Light cone expansion and four point function

The behaviour of products of local fields for lightlike distances is investigated. If a light cone expansion ofA(x)A(y) exists, then already the four point function carries the singularity arising in the expansion for (x–y)²0. For a special class of field theories, discussed by S. Schlieder and E. Seiler, it is shown that the light cone expansion is possible. Notation. the Schwartz space of strongly decreasing testfunctions over ⁿ A=scalar field operator, which fulfils the Wightman axioms [we freely writeA(x),x ⁴ andA(g),g ]. =Hilbert space. =vacuum state. is the linear hull of the vectors (With respect to the definition of operators with complex argument cf.[6]!) By (x ²) (x ²) we denote a sequence of functions which converges to (x ²) as 0.     

Conformally Invariant Quantization at Order Three

Let (M, g) be a pseudo-Riemannian manifold and the space of densities of degree on M. Denote the space of differential operators from to of order k and S _k with = – the corresponding space of symbols. We construct (the unique) conformally invariant quantization map . This result generalizes that of Duval and Ovsienko.     

Phase uniqueness and correlation length in diluted-field Ising models

The diluted-field Ising model, a random nonnegative field ferromagnetic model, is shown to have a unique Gibbs measure with probability I when the field mean is positive. Our methods involve comparisons with ordinary uniform field Ising models. They yield as a corollary a way of obtaining spontaneous magnetization through the application of a vanishing random magnetic field. The correlation lengths of this model defined as (lim _n-(1/n) log ₀; _n)^-1, wheren is the site on the first coordinate axis at distancen from the origin and ₀; _n is the origin ton two-point truncated correlation function, is non-random. We derive an upper bound for it in terms of the correlation length of an ordinary nonrandom model with uniform field related to the field distribution of the diluted model.     

Novel perturbation expansion for the Langevin equation

We discuss the randomly driven systemdx/dt= -W(x) +f(t), wheref(t) is a Gaussian random function or stirring force withf(t)f(t)=2(t–t), andW(x) is of the formgx ¹⁺². The parameter is a measure of the nonlinearity of the equation. We show how to obtain the correlation functionsx(t)f(t)···x(t( n)) _f as a power series in. We obtain three terms in the expansion and show how to use Padé approximants to analytically continue the answer in the variable. By using scaling relations, we show how to get a uniform approximation to the equal-time correlation functions valid for allg and.     

A lower bound for the memory capacity in the Potts-Hopfield model

We consider Potts-Hopfield networks of sizeN. We prove the result: _c >0 such that for all 0<< _c we can find, >0 in such a way that, whenN, we can store N patterns, all of them being sorrounded by -energy barriers at distance.     

The peak constrained positive exponential sum method of inverting Laplace transform applied to correlation spectroscopy

As a contribution to the basic problem of correlation spectroscopy, a method has been developed for the Laplace transform inversion with a given number of maxima in the nonnegative inverted function() (i.e. in the distribution function of decay times recalculated as a density function on a logarithmic scale) by the least squares method. The resulting solution consists of the given number of-functions, each of which may be accompanied on one or both sides by one or several histogram bins decreasing away from the-function. When applied to simulated data for quasielastic light scattering (QELS), the method yields good agreement of the calculated distributions with the simulated ones, except that it yields sharp edges to the histogram bins and artefact-functions at the maxima of all the bands. An example shows the method to be a useful tool in interpreting QELS data.     

A Rigorous Derivation of a Linear Kinetic Equation of Fokker–Planck Type in the Limit of Grazing Collisions

We rigorously derive a linear kinetic equation of Fokker–Planck type for a 2-D Lorentz gas in which the obstacles are randomly distributed. Each obstacle of the Lorentz gas generates a potential V( ), where V is a smooth radially symmetric function with compact support, and >0. The density of obstacles diverges as ^– , where >0. We prove that when 0< <1/8 and =2+1, the probability density of a test particle converges as 0 to a solution of our kinetic equation.     

Spectral and scattering theory for a Schrödinger operator with a class of momentum-dependent long-range potentials

Let be the selfadjoint operator for the static electromagnetic field where W _j for 0, 1, 2, ..., n is a sum of (i) a short-range potential and (ii) a smooth long-range potential decreasing at as |x|^- with in (0, 1]. Then for >1/2, asymptotic completeness holds for the scattering system (H, H ₀).     

Mosaic Structure of (001)YBa2Cu3O7-δ/(10.2)Al2O3 Epitaxial Films and Millimeter Waveband Properties of Microstrip Resonators

The c-axis single-phase YBa₂Cu₃O_7- films ( = 0-0.15) on sapphire substrates prepared by the laser ablation technique and the band-pass stripline resonators for 34 GHz-range have been investigated. Increasing disorientation of mosaic block structure of YBa₂Cu₃O_7- films is related to increasing surface resistance R_s at 135 GHz-range and decreasing unloaded quality factor Q_o of linear stripline resonators. The linear dependence between the YBa₂Cu₃O_7- film mosaicity (M) and half-width B₁ of 00.13 reflecting component is determined. The reflection spreading is due to microstrains resulted mainly from the coherent adjustment of the YBa₂Cu₃O_7- film lattice to GdBa₂Cu₃O_7- sub-layer and sapphire substrate. Increasing number of the block characterized by a weak radial lattice adjustment () is demonstrated by spreading of 00.13 reflection. It is found out that depends on the Bragg angle of reflection due to inhomogenity of YBa₂Cu₃O_7- mosaic structure, which resulted from the gradual mosaicity decreasing with the depth.     

