Collinear asymptotic dynamics for massive particles

The dynamics of massive particles in the collinear high momentum regime is investigated. Methods hitherto exploiting large time asymptotic Hamiltonians in the Dirac picture for the treatment of infrared divergences are adapted to the collinear asymptotic dynamics. The essential role of time ordering of the dressing operators is brought out.     

Some asymptotic formulae for one-electron two-center problem

Asymptotic formulae of some expectation values related to the relativistic corrections in inverse powers of the internuclear distance R for the lsσ _g electron state of hydrogen molecular ion H₂⁺ and the lsσ molecule-like state of antiprotonic helium atom He⁺ are obtained with the use of the first-order perturbation function. Using these asymptotic formulae, the relativistic correction of order mα⁶ for these states in reciprocal powers of the internuclear distance R is derived to accuracy of (R ⁻⁴). The article is published in the original.     

Complete far-field asymptotic series for free fields

The closed form of the complete far-field asymptotic series is provided for the scalar and electromagnetic monochromatic fields in free space whose angular spectrum is smooth over the sphere of directions. The first few terms of this series are also shown to give corrections to the Fraunhofer diffraction formula. The application of this series is illustrated with two examples corresponding to a highly focused radially polarized field and to the scalar diffraction from a circular aperture.     

Theorems for asymptotic safety of gauge theories

We classify the weakly interacting fixed points of general gauge theories coupled to matter and explain how the competition between gauge and matter fluctuations gives rise to a rich spectrum of high- and low-energy fixed points. The pivotal role played by Yukawa couplings is emphasised. Necessary and sufficient conditions for asymptotic safety of gauge theories are also derived, in conjunction with strict no go theorems. Implications for phase diagrams of gauge theories and physics beyond the Standard Model are indicated.     

Logarithmic asymptotic flatness

We present a general family of asymptotic solutions to Einstein's equation which are asymptotically flat but do not satisfy the peeling theorem. Near scri, the Weyl tensor obeys a logarithmic asymptotic flatness condition and has a partial peeling property. The physical significance of this asymptotic behavior arises from a quasi-Newtonian treatment of the radiation from a collapsing dust cloud. Practically all the scri formalism carries over intact to this new version of asymptotic flatness.     

Uniform asymptotic formulae for the spheroidal angular function

The problem of wave scattering by a spheroid is treated. Special interest is paid to the solution of the differential wave equation related to the angular spheroidal functions. A solution is obtained using uniform asymptotic formulae along with semiclassical methods. The developed method shows that it is possible to interpolate uniformly the spheroidal angular function with Weber's parabolic cylindric functions and Legendre's functions.     

Evidence for asymptotic safety from lattice quantum gravity

We calculate the spectral dimension for nonperturbative quantum gravity defined via Euclidean dynamical triangulations. We find that it runs from a value of ～3/2 at short distance to ～4 at large distance scales, similar to results from causal dynamical triangulations. We argue that the short-distance value of 3/2 for the spectral dimension may resolve the tension between asymptotic safety and the holographic principle.     

Lattice QCD: Waiting for the asymptotic scaling

It is argued that there is no contradiction between some recent Monte-Carlo renormalization group evaluations of the lattice β-function and the rather well established asymptotic scaling behavior of the mass of the 0⁺⁺ glueball state. The different behavior of the β-function in these cases may be a manifestation of the simple fact well-known from perturbation theory: there is no unique β-function in QCD.     

Concentratable functionals and asymptotic relations for scattering amplitudes

Very wide classes of concentratable functionals are considered, i.e. classes where the notion of concentrating, which satisfies a certain six axioms, can be introduced, and where it is possible to formulate the microcausality (or the local-commutativity) principle as the requirement of concentration of functionals in the corresponding space-time region. Every such class of functionals is essentially wider than the class of tempered distributions and is defined on some analytic functions only. It is proved that the asymptotic smoothed partially-microcausal amplitude of an arbitrary reaction, under corresponding conditions imposed only in the physical region of changing arguments, satisfies all the asymptotic relations.     

Equilibration implies asymptotic stationarity for open quantum systems

We use the exact Nakajima–Zwanzig form of the master equation to show that open quantum systems which exhibit equilibration (or thermalization) by evolving to a time independent asymptotic state, have under certain conditions a reduced density matrix for the system which commutes with the effective system Hamiltonian. We also show that if the initial system–bath density matrix is of product form then the asymptotic reduced density matrix of the system depends only on the diagonal elements of the initial system density matrix in the eigenbasis of the effective Hamiltonian.     

On asymptotic flatness

Starting with a few basic assumptions on the local asymptotic behavior of space-time and using Penrose's conformal technique the asymptotic behavior of both the physical and unphysical metric is obtained in a Bondi-type coordinate system. The space-times under consideration are not necessarily empty in the asymptotic region nor are they necessarily asymptotically flat. However, they do have the usual falloff behavior as one goes out toward infinity in a given null direction. The assumptions made in this paper and the resultant metrics are compared with those of Persides in his recent paper on the definition of asymptotic flatness.     

Low-fugacity asymptotic expansion for classical lattice dipole gases

We consider a classical dipole gas in the grand canonical ensemble. We prove that in dimensions greater than or equal to three, and for all temperatures, the free energy and the charges-dipoles correlation functions have an expansion in powers ofz, the fugacity of the system, which is asymptotic to all orders. We also give some information about the decay of correlations.on leave from Institut de Physique Théorique Université de Louvian, Belgium. Supported by N.S.F. grant No. PHY-15920.     

An asymptotic expansion for the Neumann sieve problem

In this paper, we study the Neumann sieve problem for the Laplace equation. Our objective is to compute the complete asymptotic expansion for the problem. The expansion consists of the interior part, in the vicinity of the filter, and an exterior part, far away from the filter. The interior approximation is a Bakhvalov-Panasenko-type expansion with terms defined by a sequence of auxiliary problems on infinite stripes and matching with the exterior expansion. We prove the related error estimate.     

Nonlinear asymptotic impedance model for a Helmholtz resonator liner

The usual nonlinear corrections for a Helmholtz resonator type impedance do not seem to be based on a systematic asymptotic solution of the pertaining equations. We aim to present a systematic derivation of a solution of the nonlinear Helmholtz resonator equation, in order to obtain analytically expressions for impedances close to resonance, while including nonlinear effects. The amplitude regime considered is such that when we stay away from the resonance condition, the nonlinear terms are relatively small and the solution obtained is of the linear equation (formed after neglecting the nonlinear terms). Close to the resonance frequency, the nonlinear terms can no longer be neglected and algebraic equations are obtained that describe the corresponding nonlinear impedance. Sample results are presented including a few comparisons with measurements available in the literature. The validity of the model is understood in the near resonance and non-resonance regimes.     

Counting tree diagrams: asymptotic results for QCD-like theories

We discuss the enumeration of Feynman diagrams at tree order for processes with external lines of different types. We show how this can be done by iterating algebraic Schwinger–Dyson equations. Asymptotic estimates for very many external lines are derived. Applications include QED, QCD and scalar QED, and the asymptotic estimates are numerically confronted with the exact results. Received: 17 October 2001 / Published online: 5 April 2002