Geometric Exponents of Dilute Logarithmic Minimal Models

The fractal dimensions of the hull, the external perimeter and of the red bonds are measured through Monte Carlo simulations for dilute minimal models, and compared with predictions from conformal field theory and SLE methods. The dilute models used are those first introduced by Nienhuis. Their loop fugacity is beta = -2cos(pi/barkappa}) where the parameter barkappa is linked to their description through conformal loop ensembles. It is also linked to conformal field theories through their central charges c = 13 - 6(barkappa + barkappa^{-1}) and, for the minimal models of interest here, barkappa = p/p' where p and p' are two coprime integers. The geometric exponents of the hull and external perimeter are studied for the pairs (p,p') = (1,1), (2,3), (3,4), (4,5), (5,6), (5,7), and that of the red bonds for (p,p') = (3,4). Monte Carlo upgrades are proposed for these models as well as several techniques to improve their speeds. The measured fractal dimensions are obtained by extrapolation on the lattice size H,V -> infinity. The extrapolating curves have large slopes; despite these, the measured dimensions coincide with theoretical predictions up to three or four digits. In some cases, the theoretical values lie slightly outside the confidence intervals; explanations of these small discrepancies are proposed.Comment: 41 pages, 32 figures, added reference

Staggered Chiral Perturbation Theory for Heavy-Light Mesons

We incorporate heavy-light mesons into staggered chiral perturbation theory, working to leading order in 1/m_Q, where m_Q is the heavy quark mass. At first non-trivial order in the chiral expansion, staggered taste violations affect the chiral logarithms for heavy-light quantities only through the light meson propagators in loops. There are also new analytic contributions coming from additional terms in the Lagrangian involving heavy-light and light mesons. Using this heavy-light staggered chiral perturbation theory, we perform the one-loop calculation of the B (or D) meson leptonic decay constant in the partially quenched and full QCD cases. In our treatment, we assume the validity both of the "fourth root trick" to reduce four staggered tastes to one, and of the prescription to represent this trick in the chiral theory by insertions of factors of 1/4 for each sea quark loop.Comment: 48 pages, 6 figures. v3: Some clarifying comments/caveats added; typos fixed. Corresponds to published versio

Quantum Pumping with Ultracold Atoms on Microchips: Fermions versus Bosons

We present a design for simulating quantum pumping of electrons in a mesoscopic circuit with ultra-cold atoms in a micro-magnetic chip trap. We calculate theoretical results for quantum pumping of both bosons and fermions, identifying differences and common features, including geometric behavior and resonance transmission. We analyze the feasibility of experiments with bosonic $^{87}$Rb and fermionic $^{40}$K atoms with an emphasis on reliable atomic current measurements.Comment: 4 pages; 4 figure

Structure and evolution of strange attractors in non-elastic triangular billiards

We study pinball billiard dynamics in an equilateral triangular table. In such dynamics, collisions with the walls are non-elastic: the outgoing angle with the normal vector to the boundary is a uniform factor $\lambda < 1$ smaller than the incoming angle. This leads to contraction in phase space for the discrete-time dynamics between consecutive collisions, and hence to attractors of zero Lebesgue measure, which are almost always fractal strange attractors with chaotic dynamics, due to the presence of an expansion mechanism. We study the structure of these strange attractors and their evolution as the contraction parameter $\lambda$ is varied. For $\lambda$ in the interval (0, 1/3), we prove rigorously that the attractor has the structure of a Cantor set times an interval, whereas for larger values of $\lambda$ the billiard dynamics gives rise to nonaccessible regions in phase space. For $\lambda$ close to 1, the attractor splits into three transitive components, the basins of attraction of which have fractal basin boundaries.Comment: 12 pages, 10 figures; submitted for publication. One video file available at http://sistemas.fciencias.unam.mx/~dsanders

Identifying and Assessing Conflicts Between Future Development and Current Migratory Bird Habitat Around Farmington Bay, Utah

