The 1 Teraflops QCDSP computer

The QCDSP computer (Quantum Chromodynamics on Digital Signal Processors) is an inexpensive, massively parallel computer intended primarily for simulations in lattice gauge theory. Currently, two large QCDSP machines are in full-time use: an 8,192 processor, 0.4 Teraflops machine at Columbia University and an 12,288 processor, 0.6 Teraflops machine at the RIKEN-BNL Research Center at Brookhaven National Laboratory. We describe the design process, architecture, software and current physics projects of these computers.Comment: 19 pages, 3 figure

Numerical techniques for lattice QCD in the ϵ\epsilon--regime

In lattice QCD it is possible, in principle, to determine the parameters in the effective chiral lagrangian (including weak interaction couplings) by performing numerical simulations in the $\epsilon$--regime, i.e. at quark masses where the physical extent of the lattice is much smaller than the Compton wave length of the pion. The use of a formulation of the lattice theory that preserves chiral symmetry is attractive in this context, but the numerical implementation of any such approach requires special care in this kinematical situation due to the presence of some very low eigenvalues of the Dirac operator. We discuss a set of techniques (low-mode preconditioning and adapted-precision algorithms in particular) that make such computations numerically safe and more efficient by a large factor.Comment: Plain TeX source, 32 pages, figures include

Numerical Stochastic Perturbation Theory for full QCD

We give a full account of the Numerical Stochastic Perturbation Theory method for Lattice Gauge Theories. Particular relevance is given to the inclusion of dynamical fermions, which turns out to be surprisingly cheap in this context. We analyse the underlying stochastic process and discuss the convergence properties. We perform some benchmark calculations and - as a byproduct - we present original results for Wilson loops and the 3-loop critical mass for Wilson fermions.Comment: 35 pages, 5 figures; syntax revise

The MultiBoson method

This review describes the multiboson algorithm for Monte Carlo simulations of lattice QCD, including its static and dynamical aspects, and presents a comparison with Hybrid Monte Carlo.Comment: to be published in Parallel Computing, 17 pages, 1 figur

Brun-Type Formalism for Decoherence in Two Dimensional Quantum Walks

We study decoherence in the quantum walk on the xy-plane. We generalize the method of decoherent coin quantum walk, introduced by [T.A. Brun, et.al, Phys.Rev.A 67 (2003) 032304],which could be applicable to all sorts of decoherence in two dimensional quantum walks, irrespective of the unitary transformation governing the walk. As an application we study decoherence in the presence of broken line noise in which the quantum walk is governed by the two-dimensional Hadamard operator.Comment: Presented as Poster Talk in "The International Meeting on Quantum Foundations and Quantum Information" at Seoul National Universit

Lattice dynamics of photoexcited insulators from constrained density-functional perturbation theory

We present a constrained density functional perturbation theory scheme for the calculation of structural and harmonic vibrational properties of insulators in the presence of an excited and thermalized electron-hole plasma. The method is ideal to tame ultrafast light induced structural transitions in the regime where the photocarriers thermalize faster than the lattice, the electron-hole recombination time is longer than the phonon period and the photocarrier concentration is large enough to be approximated by an electron-hole plasma. The complete derivation presented here includes total energy, forces and stress tensor, variable cell structural optimization, harmonic vibrational properties and the electron-phonon interaction. We discuss in detail the case of zone center optical phonons not conserving the number of electrons and inducing a Fermi shift in the photo-electron and hole distributions. We validate our implementation by comparing with finite differences in Te and VSe2. By calculating the evolution of the phonon spectrum of Te, Si and GaAs as a function of the fluence of the incoming laser light, we demonstrate that even at low fluences, corresponding to approximately 0.1 photocarriers per cell, the phonon spectrum is substantially modified with respect to the ground state one with new Kohn anomalies appearing and a substantial softening of zone center optical phonons. Our implementation can be efficiently used to detect reversible transient phases and irreversible structural transition induced by ultrafast light absorption

