MADNESS: A Multiresolution, Adaptive Numerical Environment for Scientific Simulation

MADNESS (multiresolution adaptive numerical environment for scientific simulation) is a high-level software environment for solving integral and differential equations in many dimensions that uses adaptive and fast harmonic analysis methods with guaranteed precision based on multiresolution analysis and separated representations. Underpinning the numerical capabilities is a powerful petascale parallel programming environment that aims to increase both programmer productivity and code scalability. This paper describes the features and capabilities of MADNESS and briefly discusses some current applications in chemistry and several areas of physics

Casimir Effect on the Worldline

We develop a method to compute the Casimir effect for arbitrary geometries. The method is based on the string-inspired worldline approach to quantum field theory and its numerical realization with Monte-Carlo techniques. Concentrating on Casimir forces between rigid bodies induced by a fluctuating scalar field, we test our method with the parallel-plate configuration. For the experimentally relevant sphere-plate configuration, we study curvature effects quantitatively and perform a comparison with the ``proximity force approximation'', which is the standard approximation technique. Sizable curvature effects are found for a distance-to-curvature-radius ratio of a/R >~ 0.02. Our method is embedded in renormalizable quantum field theory with a controlled treatment of the UV divergencies. As a technical by-product, we develop various efficient algorithms for generating closed-loop ensembles with Gaussian distribution.Comment: 27 pages, 10 figures, Sect. 2.1 more self-contained, improved data for Fig. 6, minor corrections, new Refs, version to be published in JHE

Perturbative Computation of the Gluonic Effective Action via Polyaokov's World-Line Path Integral

The Polyakov world-line path integral describing the propagation of gluon field quanta is constructed by employing the background gauge fixing method and is subsequently applied to analytically compute the divergent terms of the one (gluonic) loop effective action to fourth order in perturbation theory. The merits of the proposed approach is that, to a given order, it reduces to performing two integrations, one over a set of Grassmann and one over a set of Feynman-type parameters through which one manages to accomodate all Feynman diagrams entering the computation at once.Comment: 21 page

Off-Diagonal Elements of the DeWitt Expansion from the Quantum Mechanical Path Integral

The DeWitt expansion of the matrix element M_{xy} = \left\langle x \right| \exp -[\case{1}{2} (p-A)^2 + V]t \left| y \right\rangle, $(p=-i\partial)$ in powers of $t$ can be made in a number of ways. For $x=y$ (the case of interest when doing one-loop calculations) numerous approaches have been employed to determine this expansion to very high order; when $x \neq y$ (relevant for doing calculations beyond one-loop) there appear to be but two examples of performing the DeWitt expansion. In this paper we compute the off-diagonal elements of the DeWitt expansion coefficients using the Fock-Schwinger gauge. Our technique is based on representing $M_{xy}$ by a quantum mechanical path integral. We also generalize our method to the case of curved space, allowing us to determine the DeWitt expansion of \tilde M_{xy} = \langle x| \exp \case{1}{2} [\case{1}{\sqrt {g}} (\partial_\mu - i A_\mu)g^{\mu\nu}{\sqrt{g}}(\partial_\nu - i A_\nu) ] t| y \rangle by use of normal coordinates. By comparison with results for the DeWitt expansion of this matrix element obtained by the iterative solution of the diffusion equation, the relative merit of different approaches to the representation of $\tilde M_{xy}$ as a quantum mechanical path integral can be assessed. Furthermore, the exact dependence of $\tilde M_{xy}$ on some geometric scalars can be determined. In two appendices, we discuss boundary effects in the one-dimensional quantum mechanical path integral, and the curved space generalization of the Fock-Schwinger gauge.Comment: 16pp, REVTeX. One additional appendix concerning end-point effects for finite proper-time intervals; inclusion of these effects seem to make our results consistent with those from explicit heat-kernel method

