model performed best for 30-minute mean ventilation rates, all four models tested underestimated ventilation rates by a factor of 10. As wind dominated the stack effect, new coefficients were derived for the WP85 wind-driven model as a function of wind angle. Predictions were mostly improved, except for directions with complex flow patterns during the sheltered case. For the first time, the relation between ventilation rate and turbulence intensity (TI) around a full-scale building was tested. Results indicate that the wind-driven model for single-sided ventilation in highly turbulent flows (0.5<TI<4) can be improved by including TI as a multiplicative factor. Although small window openings with highly turbulent flows are common for sheltered buildings in urban areas, future model development should include a variety of configurations to assess the generality of these results

Generalized seniority for the shell model with realistic interactions

The generalized seniority scheme has long been proposed as a means of dramatically reducing the dimensionality of nuclear shell model calculations, when strong pairing correlations are present. However, systematic benchmark calculations, comparing results obtained in a model space truncated according to generalized seniority with those obtained in the full shell model space, are required to assess the viability of this scheme. Here, a detailed comparison is carried out, for semimagic nuclei taken in a full major shell and with realistic interactions. The even-mass and odd-mass Ca isotopes are treated in the generalized seniority scheme, for generalized seniority v<=3. Results for level energies, orbital occupations, and electromagnetic observables are compared with those obtained in the full shell model space.Comment: 13 pages, 8 figures; published in Phys. Rev.

Beating of the oscillations in the transport coefficients of a one-dimensionally periodically modulated two-dimensional electron gas in the presence of spin-orbit interaction

Transport properties of a two-dimensional electron gas (2DEG) are studied in the presence of a perpendicular magnetic field $B$, of a {\it weak} one-dimensional (1D) periodic potential modulation, and of the spin-orbit interaction (SOI) described only by the Rashba term. In the absence of the modulation the SOI mixes the spin-up and spin-down states of neighboring Landau levels into two new, unequally spaced energy branches. The levels of these branches broaden into bands in the presence of the modulation and their bandwidths oscillate with the field $B$. Evaluated at the Fermi energy, the $n$-th level bandwidth of each series has a minimum or vanishes at different values of the field $B$. In contrast with the 1D-modulated 2DEG without SOI, for which only one flat-band condition applies, here there are two flat-band conditions that can change considerably as a function of the SOI strength $\alpha$ and accordingly influence the transport coefficients of the 2DEG. The phase and amplitude of the Weiss and Shubnikov-de Haas (SdH) oscillations depend on the strength $\alpha$. For small values of $\alpha$ both oscillations show beating patterns. Those of the former are due to the independently oscillating bandwidths whereas those of the latter are due to modifications of the density of states, exhibit an even-odd filling factor transition, and are nearly independent of the modulation strength. For strong values of $\alpha$ the SdH oscillations are split in two

Recursive relations for a quiver gauge theory

We study the recursive relations for a quiver gauge theory with the gauge group $SU(N_1)\times SU(N_2)$ with bifundamental fermions transforming as $(N_1,\bar{N_2})$. We work out the recursive relation for the amplitudes involving a pair of quark and antiquark and gluons of each gauge group. We realize directly in the recursive relations the invariance under the order preserving permutations of the gluons of the first and the second gauge group. We check the proposed relations for MHV, 6-point and 7-point amplitudes and find the agreements with the known results and the known relations with the single gauge group amplitudes. The proposed recursive relation is much more efficient in calculating the amplitudes than using the known relations with the amplitudes of the single gauge group.Comment: 33 pages and 2 figures, minor correction

Search for the QCD Critical Point: Higher Moments of Net-proton Multiplicity Distributions

Higher moments of event-by-event net-proton multiplicity distributions have been applied to search for the QCD critical point. Model results are used to provide a baseline for this search. The measured moment products, $\kappa\sigma^2$ and $S\sigma$ of net-proton distributions, which are directly connected to the thermodynamical baryon number susceptibility ratio in Lattice QCD and Hadron Resonance Gas (HRG) model, are compared to the transport and thermal model results. We argue that a non-monotonic dependence of $\kappa \sigma^2$ and $S \sigma$ as a function of beam energy can be used to search for the QCD critical point.Comment: 7 pages, 3 figures. CPOD 2010 Proceeding