Every year, the Great Salt Lake (GSL) and its associated wetlands provide critical habitat for over 250 migratory bird species from both the Pacific and Central Flyways. The GSL borders the Wasatch Front, which is the fastest growing and most populous region in Utah. To support the ever-increasing working population, the government of Utah aspires to increase the robust economic growth of the region through economic incentives and development of infrastructure. As this area continues to develop, greater pressure will be placed on the surrounding natural resources, including the GSL, its wetlands, and the open space and agricultural land that act as buffers from the urbanizing Wasatch Front. The primary objective of this research was to identify and assess possible conflicts between current migratory bird habitat and three proposed future development projects around Farmington Bay of the GSL. To identify and assess potential conflicts, I first created habitat maps for three migratory bird guilds that use the Farmington Bay area by combining five individual species’ habitat distributions within each guild. Then, I collected and prepared spatial data for three proposed development projects that are likely to develop by the year 2040. Next, I overlaid the development projects onto each guild’s and species’ habitat map to first identify conflict areas and then assess the spatial impacts to habitat for each species and guild. Finally, I made recommendations for future development that promote the conservation of migratory bird habitat within the study area. Overall, I found that all three of the proposed development projects produce substantial amounts of conflict with the current migratory bird habitat in the region. Based on these findings, I recommend three development initiatives. First, promote ‘centered growth’ and higher-density housing to reduce the sprawl of single-family residential neighborhoods. Second, retain and protect open space and agricultural lands as buffers around Farmington Bay to reduce habitat fragmentation and urban encroachment. Third, reconsider the construction of a new four-lane highway along the eastern edge of Farmington Bay. If these recommendations are implemented, the region’s migratory bird habitat will have greater protection from economic expansion and urban development

Conflicts Abound: How Future Development Along the Wasatch Front Will Replace Critical Migratory Bird Habitat Around Farmington Bay

Every year, the Great Salt Lake (GSL) and its associated wetlands provide critical habitat to over 250 migratory bird species from both the Pacific and Central Flyways. The GSL borders the Wasatch Front, which is the fastest growing and most populous region in Utah. To support the ever-increasing working population, the government of Utah aspires to increase economic growth in the region through more economic incentives and infrastructure development. As this area continues to develop, greater pressure will be placed on the surrounding natural resources, including the GSL, its wetlands, and the open space and agricultural lands that act as buffers from the urbanizing Wasatch Front. The primary objective of this research was to identify and assess possible conflicts between current migratory bird habitat and three proposed future development projects around Farmington Bay of the GSL. To identify and assess potential conflicts, the first step was to create habitat maps for three migratory bird guilds that use the Farmington Bay area by combining five representative species\u27 habitat distributions for each guild. The next step was to collect and prepare spatial data for three proposed development projects that are slated for development by 2040. Next, the development projects were overlaid onto each guild\u27s and species\u27 habitat map to first identify conflict areas and then assess the spatial impacts on habitat for each species and guild. This report ends with recommendations for future development that promote the conservation of migratory bird habitat within the study area. Overall, the three of the proposed development projects examined in this study produce substantial amounts of conflict with the current migratory bird habitat in the region. Based on these findings, recommendations were made for three development initiatives. First, promote \u27centered growth\u27 and higher-density housing to reduce the sprawl of single-family home neighborhoods. Second, retain and protect open space and agricultural lands as buffers around Farmington Bay to reduce the effects of habitat fragmentation and urban encroachment. Third, reconsider the construction of a new four-lane highway along the eastern edge of Farmington Bay. If these recommendations are implemented, the region\u27s migratory bird habitat will remain protected from the impending economic expansion and urban development in the coming years