Categorizing Different Approaches to the Cosmological Constant Problem

We have found that proposals addressing the old cosmological constant problem come in various categories. The aim of this paper is to identify as many different, credible mechanisms as possible and to provide them with a code for future reference. We find that they all can be classified into five different schemes of which we indicate the advantages and drawbacks. Besides, we add a new approach based on a symmetry principle mapping real to imaginary spacetime.Comment: updated version, accepted for publicatio

Heavy Quarks and Heavy Quarkonia as Tests of Thermalization

We present here a brief summary of new results on heavy quarks and heavy quarkonia from the PHENIX experiment as presented at the "Quark Gluon Plasma Thermalization" Workshop in Vienna, Austria in August 2005, directly following the International Quark Matter Conference in Hungary.Comment: 8 pages, 5 figures, Quark Gluon Plasma Thermalization Workshop (Vienna August 2005) Proceeding

Single Electrons from Heavy Flavor Decays in p+p Collisions at sqrt(s) = 200 GeV

The invariant differential cross section for inclusive electron production in p+p collisions at sqrt(s) = 200 GeV has been measured by the PHENIX experiment at the Relativistic Heavy Ion Collider over the transverse momentum range $0.4 <= p_T <= 5.0 GeV/c at midrapidity (eta <= 0.35). The contribution to the inclusive electron spectrum from semileptonic decays of hadrons carrying heavy flavor, i.e. charm quarks or, at high p_T, bottom quarks, is determined via three independent methods. The resulting electron spectrum from heavy flavor decays is compared to recent leading and next-to-leading order perturbative QCD calculations. The total cross section of charm quark-antiquark pair production is determined as sigma_(c c^bar) = 0.92 +/- 0.15 (stat.) +- 0.54 (sys.) mb.Comment: 329 authors, 6 pages text, 3 figures. Submitted to Phys. Rev. Lett. Plain text data tables for the points plotted in figures for this and previous PHENIX publications are (or will be) publicly available at http://www.phenix.bnl.gov/papers.htm

Nuclear Modification of Electron Spectra and Implications for Heavy Quark Energy Loss in Au+Au Collisions at sqrt(s_NN)=200 GeV

The PHENIX experiment has measured mid-rapidity transverse momentum spectra (0.4 < p_T < 5.0 GeV/c) of electrons as a function of centrality in Au+Au collisions at sqrt(s_NN)=200 GeV. Contributions from photon conversions and from light hadron decays, mainly Dalitz decays of pi^0 and eta mesons, were removed. The resulting non-photonic electron spectra are primarily due to the semi-leptonic decays of hadrons carrying heavy quarks. Nuclear modification factors were determined by comparison to non-photonic electrons in p+p collisions. A significant suppression of electrons at high p_T is observed in central Au+Au collisions, indicating substantial energy loss of heavy quarks.Comment: 330 authors, 6 pages text, 3 figures. Submitted to Phys. Rev. Lett. Plain text data tables for the points plotted in figures for this and previous PHENIX publications are (or will be) publicly available at http://www.phenix.bnl.gov/papers.htm

Dilepton mass spectra in p+p collisions at sqrt(s)= 200 GeV and the contribution from open charm

The PHENIX experiement has measured the electron-positron pair mass spectrum from 0 to 8 GeV/c^2 in p+p collisions at sqrt(s)=200 GeV. The contributions from light meson decays to e^+e^- pairs have been determined based on measurements of hadron production cross sections by PHENIX. They account for nearly all e^+e^- pairs in the mass region below 1 GeV/c^2. The e^+e^- pair yield remaining after subtracting these contributions is dominated by semileptonic decays of charmed hadrons correlated through flavor conservation. Using the spectral shape predicted by PYTHIA, we estimate the charm production cross section to be 544 +/- 39(stat) +/- 142(syst) +/- 200(model) \mu b, which is consistent with QCD calculations and measurements of single leptons by PHENIX.Comment: 375 authors from 57 institutions, 18 pages, 4 figures, 2 tables. Submitted to Physics Letters B. v2 fixes technical errors in matching authors to institutions. Plain text data tables for the points plotted in figures for this and previous PHENIX publications are (or will be) publicly available at http://www.phenix.bnl.gov/papers.htm