Surface Phonons and Other Localized Excitations

The diatomic linear chain of masses coupled by harmonic springs is a textboook model for vibrational normal modes (phonons) in crystals. In addition to propagating acoustic and optic branches, this model is known to support a ``gap mode'' localized at the surface, provided the atom at the surface has light rather than heavy mass. An elementary argument is given which explains this mode and provides values for the frequency and localization length. By reinterpreting this mode in different ways, we obtain the frequency and localization lengths for three other interesting modes: (1) the surface vibrational mode of a light mass impurity at the surface of a monatomic chain; (2) the localized vibrational mode of a stacking fault in a diatomic chain; and (3) the localized vibrational mode of a light mass impurity in a monatomic chain.Comment: 5 pages with 4 embedded postscript figures. This paper will appear in the American Journal of Physic

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.

Light hadrons with improved staggered quarks: approaching the continuum limit

We have extended our program of QCD simulations with an improved Kogut-Susskind quark action to a smaller lattice spacing, approximately 0.09 fm. Also, the simulations with a approximately 0.12 fm have been extended to smaller quark masses. In this paper we describe the new simulations and computations of the static quark potential and light hadron spectrum. These results give information about the remaining dependences on the lattice spacing. We examine the dependence of computed quantities on the spatial size of the lattice, on the numerical precision in the computations, and on the step size used in the numerical integrations. We examine the effects of autocorrelations in "simulation time" on the potential and spectrum. We see effects of decays, or coupling to two-meson states, in the 0++, 1+, and 0- meson propagators, and we make a preliminary mass computation for a radially excited 0- meson.Comment: 43 pages, 16 figure

Heavy Viable Trajectories of Controlled Systems

We define and study the concept of heavy viable trajectories of a controlled system with feedbacks. Viable trajectories are trajectories satisfying at each instant given constraints on the state. The controls regulating viable trajectories evolve according a set-valued feedback map. Heavy viable trajectories are the ones which are associated to the controls in the feedback map whose velocity has at each instant the minimal norm. We construct the differential equation governing the evolution of the controls associated to heavy viable trajectories and we prove their existence

Approach of a class of discontinuous dynamical systems of fractional order: existence of the solutions

In this letter we are concerned with the possibility to approach the existence of solutions to a class of discontinuous dynamical systems of fractional order. In this purpose, the underlying initial value problem is transformed into a fractional set-valued problem. Next, the Cellina's Theorem is applied leading to a single-valued continuous initial value problem of fractional order. The existence of solutions is assured by a P\'{e}ano like theorem for ordinary differential equations of fractional order.Comment: accepted IJBC, 5 pages, 1 figur

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

Infrared and ultraviolet properties of the Landau gauge quark propagator

We present a current summary of a program to study the quark propagator using lattice QCD. We use the Overlap and ``Asqtad'' quark actions on a number of lattice ensembles to assess systematic errors. We comment on the place of this work amongst studies of QCD Green's functions in other formulations. A preliminary calculation of the running quark mass is presented.Comment: 7 pages, Contribution to LHP03, Cairn

Dual-species quantum degeneracy of potassium-40 and rubidium-87 on an atom chip

In this article we review our recent experiments with a 40K-87Rb mixture. We demonstrate rapid sympathetic cooling of a 40K-87Rb mixture to dual quantum degeneracy on an atom chip. We also provide details on efficient BEC production, species-selective magnetic confinement, and progress toward integration of an optical lattice with an atom chip. The efficiency of our evaporation allows us to reach dual degeneracy after just 6 s of evaporation - more rapidly than in conventional magnetic traps. When optimizing evaporative cooling for efficient evaporation of 87Rb alone we achieve BEC after just 4 s of evaporation and an 8 s total cycle time.Comment: 8 pages, 4 figures. To be published in the Proceedings of the 20th International Conference on Atomic Physics, 2006 (Innsbruck, Austria

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

Convergence of resonances on thin branched quantum wave guides

We prove an abstract criterion stating resolvent convergence in the case of operators acting in different Hilbert spaces. This result is then applied to the case of Laplacians on a family X_\eps of branched quantum waveguides. Combining it with an exterior complex scaling we show, in particular, that the resonances on X_\eps approximate those of the Laplacian with ``free'' boundary conditions on $X_0$, the skeleton graph of X_\eps.Comment: 48 pages, 1 figur