A method for resummation of perturbative series based on the stochastic solution of Schwinger-Dyson equations

We propose a numerical method for resummation of perturbative series, which is based on the stochastic perturbative solution of Schwinger-Dyson equations. The method stochastically estimates the coefficients of perturbative series, and incorporates Borel resummation in a natural way. Similarly to the “worm” algorithm, the method samples open Feynman diagrams, but with an arbitrary number of external legs. As a test of our numerical algorithm, we study the scale dependence of the renormalized coupling constant in a theory of one-component scalar field with quartic interaction. We confirm the triviality of this theory in four and five space-time dimensions, and the instability of the trivial fixed point in three dimensions.     

Asymptotic structure of perturbative series for \tau lepton observables

We analyze lepton decay observables, namely the moments of the hadronic spectral density in the finite energy interval , within finite order perturbation theory including corrections. The start of the asymptotic growth of the perturbation theory series is found at this order in a scheme-invariant manner. We establish the ultimate accuracy of finite order perturbation theory predictions and discuss the construction of optimal observables. Received: 6 September 1999 / Published online: 21 December 1999     

A fast,accurate phase unwrapping method for wavelet-transform profilometry

A novel phase unwrapping method used in wavelet-transform profilometry is presented to improve the accuracy and speed of the unwrapping process. The wrapped phase of the fringe image is extracted by using wavelet transform. How to establish quality map using scale factor at wavelet ridge is discussed firstly. The proposed method can reflect the reliability of the pixels in fringe image effectively. As the consuming time of traditional flood-fill phase unwrapping algorithm is too long, an improved quality-guided method is used in phase unwrapping process. We divide the wrapped phase map into two levels following the established quality map, and process these two levels using different algorithms. Compared with the traditional flood-fill algorithm, we can get the accurate result while the consuming time of the phase unwrapping process is much less by using the proposed method. Simulation and experiment results verify that the 3D information of the measured object can be obtained rapidly and accurately by using the proposed method. Also the dynamic object can be measured too.     

Soft-gluon resummation for single-particle inclusive hadroproduction at high transverse momentum

We consider the cross section for one-particle inclusive production at high transverse momentum in hadronic collisions. We present the all-order resummation formula that controls the logarithmically-enhanced perturbative QCD contributions to the partonic cross section in the threshold region, at fixed rapidity of the observed parton (hadron). The explicit resummation up to next-to-leading logarithmic accuracy is supplemented with the computation of the general structure of the near-threshold contributions to the next-to-leading order cross section. This next-to-leading order computation allows us to extract the one-loop hard-virtual amplitude that enters into the resummation formula. This is a necessary ingredient to explicitly extend the soft-gluon resummation beyond the next-to-leading logarithmic accuracy. These results equally apply to both spin-unpolarized and spin-polarized scattering processes.     

A fast and accurate calibration method for the structured light system based on trapezoidal phase-shifting pattern

Calibration plays an important part in the structured light system. It used to be regarded as time-consuming, expensive and hard to implement. In this paper, we introduce a novel and fast method to calibrate the structured light system by using the camera to control the projector to “capture” images. Firstly, we projected just six trapezoidal grayscale pattern to establish the corresponding pixel between the camera and the projector, then we converted the camera image to its corresponding projector image. Thus the structured light system can be easy controlled by the camera calibration. Experiments showed that the present calibration method is fast, easy and accurate.     

Combined effect of QCD resummation and QED radiative correction to W boson observables at the Tevatron

A precise determination of the W boson mass at the Fermilab Tevatron requires a theoretical calculation in which the effects of the initial-state multiple soft-gluon emission and the final-state photonic correction are simultaneously included. Here, we present such a calculation and discuss its prediction on the transverse mass distribution of the W boson and the transverse momentum distribution of its decay charged lepton, which are the most relevant observables for measuring the W boson mass at hadron colliders.     

