Probability distribution of the maximum of a smooth temporal signal

We present an approximate calculation for the distribution of the maximum of a smooth stationary temporal signal X(t). As an application, we compute the persistence exponent associated with the probability that the process remains below a nonzero level M. When X(t) is a Gaussian process, our results are expressed explicitly in terms of the two-time correlation function, f(t)=X(0)X(t).     

Spatial persistence of fluctuating interfaces

We show that the probability, P0(l), that the height of a fluctuating (d+1)-dimensional interface in its steady state stays above its initial value up to a distance l, along any linear cut in the d-dimensional space, decays as P0(l) approximately l(theta). Here straight theta is a "spatial" persistence exponent, and takes different values, straight theta(s) or straight theta(0), depending on how the point from which l is measured is specified. These exponents are shown to map onto corresponding temporal persistence exponents for a generalized d = 1 random-walk equation. The exponent straight theta(0) is nontrivial even for Gaussian interfaces.     

Statistics of the number of zero crossings: from random polynomials to the diffusion equation

We consider a class of real random polynomials, indexed by an integer d, of large degree n and focus on the number of real roots of such random polynomials. The probability that such polynomials have no real root in the interval [0, 1] decays as a power law n(-theta(d)) where theta(d)>0 is the exponent associated with the decay of the persistence probability for the diffusion equation with random initial conditions in space dimension d. For n even, the probability that such polynomials have no root on the full real axis decays as n(-2[theta(d)+theta(2)]). For d=1, this connection allows for a physical realization of real random polynomials. We further show that the probability that such polynomials have exactly k real roots in [0, 1] has an unusual scaling form given by n(-phi(k/logn)) where phi(x) is a universal large deviation function.     

Series expansion calculation of persistence exponents

We consider an arbitrary Gaussian stationary process X(T) with known correlator C(T), sampled at discrete times Tn = nDeltaT. The probability that (n+1) consecutive values of X have the same sign decays as Pn approximately exp(-theta(D)Tn). We calculate the discrete persistence exponent theta(D) as a series expansion in the correlator C(DeltaT) up to fourteenth order, and extrapolate to DeltaT = 0 using constrained Padé approximants to obtain the continuum persistence exponent thetas. For the diffusion equation our results are in exceptionally good agreement with recent numerical estimates.     

Measurement of persistence in 1D diffusion

Using a novel NMR scheme we observed persistence in 1D gas diffusion. Analytical approximations and numerical simulations have indicated that for an initially random array of spins undergoing diffusion, the probability p(t) that the average spin magnetization in a given region has not changed sign (i.e., "persists") up to time t follows a power law t(-straight theta), where straight theta depends on the dimensionality of the system. Using laser-polarized 129Xe gas, we prepared an initial "quasirandom" 1D array of spin magnetization and then monitored the ensemble's evolution due to diffusion using real-time NMR imaging. Our measurements are consistent with analytical and numerical predictions of straight theta approximately 0.12.     

Experimental persistence probability for fluctuating steps

The persistence behavior for fluctuating steps on the Si(111)-(sqrt[3]xsqrt[3])R30 degrees -Al surface was determined by analyzing time-dependent STM images for temperatures between 770 and 970 K. Using the standard persistence definition, the measured persistence probability displays power-law decay with an exponent of theta=0.77+/-0.03. This is consistent with the value of theta=3/4 predicted for attachment-detachment limited step kinetics. If the persistence analysis is carried out in terms of return to a fixed-reference position, the measured probability decays exponentially. Numerical studies of the Langevin equation used to model step motion corroborate the experimental observations.     

