On the parallelization of the acoustic wave equation with absorbing boundary conditions

Many practical problems involve wave propagation through atmosphere, oceans, or terrestrial crust. Modeling and analysis of these problems is usually done in (semi)infinite domains, but numerical calculations obviously impose restriction to finite domains. To mimic the actual behavior in the (semi)infinite medium, artificial absorbing boundary conditions are imposed at the boundaries, whereby waves can only exit, but not enter the finite computational domain. Efficient absorbing boundary conditions are difficult to analyze and costly to run. In particular, it is of interest to assess whether the wave equation with (approximate or exact) absorbing boundary conditions admits a suitable diagonalization. This would open the possibility for parallelizing many important numerical codes used in applications. In this paper the authors propose a set of stable, local, absorbing boundary conditions for the discrete acoustic wave equation. They show that the acoustic wave equation with absorbing boundary conditions cannot be exactly diagonalized

Fixing the conformal window in QCD

A physical characterization of Landau singularities is emphasized, which should trace the lower boundary N_f^* of the conformal window in QCD and supersymmetric QCD. A natural way to disentangle ``perturbative'' from ``non-perturbative'' contributions to amplitudes below N_f^* is suggested. Assuming an infrared fixed point persists in the perturbative part of the QCD coupling even below N_f^* leads to the condition \gamma(N_f^*)=1, where \gamma is the critical exponent. Using the Banks-Zaks expansion, one gets 4<N_f^*<6. This result is incompatible with the existence of an analogue of Seiberg duality in QCD. The presence of a negative ultraviolet fixed point is required both in QCD and in supersymmetric QCD to preserve causality within the conformal window. Evidence for the existence of such a fixed point in QCD is provided.Comment: 10 pages, 1 figure, extended version of a talk given at the QCDNET2000 meeting, Paris, September 11-14 2000; main new material added is evidence for negative ultraviolet fixed point in QC

The one-dimensional Bose-Hubbard Model with nearest-neighbor interaction

We study the one-dimensional Bose-Hubbard model using the Density-Matrix Renormalization Group (DMRG).For the cases of on-site interactions and additional nearest-neighbor interactions the phase boundaries of the Mott-insulators and charge density wave phases are determined. We find a direct phase transition between the charge density wave phase and the superfluid phase, and no supersolid or normal phases. In the presence of nearest-neighbor interaction the charge density wave phase is completely surrounded by a region in which the effective interactions in the superfluid phase are repulsive. It is known from Luttinger liquid theory that a single impurity causes the system to be insulating if the effective interactions are repulsive, and that an even bigger region of the superfluid phase is driven into a Bose-glass phase by any finite quenched disorder. We determine the boundaries of both regions in the phase diagram. The ac-conductivity in the superfluid phase in the attractive and the repulsive region is calculated, and a big superfluid stiffness is found in the attractive as well as the repulsive region.Comment: 19 pages, 30 figure

The Haldane gap for the S=2 antiferromagnetic Heisenberg chain revisited

Using the density matrix renormalization group (DMRG) technique, we carry out a large scale numerical calculation for the S=2 antiferromagnetic Heisenberg chain. Performing systematic scaling analysis for both the chain length $L$ and the number of optimal states kept in the iterations $m$, the Haldane gap $\Delta (2)$ is estimated accurately as $(0.0876\pm0.0013)J$. Our systematic analysis for the S=2 chains not only ends the controversies arising from various DMRG calculations and Monte Carlo simulations, but also sheds light on how to obtain reliable results from the DMRG calculations for other complicated systems.Comment: 4 pages and 1 figur

Regge description of two pseudoscalar meson production in antiproton-proton annihilation

A Regge-inspired model is used to discuss the hard exclusive two-body hadronic reactions (pbar p ----> pi+ pi-, pi0 pi0, K+ K-, Kbar0 K0) for the FAIR facility project at GSI with the Panda detector. The comparison between the differential cross sections predictions and the available data is shown to determine the values of the few parameters of the model.Comment: 9 pages, 13 figure

