Theoretical Analysis of Acceptance Rates in Multigrid Monte Carlo

We analyze the kinematics of multigrid Monte Carlo algorithms by investigating acceptance rates for nonlocal Metropolis updates. With the help of a simple criterion we can decide whether or not a multigrid algorithm will have a chance to overcome critial slowing down for a given model. Our method is introduced in the context of spin models. A multigrid Monte Carlo procedure for nonabelian lattice gauge theory is described, and its kinematics is analyzed in detail.Comment: 7 pages, no figures, (talk at LATTICE 92 in Amsterdam

Small-Scale Variations of HI Spectra from Interstellar Scintillatio

I suggest that radio-wave scattering by the interstellar plasma, in combination with subsonic gradients in the Doppler velocity of interstellar HI, is responsible for the observed small-scale variation in HI absorption spectra of pulsars. Velocity gradients on the order of 0.05 to 0.3 km/s across 1 AU can produce the observed variations. I suggest observational tests to distinguish between this model and the traditional picture of small-scale opacity variations from cloudlets.Comment: 24 pages, 2 figures, Latex, uses AASTe

Screening of nuclear pairing in nuclear and neutron matter

The screening potential in the $^1S_0$ and $^3S_1$ pairing channels in neutron and nuclear matter in different approximations is discussed. It is found that the vertex corrections to the potential are much stronger in nuclear matter than in neutron matter.Comment: 11 pages, 8 figures, revtex4 styl

Comparison of the INRIM and PTB lattice-spacing standards

To base the kilogram definition on the atomic mass of the silicon 28 atom, the present relative uncertainty of the silicon 28 lattice parameter must lowered to 3E-9. To achieve this goal, a new experimental apparatus capable of a centimetre measurement-baseline has been made at the INRIM. The comparison between the determinations of the lattice parameter of crystals MO*4 of INRIM and WASO4.2a of PTB is intended to verify the measurement capabilities and to assess the limits of this experiment.Comment: 10 pages, 8 figures, submitted to Metrologi

Localization of correlated fermions in optical lattices with speckle disorder

Strongly correlated fermions in three- and two-dimensional optical lattices with experimentally realistic speckle disorder are investigated. We extend and apply the statistical dynamical mean-field theory, which treats local correlations non-perturbatively, to incorporate on-site and hopping-type randomness on equal footing. Localization due to disorder is detected via the probability distribution function of the local density of states. We obtain a complete paramagnetic ground state phase diagram for experimentally realistic parameters and find a strong suppression of the correlation-induced metal insulator transition due to disorder. Our results indicate that the Anderson-Mott and the Mott insulator are not continuously connected due to the specific character of speckle disorder. Furthermore, we discuss the effect of finite temperature on the single-particle spectral function.Comment: 12 pages, 16 figures, published versio

Transition from BCS pairing to Bose-Einstein condensation in low-density asymmetric nuclear matter

We study the isospin-singlet neutron-proton pairing in bulk nuclear matter as a function of density and isospin asymmetry within the BCS formalism. In the high-density, weak-coupling regime the neutron-proton paired state is strongly suppressed by a minor neutron excess. As the system is diluted, the BCS state with large, overlapping Cooper pairs evolves smoothly into a Bose-Einstein condensate of tightly bound neutron-proton pairs (deuterons). In the resulting low-density system a neutron excess is ineffective in quenching the pair correlations because of the large spatial separation of the deuterons and neutrons. As a result, the Bose-Einstein condensation of deuterons is weakly affected by an additional gas of free neutrons even at very large asymmetries.Comment: 17 pages, uncluding 7 figures, PRC in pres