A systematic extended iterative solution for quantum chromodynamics

An outline is given of an extended perturbative solution of Euclidean QCD which systematically accounts for a class of nonperturbative effects, while still allowing renormalization by the perturbative counterterms. Euclidean proper verticesΓ are approximated by a double sequenceΓ ^[r,p] , wherer denotes the degree of rational approximation with respect to the spontaneous mass scaleΛ _QCD, nonanalytic in the couplingg ², whilep represents the order of perturbative corrections ing ² calculated fromΓ ^[r,0]-rather than from the perturbative Feynman rulesΓ ^(0)pert-as a starting point. The mechanism allowing the nonperturbative terms to reproduce themselves in the Dyson-Schwinger equations preserves perturbative renormalizability and is intimately tied to the divergence structure of the theory. As a result, it restricts the self-consistency problem for theΓ ^[r,0] rigorously — i.e. without decoupling approximations — to the seven superficially divergent vertices. An interesting aspect of the solution is that rational-function sequences for the QCD propagators contain subsequences describing short-lived elementary excitations. The method is calculational, in that it allows the known techniques of loop computation to be used while dealing with integrands of truly nonperturative content.     

Nonperturbative and perturbative aspects of photo- and electroproduction of vector mesons

We discuss various aspects of vector meson production, first analysing the interplay between perturbative and nonperturbative aspects of the QCD calculation. Using a general method adapted to incorporate both perturbative and nonperturbative aspects, we show that nonperturbative effects are important for all experimentally available values of the photon virtuality Q². We compare the huge amount of experimental information now available with our theoretical results obtained using a specific nonperturbative model without free parameters, showing that quite simple features are able to explain the data.     

Nonperturbative expansion in QCD

The purpose of this article is to construct the nonperturbative expansion in quantum chromodynamics using a new small parameter and apply it to the investigation of the connection between nonperturbative and perturbative regimes of the effective coupling constant. We calculate the nonperturbative renormalization group β-function and discuss the properties of the series convergence using the two-loop approximation in this method. Based on the information from meson spectroscopy we derive the effective coupling constant in the perturbative region.     

Polarization measurements in high-energy deuteron photodisintegration

We present measurements of the recoil proton polarization for the d(gamma-->,p-->)n reaction at straight theta(c.m.) = 90 degrees for photon energies up to 2.4 GeV. These are the first data in this reaction for polarization transfer with circularly polarized photons. The induced polarization p(y) vanishes above 1 GeV, contrary to meson-baryon model expectations, in which resonances lead to large polarizations. However, the polarization transfer Cx does not vanish above 1 GeV, inconsistent with hadron helicity conservation. Thus, we show that the scaling behavior observed in the d(gamma,p)n cross sections is not a result of perturbative QCD. These data should provide important tests of new nonperturbative calculations in the intermediate energy regime.     

Perturbative and nonperturbative processes in adiabatic population transfer

With the help of superadiabatic techniques for quantum systems depending slowly on time, we demonstrate how the total transition amplitude, tracked in time in the usual adiabatic basis, can be decomposed into a perturbative part consisting of terms proportional to powers of the adiabaticity parameter, and a nonperturbative component. The interference of both components underlies the oscillations that accompany transitions in the adiabatic basis. Whereas for traditionally considered systems the final nonadiabatic transition probability is determined by the nonperturbative part alone, this is no longer correct for models describing stimulated Raman adiabatic passage (STIRAP). We explain the recently discovered breakdown of the Dykhne-Davis-Pechukas formula on general grounds, and provide simple, but accurate approximations for transition amplitudes in STIRAP systems. Received: 22 January 1998 / Revised: 17 March 1998 / Accepted: 31 March 1998     

Residence time distribution for a class of Gaussian Markov processes

We study the distribution of residence time or equivalently that of "mean magnetization" for a family of Gaussian Markov processes indexed by a positive parameter alpha. The persistence exponent for these processes is simply given by theta=alpha but the residence time distribution is nontrivial. The shape of this distribution undergoes a qualitative change as theta increases, indicating a sharp change in the ergodic properties of the process. We develop two alternate methods to calculate exactly but recursively the moments of the distribution for arbitrary alpha. For some special values of alpha, we obtain closed form expressions of the distribution function.     