The spectrum of a quasiperiodic Schrödinger operator

The spectrum (H) of the tight binding Fibonacci Hamiltonian (H _mn= _m,n+1+ _m+1,n + _m,n v(n),v(n)= ((n–1)), 1/ is the golden number) is shown to coincide with the dynamical spectrum, the set on which an infinite subsequence of traces of transfer matrices is bounded. The point spectrum is absent for any , and (H) is a Cantor set for 4. Combining this with Casdagli's earlier result, one finds that the spectrum is singular continuous for 16.On leave from the Central Research Institute for Physics, Budapest, Hungary     

A note on nuclear excitation by positron annihilation with K-shell electrons

Experimental data for the nuclear excitation of¹¹⁵In by positron annihilation with K-shell electrons have been examined, taking account of the effective thickness of an In target used, and then the cross section _res for resonance excitation to the 1078 keV energy level by positron annihilation has been reevaluated. The cross section for the process is induced by the measured effective cross section _eff of nuclear excitation of the isomeric level^115mIn. In this work the effective thicknesses of the In target for positrons with kinetic energies 83.9 and 470 keV have been estimated. The effective thickness r has been determined from a relation r=E/ ¦dE/dr¦, where E is the positron energy width at 83.9 or 470 keV, r is the mean distance traversed by them, and ¦dE/dr¦ the stopping power of indium for them. In the present case, _K, the atomic-level width of the K-level of indium, is used as E. Neglecting a contribution from the 1464 keV level being much smaller than that from the 1078 keV level, a reevaluated value of _res has been obtained as 1.7×10^–25 cm².     

Letter: Cosmic Rays and Large Extra Dimensions

We have proposed that the cosmic ray spectrum knee, the steepening of the cosmic ray spectrum at energy E 10^15.5 eV, is due to new physics, namely new interactions at TeV cm energies which produce particles undetected by the experimental apparatus. In this letter we examine specifically the possibility that this interaction is low scale gravity. We consider that the graviton propagates, besides the usual four dimensions, into an additional , compactified, large dimensions and we estimate the graviton production in pp collisions in the high energy approximation where graviton emission is factorized. We find that the cross section for graviton production rises as fast as ( /M _f)²⁺, where M _f is the fundamental scale of gravity in 4 + dimensions, and that the distribution of radiating a fraction y of the initial particle's energy into gravitational energy (which goes undetected) behaves as y ^{– 1}. The missing energy leads to an underestimate of the true energy and generates a break in the inferred cosmic ray spectrum (the knee). By fitting the cosmic ray spectrum data we deduce that the favorite values for the parameters of the theory are M _f 8 TeV and = 4.     

The slow passage through a steady bifurcation: Delay and memory effects

We consider the following problem as a model for the slow passage through a steady bifurcation: dy/dt = (t) y – y³ +, where is a slowly increasing function oft given by= _i + t ( ⁱ,<0). Both and are small parameters. This problem is motivated by laser experiments as well as theoretical studies of laser problems. In addition, this equation is a typical amplitude equation for imperfect steady bifurcations with cubic nonlinearities. When=0, we have found that=0 is not the point where the bifurcation transition is observed. This transition appears at a value = ^j > 0. We call ^j the delay of the bifurcation transition. We study this delay as a function of ⁱ, the initial position of, and, the imperfection parameter. To this end, we propose an asymptotic study of this equation as 0, small but fixed. Our main objective is to describe this delay in terms of the relative magnitude of and. Since time-dependent imperfections are always present in experiments, we analyze in the second part of the paper the effect of a small-amplitude but time-periodic imperfection given by (t) = cos(t).     

A theory of 1/f noise

Letu() be an absolutely integrable function and define the random process where thet _i are Poisson arrivals and thes _i, are identically distributed nonnegative random variables. Under routine independence assumptions, one may then calculate a formula for the spectrum ofn(t), S _n(), in terms of the probability density ofs, p_s(). If any probability density p_s() having the property p_s() I for small is substituted into this formula, the calculated S_n() is such that S_n() 1 for small . However, this is not a spectrum of a well-defined random process; here, it is termed alimit spectrum. If a probability density having the property p_s() for small , where > 0, is substituted into the formula instead, a spectrum is calculated which is indeed the spectrum of a well-defined random process. Also, if the latter p_s is suitably close to the former p_s, then the spectrum in the second case approximates, to an arbitrary, degree of accuracy, the limit spectrum. It is shown how one may thereby have 1/f noise with low-frequency turnover, and also strict 1/f ^1– noise (the latter spectrum being integrable for > 0). Suitable examples are given. Actually, u() may be itself a random process, and the theory is developed on this basis.     