UHECR Acceleration in Dark Matter Filaments of Cosmological Structure Formation

A mechanism for proton acceleration to ~10^21eV is suggested. It may operate in accretion flows onto thin dark matter filaments of cosmic structure formation. The flow compresses the ambient magnetic field to strongly increase and align it with the filament. Particles begin the acceleration by the ExB drift with the accretion flow. The energy gain in the drift regime is limited by the conservation of the adiabatic invariant p_perp^2/B. Upon approaching the filament, the drift turns into the gyro-motion around the filament so that the particle moves parallel to the azimuthal electric field. In this 'betatron' regime the acceleration speeds up to rapidly reach the electrodynamic limit $cp_{max}=eBR$ for an accelerator with magnetic field $B$ and the orbit radius $R$ (Larmor radius). The periodic orbit becomes unstable and the particle slings out of the filament to the region of a weak (uncompressed) magnetic field, which terminates the acceleration. The mechanism requires pre-acceleration that is likely to occur in structure formation shocks upstream or nearby the filament accretion flow. Previous studies identify such shocks as efficient proton accelerators to a firm upper limit ~10^19.5 eV placed by the catastrophic photo-pion losses. The present mechanism combines explosive energy gain in its final (betatron) phase with prompt particle release from the region of strong magnetic field. It is this combination that allows protons to overcome both the photo-pion and the synchrotron-Compton losses and therefore attain energy 10^21 eV. A requirement on accelerator to reach a given E_max placed by the accelerator energy dissipation \propto E_{max}^{2}/Z_0 due to the finite vacuum impedance Z_0 is circumvented by the cyclic operation of the accelerator.Comment: 34 pages, 10 figures, to be published in JCA

CBR Anisotropy from Primordial Gravitational Waves in Two-Component Inflationary Cosmology

We examine stochastic temperature fluctuations of the cosmic background radiation (CBR) arising via the Sachs-Wolfe effect from gravitational wave perturbations produced in the early universe. We consider spatially flat, perturbed FRW models that begin with an inflationary phase, followed by a mixed phase containing both radiation and dust. The scale factor during the mixed phase takes the form $a(\eta)=c_1\eta^2+c_2\eta+c_3$, where $c_i$ are constants. During the mixed phase the universe smoothly transforms from being radiation to dust dominated. We find analytic expressions for the graviton mode function during the mixed phase in terms of spheroidal wave functions. This mode function is used to find an analytic expression for the multipole moments $\langle a_l^2\rangle$ of the two-point angular correlation function $C(\gamma)$ for the CBR anisotropy. The analytic expression for the multipole moments is written in terms of two integrals, which are evaluated numerically. The results are compared to multipoles calculated for models that are {\it completely} dust dominated at last-scattering. We find that the multipoles $\langle a_l^2\rangle$ of the CBR temperature perturbations for $l>10$ are significantly larger for a universe that contains both radiation and dust at last-scattering. We compare our results with recent, similar numerical work and find good agreement. The spheroidal wave functions may have applications to other problems of cosmological interest.Comment: 28 pgs + 6 postscript figures, RevTe

Entropy and Quantum Kolmogorov Complexity: A Quantum Brudno's Theorem

In classical information theory, entropy rate and Kolmogorov complexity per symbol are related by a theorem of Brudno. In this paper, we prove a quantum version of this theorem, connecting the von Neumann entropy rate and two notions of quantum Kolmogorov complexity, both based on the shortest qubit descriptions of qubit strings that, run by a universal quantum Turing machine, reproduce them as outputs.Comment: 26 pages, no figures. Reference to publication added: published in the Communications in Mathematical Physics (http://www.springerlink.com/content/1432-0916/

CBR Anisotropy and the Running of the Scalar Spectral Index

Accurate ($\lesssim 1\%$) predictions for the anisotropy of the Cosmic Background Radiation (CBR) are essential for using future high-resolution ($\lesssim 1^\circ$) CBR maps to test cosmological models. In many inflationary models the variation (``running'') of the spectral index of the spectrum of density perturbations is a significant effect and leads to changes of around 1\% to 10\% in the CBR power spectrum. We propose a general method for taking running into account which uses the derivative of the spectral index ($dn/d\ln k$). Conversely, high-resolution CBR maps may be able to determine $dn/d\ln k$, giving important information about the inflationary potential.Comment: Discussion of calculation clarified; error corrected which reduces estimated effect for chaotic inflatio

Template-stripped gold surfaces with 0.4 nm rms roughness suitable for force measurements. Application to the Casimir force in the 20-100 nm range

Using a template-stripping method, macroscopic gold surfaces with root-mean-square (rms) roughness less than 0.4 nm have been prepared, making them useful for studies of surface interactions in the nanometer range. The utility of such substrates is demonstrated by measurements of the Casimir force at surface separations between 20 and 100 nm, resulting in good agreement with theory. The significance and quantification of this agreement is addressed, as well as some methodological aspects regarding the measurement of the Casimir force with high accuracy.Comment: 7 figure