Perturbative and non-perturbative two component model of deep inelastic scattering

We propose a two-component model for describing deep inelastic scattering, based on nonperturbative and perturbative mechanisms. The nonperturbative dynamics obey the usualS-matrix constraints, as realized by the Dual Topological Unitarization Scheme, whereas the perturbative component stems from the underlying field theory. However, these two components arenot independent.     

Aging in 1D discrete spin models and equivalent systems

We derive exact expressions for a number of aging functions that are scaling limits of nonequilibrium correlations, R(t(w),t(w)+t) as t(w)-->infinity, t/t(w)-->theta, in the 1D homogenous q-state Potts model for all q with T = 0 dynamics following a quench from T = infinity. One such quantity is (0)(t(w));sigma-->(n)(t(w)+t)> when n/square root of ([t(w))-->z. Exact, closed-form expressions are also obtained when an interlude of T = infinity dynamics occurs. Our derivations express the scaling limit via coalescing Brownian paths and a "Brownian space-time spanning tree," which also yields other aging functions, such as the persistence probability of no spin flip at 0 between t(w) and t(w)+t.     

Remarks on Independent Value Model

By nonperturbative investigation of the generating functional for simple ⁴ model without gradient term we have shown that triviality of the model (independence of the result on the coupling) may be a perturbative calculation relict.     

Measurement of the shape of the boson-transverse momentum distribution in pp --> Z/gamma* --> e+e- + X events produced at square root s = 1.96 TeV

We present a measurement of the shape of the Z/gamma* boson transverse momentum (q(T)) distribution in pp --> Z/gamma* --> e(+)e(-) + X events at a center-of-mass energy of 1.96 TeV using 0.98 fb(-1) of data collected with the D0 detector at the Fermilab Tevatron collider. The data are found to be consistent with the resummation prediction at low q(T), but above the perturbative QCD calculation in the region of q(T)>30 GeV/c. Using events with q(T)<30 GeV/c, we extract the value of g(2), one of the nonperturbative parameters for the resummation calculation. Data at large boson rapidity y are compared with the prediction of resummation and with alternative models that employ a resummed form factor with modifications in the small Bjorken x region of the proton wave function.     

The Feynman-Schwinger Representation in QCD

The proper time path integral representation is derived explicitly for Green's functions in QCD. After an introductory analysis of perturbative properties, the total gluonic field is separated in a rigorous way into a nonperturbative background and valence gluon part. For nonperturbative contributions the background perturbation theory is used systematically, yielding two types of expansions, illustrated by direct physical applications. As an application, we discuss the collinear singularities in the Feynman-Schwinger representation formalism. Moreover, the generalization to nonzero temperature is made and expressions for partition functions in perturbation theory and nonperturbative background are explicitly written down.     

Persistence in systems with algebraic interaction

Persistence in coarsening one-dimensional spin systems with a power-law interaction r(-1-sigma) is considered. Numerical studies indicate that for sufficiently large values of the interaction exponent sigma (sigma > or =1/2 in our simulations), persistence decays as an algebraic function of the length scale L, P(L) approximately L(-theta). The persistence exponent theta is found to be independent on the force exponent sigma and close to its value for the extremal (sigma-->infinity) model, theta =0.175 075 88. For smaller values of the force exponent (sigma < 1/2), finite size effects prevent the system from reaching the asymptotic regime. Scaling arguments suggest that in order to avoid significant boundary effects for small sigma, the system size should grow as [O(1/sigma)](1/sigma).     

Numerical renormalization group for bosonic systems and application to the sub-ohmic spin-boson model

We describe the generalization of Wilson's numerical renormalization group method to quantum impurity models with a bosonic bath, providing a general nonperturbative approach to bosonic impurity models which can access exponentially small energies and temperatures. As an application, we consider the spin-boson model, describing a two-level system coupled to a bosonic bath with power-law spectral density, J(omega) proportional to omega(s). We find clear evidence for a line of continuous quantum phase transitions for sub-Ohmic bath exponents 0相似文献