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

Constructing and exploring wells of energy landscapes

Landscape paradigm is ubiquitous in physics and other natural sciences, but it has to be supplemented with both quantitative and qualitatively meaningful tools for analyzing the topography of a given landscape. We here consider dynamic explorations of the relief and introduce as basic topographic features ``wells of duration $T$ and altitude $y$''. We determine an intrinsic exploration mechanism governing the evolutions from an initial state in the well up to its rim in a prescribed time, whose finite-difference approximations on finite grids yield a constructive algorithm for determining the wells. Our main results are thus (i) a quantitative characterization of landscape topography rooted in a dynamic exploration of the landscape, (ii) an alternative to stochastic gradient dynamics for performing such an exploration, (iii) a constructive access to the wells and (iv) the determination of some bare dynamic features inherent to the landscape. The mathematical tools used here are not familiar in physics: They come from set-valued analysis (differential calculus of set-valued maps and differential inclusions) and viability theory (capture basins of targets under evolutionary systems) which have been developed during the last two decades; we therefore propose a minimal appendix exposing them at the end of this paper to bridge the possible gap.Comment: 28 pages, submitted to J. Math. Phys -

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

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

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

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.

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

Effects of electron-phonon interactions on the electron tunneling spectrum of PbS quantum dots

We present a tunnel spectroscopy study of single PbS Quantum Dots (QDs) as function of temperature and gate voltage. Three distinct signatures of strong electron-phonon coupling are observed in the Electron Tunneling Spectrum (ETS) of these QDs. In the shell-filling regime, the $8\times$ degeneracy of the electronic levels is lifted by the Coulomb interactions and allows the observation of phonon sub-bands that result from the emission of optical phonons. At low bias, a gap is observed in the ETS that cannot be closed with the gate voltage, which is a distinguishing feature of the Franck-Condon (FC) blockade. From the data, a Huang-Rhys factor in the range $S\sim 1.7 - 2.5$ is obtained. Finally, in the shell tunneling regime, the optical phonons appear in the inelastic ETS $d^2I/dV^2$.Comment: 5 pages, 5 figure