A fast and accurate method for the determination of precious alloys caratage by Laser Induced Plasma Spectroscopy

The purpose of this paper is to present a new and efficient technique for precious alloys caratage based on the Laser Induced Plasma Spectroscopy (LIPS) method. The LIPS analysis can be carried out in few minutes and in an essentially non-destructive way on samples of arbitrary shape. Experimental results showing the feasibility of the method for fast and precise analysis of gold jewellery without the need of calibration are presented. Using a new technique of LIPS spectra analysis, recently developed and patented by the Applied Laser Spectroscopy Laboratory at IFAM, we were able to obtain quantitative information about all the alloy components, including trace elements at concentration down to the order of 1 ppm. Matrix effects do not affect the accuracy of the technique. Received 10 July 2000 and Received in final form 13 November 2000     

A perturbative nonequilibrium renormalization group method for dissipative quantum mechanics

We study a generic problem of dissipative quantum mechanics, a small local quantum system with discrete states coupled in an arbitrary way (i.e. not necessarily linear) to several infinitely large particle or heat reservoirs. For both bosonic or fermionic reservoirs we develop a quantum field-theoretical diagrammatic formulation in Liouville space by expanding systematically in the reservoir-system coupling and integrating out the reservoir degrees of freedom. As a result we obtain a kinetic equation for the reduced density matrix of the quantum system. Based on this formalism, we present a formally exact perturbative renormalization group (RG) method from which the kernel of this kinetic equation can be calculated. It is demonstrated how the nonequilibrium stationary state (induced by several reservoirs kept at different chemical potentials or temperatures), arbitrary observables such as the transport current, and the time evolution into the stationary state can be calculated. Most importantly, we show how RG equations for the relaxation and dephasing rates can be derived and how they cut off generically the RG flow of the vertices. The method is based on a previously derived real-time RG technique [1-4] but formulated here in Laplace space and generalized to arbitrary reservoir-system couplings. Furthermore, for fermionic reservoirs with flat density of states, we make use of a recently introduced cutoff scheme on the imaginary frequency axis [5] which has several technical advantages. Besides the formal set-up of the RG equations for generic problems of dissipative quantum mechanics, we demonstrate the method by applying it to the nonequilibrium isotropic Kondo model. We present a systematic way to solve the RG equations analytically in the weak-coupling limit and provide an outlook of the applicability to the strong-coupling case.     

Factorization and resummation for jet broadening

Jet broadening is an event-shape variable probing the transverse momenta of particles inside jets. It has been measured precisely in e⁺e⁻ annihilations and is used to extract the strong coupling constant. The factorization of the associated cross section at small values of the broadening is afflicted by a collinear anomaly. Based on an analysis of this anomaly, we present an all-order factorization theorem for jet-broadening distributions, which is free of large perturbative logarithms in the two-jet limit. Our formula reproduces known results at next-to-leading logarithmic order but also extends to higher orders.     

一种用于中子散射成像的快速反投影重建方法

针对中子散射成像建立了一种快速反投影重建方法,这种方法首先根据每一个散射事件确定粒子可能所在的空间范围,然后该空间范围中进行重建,大大减少了重建的运行时间。应用所建立的方法对模拟的成像数据进行处理,结果表明:重建源与实际源的位向一致,对1000个散射数据进行处理,用时约3 s;对5探测单元成像得到的模拟数据处理,得到重建后点源的位向分辨为8.0°;重建源的位向分辨不随设定重建平面的位置而改变,但重建平面距探测平面越近,重建速度越快;当重建平面达到一定尺寸时,继续增加大重建平面尺寸,重建的运行时间增加不明显,该方法在大视场空间探测成像应用中,具有较高的重建效率。     

