Atomic Ground-State Energies

It is demonstrated that atomic Hartree–Fock binding energies may be reproduced with great accuracy (within about four parts in a thousand) by a scaled model system in which the electrons are noninteracting, and are bound in a bare Coulomb potential. </jats:p

An Approximate Light Cone Method to Investigate Meson Structure

To appear in the proceedings of The Phenomenology of Large N(c) QCD, Tempe, Arizona, 9-11 Jan 2002.Comment: 5 pages, 2 figures, other comment

On Subleading Contributions to the AdS/CFT Trace Anomaly

In the context of the AdS/CFT correspondence, we perform a direct computation in AdS_5 supergravity of the trace anomaly of a d=4, N=2 SCFT. We find agreement with the field theory result up to next to leading order in the 1/N expansion. In particular, the order N gravitational contribution to the anomaly is obtained from a Riemann tensor squared term in the 7-brane effective action deduced from heterotic - type I duality. We also discuss, in the AdS/CFT context, the order N corrections to the trace anomaly in d=4, N=4 SCFTs involving SO or Sp gauge groups.Comment: 25 pages, LaTeX, v2: references adde

Complex Matrix Models and Statistics of Branched Coverings of 2D Surfaces

We present a complex matrix gauge model defined on an arbitrary two-dimensional orientable lattice. We rewrite the model's partition function in terms of a sum over representations of the group U(N). The model solves the general combinatorial problem of counting branched covers of orientable Riemann surfaces with any given, fixed branch point structure. We then define an appropriate continuum limit allowing the branch points to freely float over the surface. The simplest such limit reproduces two-dimensional chiral U(N) Yang-Mills theory and its string description due to Gross and Taylor.Comment: 21 pages, 2 figures, TeX, harvmac.tex, epsf.tex, TeX "big

Symmetrized importance samplers for stochastic differential equations

We study a class of importance sampling methods for stochastic differential equations (SDEs). A small-noise analysis is performed, and the results suggest that a simple symmetrization procedure can significantly improve the performance of our importance sampling schemes when the noise is not too large. We demonstrate that this is indeed the case for a number of linear and nonlinear examples. Potential applications, e.g., data assimilation, are discussed.Comment: Added brief discussion of Hamilton-Jacobi equation. Also made various minor corrections. To appear in Communciations in Applied Mathematics and Computational Scienc

Small-noise analysis and symmetrization of implicit Monte Carlo samplers

Implicit samplers are algorithms for producing independent, weighted samples from multi-variate probability distributions. These are often applied in Bayesian data assimilation algorithms. We use Laplace asymptotic expansions to analyze two implicit samplers in the small noise regime. Our analysis suggests a symmetrization of the algo- rithms that leads to improved (implicit) sampling schemes at a rel- atively small additional cost. Computational experiments confirm the theory and show that symmetrization is effective for small noise sampling problems

Spin excitations in fluctuating stripe phases of doped cuprate superconductors

Using a phenomenological lattice model of coupled spin and charge modes, we determine the spin susceptibility in the presence of fluctuating stripe charge order. We assume the charge fluctuations to be slow compared to those of the spins, and combine Monte Carlo simulations for the charge order parameter with exact diagonalization of the spin sector. Our calculations unify the spin dynamics of both static and fluctuating stripe phases and support the notion of a universal spin excitation spectrum in doped cuprate superconductors.Comment: 4 pages, 4 figs, minor changes, final version as publishe