Theory of Nonlinear Dispersive Waves and Selection of the Ground State

A theory of time dependent nonlinear dispersive equations of the Schroedinger / Gross-Pitaevskii and Hartree type is developed. The short, intermediate and large time behavior is found, by deriving nonlinear Master equations (NLME), governing the evolution of the mode powers, and by a novel multi-time scale analysis of these equations. The scattering theory is developed and coherent resonance phenomena and associated lifetimes are derived. Applications include BEC large time dynamics and nonlinear optical systems. The theory reveals a nonlinear transition phenomenon, ``selection of the ground state'', and NLME predicts the decay of excited state, with half its energy transferred to the ground state and half to radiation modes. Our results predict the recent experimental observations of Mandelik et. al. in nonlinear optical waveguides

Ground and excited states Gamow-Teller strength distributions of iron isotopes and associated capture rates for core-collapse simulations

This paper reports on the microscopic calculation of ground and excited states Gamow-Teller (GT) strength distributions, both in the electron capture and electron decay direction, for $^{54,55,56}$Fe. The associated electron and positron capture rates for these isotopes of iron are also calculated in stellar matter. These calculations were recently introduced and this paper is a follow-up which discusses in detail the GT strength distributions and stellar capture rates of key iron isotopes. The calculations are performed within the framework of the proton-neutron quasiparticle random phase approximation (pn-QRPA) theory. The pn-QRPA theory allows a microscopic \textit{state-by-state} calculation of GT strength functions and stellar capture rates which greatly increases the reliability of the results. For the first time experimental deformation of nuclei are taken into account. In the core of massive stars isotopes of iron, $^{54,55,56}$Fe, are considered to be key players in decreasing the electron-to-baryon ratio ($Y_{e}$) mainly via electron capture on these nuclide. The structure of the presupernova star is altered both by the changes in $Y_{e}$ and the entropy of the core material. Results are encouraging and are compared against measurements (where possible) and other calculations. The calculated electron capture rates are in overall good agreement with the shell model results. During the presupernova evolution of massive stars, from oxygen shell burning stages till around end of convective core silicon burning, the calculated electron capture rates on $^{54}$Fe are around three times bigger than the corresponding shell model rates. The calculated positron capture rates, however, are suppressed by two to five orders of magnitude.Comment: 18 pages, 12 figures, 10 table

Aligned Drawings of Planar Graphs

Let $G$ be a graph that is topologically embedded in the plane and let $\mathcal{A}$ be an arrangement of pseudolines intersecting the drawing of $G$. An aligned drawing of $G$ and $\mathcal{A}$ is a planar polyline drawing $\Gamma$ of $G$ with an arrangement $A$ of lines so that $\Gamma$ and $A$ are homeomorphic to $G$ and $\mathcal{A}$. We show that if $\mathcal{A}$ is stretchable and every edge $e$ either entirely lies on a pseudoline or it has at most one intersection with $\mathcal{A}$, then $G$ and $\mathcal{A}$ have a straight-line aligned drawing. In order to prove this result, we strengthen a result of Da Lozzo et al., and prove that a planar graph $G$ and a single pseudoline $\mathcal{L}$ have an aligned drawing with a prescribed convex drawing of the outer face. We also study the less restrictive version of the alignment problem with respect to one line, where only a set of vertices is given and we need to determine whether they can be collinear. We show that the problem is NP-complete but fixed-parameter tractable.Comment: Preliminary work appeared in the Proceedings of the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017

Kinematics of Multigrid Monte Carlo

We study the kinematics of multigrid Monte Carlo algorithms by means of acceptance rates for nonlocal Metropolis update proposals. An approximation formula for acceptance rates is derived. We present a comparison of different coarse-to-fine interpolation schemes in free field theory, where the formula is exact. The predictions of the approximation formula for several interacting models are well confirmed by Monte Carlo simulations. The following rule is found: For a critical model with fundamental Hamiltonian H(phi), absence of critical slowing down can only be expected if the expansion of in terms of the shift psi contains no relevant (mass) term. We also introduce a multigrid update procedure for nonabelian lattice gauge theory and study the acceptance rates for gauge group SU(2) in four dimensions.Comment: 28 pages, 8 ps-figures, DESY 92-09