一种用于中子散射成像的快速反投影重建方法

针对中子散射成像建立了一种快速反投影重建方法,这种方法首先根据每一个散射事件确定粒子可能所在的空间范围,然后该空间范围中进行重建,大大减少了重建的运行时间。应用所建立的方法对模拟的成像数据进行处理,结果表明：重建源与实际源的位向一致,对1000个散射数据进行处理,用时约3 s;对5探测单元成像得到的模拟数据处理,得到重建后点源的位向分辨为8.0;重建源的位向分辨不随设定重建平面的位置而改变,但重建平面距探测平面越近,重建速度越快;当重建平面达到一定尺寸时,继续增加大重建平面尺寸,重建的运行时间增加不明显,该方法在大视场空间探测成像应用中,具有较高的重建效率。     

A fast semi-implicit method for anisotropic diffusion

Simple finite differencing of the anisotropic diffusion equation, where diffusion is only along a given direction, does not ensure that the numerically calculated heat fluxes are in the correct direction. This can lead to negative temperatures for the anisotropic thermal diffusion equation. In a previous paper we proposed a monotonicity-preserving explicit method which uses limiters (analogous to those used in the solution of hyperbolic equations) to interpolate the temperature gradients at cell faces. However, being explicit, this method was limited by a restrictive Courant–Friedrichs–Lewy (CFL) stability timestep. Here we propose a fast, conservative, directionally-split, semi-implicit method which is second order accurate in space, is stable for large timesteps, and is easy to implement in parallel. Although not strictly monotonicity-preserving, our method gives only small amplitude temperature oscillations at large temperature gradients, and the oscillations are damped in time. With numerical experiments we show that our semi-implicit method can achieve large speed-ups compared to the explicit method, without seriously violating the monotonicity constraint. This method can also be applied to isotropic diffusion, both on regular and distorted meshes.     

A value rule for non-maximal observables

A value rule for contextualized non-maximal observables, the non-maximal value rule (NMVR), is proven from the value rule for maximal observables (VR) and the statistical functional composition principle (STAT FUNC). A consequence of NMVR, the non-maximal eigenvalue rule (NMER), is then applied to a reformulation of Mermin's Bell-EPR non-locality proof, putting this proof in the same form as other algebraic non-locality proofs. Two such reformulations have been given previously. NMVR implies an important technical lemma, which is assumed in these two reformulations, thus giving this one the same degree of rigour as other proofs, despite its greater simpliticity.     

Temporal breakdown and Borel resummation in the complex Langevin method

We reexamine the Parisi–Klauder conjecture for complex e^iθ/2?⁴$e^{i\theta /2}{?}^4$ measures with a Wick rotation angle 0≤θ/2≤π/2$0\le \theta /2\le \pi /2$ interpolating between Euclidean signature and Lorentzian signature. Our main result is that the asymptotics for short stochastic times t$t$ encapsulates information also about the equilibrium aspects. The moments evaluated with the complex measure and with the real measure defined by the stochastic Langevin equation have the same t→0$t\to 0$ asymptotic expansion which is shown to be Borel summable. The Borel transform correctly reproduces the time dependent moments of the complex measure for all t$t$, including their t→∞$t\to \infty$ equilibrium values. On the other hand the results of a direct numerical simulation of the Langevin moments are found to disagree from the ‘correct’ result for t$t$ larger than a finite t_c$t_c$. The breakdown time t_c$t_c$ increases powerlike for decreasing strength of the noise’s imaginary part but cannot be excluded to be finite for purely real noise. To ascertain the discrepancy we also compute the real equilibrium distribution for complex noise explicitly and verify that its moments differ from those obtained with the complex measure.     

A simple and accurate method for analysis of dielectric periodic structures

A simple and accurate approach for analysis of dielectric periodic structures is proposed in this paper. The method combines the coupled-mode theory with Floquet theory and joins the eigenmode expansion with the space harmonic expansion properly. As a result, the whole analysis procedure is significantly simplifid. Numerical results for the filter characteristics of some dielectric periodic structures show that the present method is effective, accurate and useful.Supported by The National Natural Science Foundation of China and The Foundation of State Educational Commission.