Nernst effect in the phase-fluctuating superconductor InOx_x

We present a study of the Nernst effect in amorphous 2D superconductor InO$_x$, whose low carrier density implies low phase rigidity and strong superconducting phase fluctuations. Instead of presenting the abrupt jump expected at a BCS transition, the Nernst signal evolves continuously through the superconducting transition as previously observed in underdoped cuprates. This contrasts with the case of Nb$_{0.15}$Si$_{0.85}$, where the Nernst signal due to vortices below T$_{c}$ and by Gaussian fluctuations above are clearly distinct. The behavior of the ghost critical field in InO$_x$ points to a correlation length which does not diverge at $T_c$, a temperature below which the amplitude fluctuations freeze, but phase fluctuations survive.Comment: 4 pages, 4 figure

A homomorphism between link and XXZ modules over the periodic Temperley-Lieb algebra

We study finite loop models on a lattice wrapped around a cylinder. A section of the cylinder has N sites. We use a family of link modules over the periodic Temperley-Lieb algebra EPTL_N(\beta, \alpha) introduced by Martin and Saleur, and Graham and Lehrer. These are labeled by the numbers of sites N and of defects d, and extend the standard modules of the original Temperley-Lieb algebra. Beside the defining parameters \beta=u^2+u^{-2} with u=e^{i\lambda/2} (weight of contractible loops) and \alpha (weight of non-contractible loops), this family also depends on a twist parameter v that keeps track of how the defects wind around the cylinder. The transfer matrix T_N(\lambda, \nu) depends on the anisotropy \nu and the spectral parameter \lambda that fixes the model. (The thermodynamic limit of T_N is believed to describe a conformal field theory of central charge c=1-6\lambda^2/(\pi(\lambda-\pi)).) The family of periodic XXZ Hamiltonians is extended to depend on this new parameter v and the relationship between this family and the loop models is established. The Gram determinant for the natural bilinear form on these link modules is shown to factorize in terms of an intertwiner i_N^d between these link representations and the eigenspaces of S^z of the XXZ models. This map is shown to be an isomorphism for generic values of u and v and the critical curves in the plane of these parameters for which i_N^d fails to be an isomorphism are given.Comment: Replacement of "The Gram matrix as a connection between periodic loop models and XXZ Hamiltonians", 31 page

Phase structure of SU(3) gauge theory with two flavors of symmetric-representation fermions

We have performed numerical simulations of SU(3) gauge theory coupled to Nf=2 flavors of symmetric representation fermions. The fermions are discretized with the tadpole-improved clover action. Our simulations are done on lattices of length L=6, 8, and 12. In all simulation volumes we observe a crossover from a strongly coupled confined phase to a weak coupling deconfined phase. Degeneracies in screening masses, plus the behavior of the pseudoscalar decay constant, indicate that the deconfined phase is also a phase in which chiral symmetry is restored. The movement of the confinement transition as the volume is changed is consistent with avoidance of the basin of attraction of an infrared fixed point of the massless theory.Comment: 12 pages, 11 figure

Heavy-Light Semileptonic Decays in Staggered Chiral Perturbation Theory

We calculate the form factors for the semileptonic decays of heavy-light pseudoscalar mesons in partially quenched staggered chiral perturbation theory (\schpt), working to leading order in $1/m_Q$, where $m_Q$ is the heavy quark mass. We take the light meson in the final state to be a pseudoscalar corresponding to the exact chiral symmetry of staggered quarks. The treatment assumes the validity of the standard prescription for representing the staggered ``fourth root trick'' within \schpt by insertions of factors of 1/4 for each sea quark loop. Our calculation is based on an existing partially quenched continuum chiral perturbation theory calculation with degenerate sea quarks by Becirevic, Prelovsek and Zupan, which we generalize to the staggered (and non-degenerate) case. As a by-product, we obtain the continuum partially quenched results with non-degenerate sea quarks. We analyze the effects of non-leading chiral terms, and find a relation among the coefficients governing the analytic valence mass dependence at this order. Our results are useful in analyzing lattice computations of form factors $B\to\pi$ and $D\to K$ when the light quarks are simulated with the staggered action.Comment: 53 pages, 8 figures, v2: Minor correction to the section on finite volume effects, and typos fixed. Version to be published in Phys. Rev.