The hydrodynamic limit of a one-dimensional nearest neighbor gradient system

We study the hydrodynamic behavior of a one-dimensional nearest neighbor gradient system with respect to a positive convex potential . In the hydrodynamic limit the density distribution is shown to evolve according to the nonlinear diffusion equation ,(q)/t= (²/dq²){F([1/₁(q)]), with F= –.     

Limiting behavior of asymptotically flat gravitational fields

Couch and Torrence suggest that the vacuum Einstein equations admit a larger class of asymptotically flat solutions than those exhibiting the peeling property. Starting with the assumption that , (d/dr) and (/x ^A ) , wherex ^A (A = 2, 3) are angular coordinates, they show that , where ₁ 2 and ₁<₀; , where ₂ 1 and ₁< ₁; and ₄ and ₃ peel as they would under the stronger peeling conditions. The Winicour-Tamburino energy-momentun and angular momentum integrals for these solutions, in general, diverge. In fact, since Couch and Torrence determine only the radial dependence of the solution, it is not clear that the solutions are well defined. We find that the stronger assumption , (d/dr) , and (/x ^A ) does result in well-defined solutions for which both the energy-momentum and angular momentum intergrals are not only finite but result in the same expressions as are obtained for peeling space-times. This assumption appears to be the minimal assumption that is necessary for investigating outgoing radiation at null infinity.In part based on a dissertation by Stephanie Novak and submitted to Syracuse University in partial fulfillment of the requirement for the Ph.D. degree.     

Effective Potential for \mathcal{P}\mathcal{T}-Symmetric Quantum Field Theories

Recently, a class of -invariant scalar quantum field theories described by the non-Hermitian Lagrangian = () ² +g ² (i) was studied. It was found that there are two regions of . For <0 the -invariance of the Lagrangian is spontaneously broken, and as a consequence, all but the lowest-lying energy levels are complex. For 0 the -invariance of the Lagrangian is unbroken, and the entire energy spectrum is real and positive. The subtle transition at =0 is not well understood. In this paper we initiate an investigation of this transition by carrying out a detailed numerical study of the effective potential V _eff (_c) in zero-dimensional spacetime. Although this numerical work reveals some differences between the <0 and the >0 regimes, we cannot yet see convincing evidence of the transition at =0 in the structure of the effective potential for -symmetric quantum field theories.     

Direction-Dependent Free Energy Singularity of the Antiferroelectric Asymmetric Six-Vertex Model

The transition from the ordered commensurate phase to the incommensurate Gaussian phase of the antiferroelectric asymmetric six-vertex model is investigated by keeping the temperature constant below the roughening point and varying the external fields (h, v). In the (h, v) plane, the phase boundary is approached along straight lines v = k h, where (h, v) measures the displacement from the phase boundary. It is found that the free energy singularity displays the exponent 3/2 typical of the Pokrovski–Talapov transition f const(h)^3/2 for any direction other than the tangential one. In the latter case f shows a discontinuity in the third derivative.     

Perturbations of flows on Banach spaces and operator algebras

For automorphism groups of operator algebras we show how properties of the difference _t – ' _t are reflected in relations between the generators , . Indeed for a von Neumann algebraM with separable predual we show that if _t – '_t 0.28 for smallt, then = 0(+)°^-1 where is an inner automorphism ofM and is a bounded derivation ofM. If the difference _t – ' _t =O(t) ast ; 0, then = + and if _t – ' _t 0.28 for allt then =. We prove analogous results for unitary groups on a Hilbert space andC ₀,C ₀ ^* groups on a Banach space.This paper subsumes an earlier work of the same title which appeared as a report from Z.I.F. der Universität BielefeldWith partial support of the U.S. National Science Foundation     

Probability distribution of internal distances of a single polymer in good solvent

IfP _ij(x) is the probability distribution function of the scaled distancex between two elementsi andj of a long polymer in a good solvent, it is shown by Monte Carlo calculations that is in good agreement with out data for allx (B is a normalization constant). As a model we consider the freely jointed chain consisting ofN=160 rigid links. We estimate the exponents to ₀=0.27±0.01, ₀=2.44±0.02 (fori=1,j=N); ₁=0.55±0.06, ₁=2.60±0.15 (fori=1,j=N/2); ₂=0.9±0.1, ₂=2.48±0.06 (fori=N/4,j=3N/4). ₀ and ₀ are in agreement with ₀=1/(1-v) and ₀=(-1)/v proposed by Fisher and des Cloiseaux respectively, but we find concerning ₁ and ₂ that our estimates differ from recent -expansion calculations, by an amount of 20–30%. We analyse the crossover between the various exponents.