Proposal for the numerical solution of planar QCD

Using quenched reduction, we propose a method for the numerical calculation of meson correlation functions in the planar limit of QCD. General features of the approach are outlined, and an example is given in the context of two-dimensional QCD.Comment: 31 pages, 10 figures, uses axodraw.sty, To appear in Physical Review

Elliptic operators with honeycomb symmetry: Dirac points, Edge States and Applications to Photonic Graphene

Consider electromagnetic waves in two-dimensional {\it honeycomb structured media}. The properties of transverse electric (TE) polarized waves are determined by the spectral properties of the elliptic operator \LA=-\nabla_\bx\cdot A(\bx) \nabla_\bx, where A(\bx) is $\Lambda_h-$ periodic ($\Lambda_h$ denotes the equilateral triangular lattice), and such that with respect to some origin of coordinates, A(\bx) is $\mathcal{P}\mathcal{C}-$ invariant (A(\bx)=\overline{A(-\bx)}) and $120^\circ$ rotationally invariant (A(R^*\bx)=R^*A(\bx)R, where $R$ is a $120^\circ$ rotation in the plane). We first obtain results on the existence, stability and instability of Dirac points, conical intersections between two adjacent Floquet-Bloch dispersion surfaces. We then show that the introduction through small and slow variations of a {\it domain wall} across a line-defect gives rise to the bifurcation from Dirac points of highly robust (topologically protected) {\it edge states}. These are time-harmonic solutions of Maxwell's equations which are propagating parallel to the line-defect and spatially localized transverse to it. The transverse localization and strong robustness to perturbation of these edge states is rooted in the protected zero mode of a one-dimensional effective Dirac operator with spatially varying mass term. These results imply the existence of {\it uni-directional} propagating edge states for two classes of time-reversal invariant media in which $\mathcal{C}$ symmetry is broken: magneto-optic media and bi-anisotropic media. Our analysis applies and extends the tools previously developed in the context of honeycomb Schr\"odinger operators.Comment: 65 pages, 8 figures, To appear in Archive for Rational Mechanics and Analysi

Fourier analysis of multi-tracer cosmological surveys

We present optimal quadratic estimators for the Fourier analysis of cosmological surveys that detect several different types of tracers of large-scale structure. Our estimators can be used to simultaneously fit the matter power spectrum and the biases of the tracers - as well as redshift-space distortions (RSDs), non-Gaussianities (NGs), or any other effects that are manifested through differences between the clusterings of distinct species of tracers. Our estimators reduce to the one by Feldman, Kaiser & Peacock (ApJ 1994, FKP) in the case of a survey consisting of a single species of tracer. We show that the multi-tracer estimators are unbiased, and that their covariance is given by the inverse of the multi-tracer Fisher matrix (Abramo, MNRAS 2013; Abramo & Leonard, MNRAS 2013). When the biases, RSDs and NGs are fixed to their fiducial values, and one is only interested in measuring the underlying power spectrum, our estimators are projected into the estimator found by Percival, Verde & Peacock (MNRAS 2003). We have tested our estimators on simple (lognormal) simulated galaxy maps, and we show that it performs as expected, being either equivalent or superior to the FKP method in all cases we analyzed. Finally, we have shown how to extend the multi-tracer technique to include the 1-halo term of the power spectrum.Comment: 20 pages, 5 figures. Comments are welcom

Free-form smearing for bottomonium and B meson spectroscopy

To obtain high-quality results from lattice QCD, it is important to use operators that produce good signals for the quantities of interest. Free-form smearing is a powerful tool that helps to accomplish that goal. The present work introduces a new implementation of free-form smearing that maintains its usefulness and reduces its computational time dramatically. Applications to the mass spectrum of $B$, $B_s$, $B_c$ and bottomonium mesons show the effectiveness of the method. Results are compared with other lattice QCD studies and with experimental data where available. The present work includes the first lattice QCD exploration for some of these mesons.Comment: 28 pages, 8 figures, published versio