Showing papers on "Correlation function (statistical mechanics) published in 1998"
TL;DR: In this article, the structure functions for the 3D-Var assimilation scheme of the European Centre for Medium-Range Weather Forecasts are evaluated from statistics of the differences between two forecasts valid at the same time.
Abstract: Structure functions for the 3D-Var assimilation scheme of the European Centre for Medium-Range Weather Forecasts are evaluated from statistics of the differences between two forecasts valid at the same time. Results compare satisfactorily with those reported in the existing literature. Non-separability of the correlation functions is a pervasive feature. Accounting for non-separability in 3D-Var is necessary to reproduce geostrophic characteristics of the statistics, such as the increase of length-scale with height for the horizontal correlation of the mass variable, sharper vertical correlations for wind than for mass and shorter horizontal length-scales for temperature than for mass. In our non-separable 3D-Var, the vertical correlations vary with total wave-number and the horizontal correlation functions vary with vertical level.
286 citations
TL;DR: In this paper, a shell model of turbulence is introduced, which exhibits improved properties in comparison to the standard Gledzer, Ohkitani, and Yamada (GOY) model.
Abstract: We introduce a shell model of turbulence that exhibits improved properties in comparison to the standard (and very popular) Gledzer, Ohkitani, and Yamada (GOY) model The nonlinear coupling is chosen to minimize correlations between different shells In particular, the second-order correlation function is diagonal in the shell index and the third-order correlation exists only between three consecutive shells Spurious oscillations in the scaling regime, which are an annoying feature of the GOY model, are eliminated by our choice of nonlinear coupling We demonstrate that the model exhibits multiscaling similar to the GOY model The scaling exponents are shown to be independent of the viscous mechanism as is expected for Navier-Stokes turbulence and other shell models These properties of the model make it optimal for further attempts to achieve understanding of multiscaling in nonlinear dynamics
240 citations
TL;DR: A Monte Carlo simulation concluded that, in order to measure the rms height and the correlation length with a precision of /spl plusmn/10%, the surface segment should be at least 40l long and 200l long, respectively, where l is the mean (or true) value of the surface correlation length.
Abstract: Whereas it is well known that electromagnetic scattering by a randomly rough surface is strongly influenced by the surface-height correlation function, it is not clear as to how long a surface-height profile is needed and at what interval it should be sampled to experimentally quantify the correlation function of a real surface. This paper presents the results of a Monte Carlo simulation conducted to answer these questions. It was determined that, in order to measure the rms height and the correlation length with a precision of /spl plusmn/10%, the surface segment should be at least 40l long and 200l long, respectively, where l is the mean (or true) value of the surface correlation length. Shorter segment lengths can be used if multiple segments are measured and then the estimated values are averaged. The second part of the study focused on the relationship between sampling interval and measurement precision. It was found that, in order to estimate the surface roughness parameters with a precision of /spl plusmn/5%, it is necessary that the surface be sampled at a spacing no longer than 0.2 of the correlation length.
207 citations
TL;DR: In this paper, the authors consider the problem of predicting the hierarchical clustering amplitudes in the strongly non-linear regime of gravitational evolution, and provide a general fitting formula for the nonlinear evolution of the bispectrum that interpolates between the weakly and strongly nonlinear regimes.
Abstract: We consider the long-standing problem of predicting the hierarchical clustering amplitudes $S_p$ in the strongly non-linear regime of gravitational evolution. N-body results for the non-linear evolution of the bispectrum (the Fourier transform of the three-point density correlation function) suggest a physically motivated ansatz that yields the strongly non-linear behavior of the skewness, $S_3$, starting from leading-order perturbation theory. When generalized to higher-order ($p>3$) polyspectra or correlation functions, this ansatz leads to a good description of non-linear amplitudes in the strongly non-linear regime for both scale-free and cold dark matter models. Furthermore, these results allow us to provide a general fitting formula for the non-linear evolution of the bispectrum that interpolates between the weakly and strongly non-linear regimes, analogous to previous expressions for the power spectrum.
111 citations
TL;DR: In this article, the authors investigate two models describing how stresses propagate and fluctuate in granular media, one is a scalar model where only the vertical component of the stress tensor is considered, and the other is a tensorial model, where the basic starting point is a wave equation that, in the absence of disorder, leads to a raylike propagation of stress.
Abstract: We investigate in detail two models describing how stresses propagate and fluctuate in granular media. The first one is a scalar model where only the vertical component of the stress tensor is considered. In the continuum limit, this model is equivalent to a diffusion equation (where the role of time is played by the vertical coordinate) plus a randomly varying convection term. We calculate the response and correlation function of this model and discuss several properties, in particular related to the stress distribution function. We then turn to the tensorial model, where the basic starting point is a wave equation that, in the absence of disorder, leads to a raylike propagation of stress. In the presence of disorder, the rays acquire a diffusive width and the angle of propagation is shifted. A striking feature is that the response function becomes negative, which suggests that the contact network is mechanically unstable to very weak perturbations. The stress correlation function reveals characteristic features related to the raylike propagation, which are absent in the scalar description. Our analytical calculations are confirmed and extended by a numerical analysis of the stochastic wave equation.
92 citations
TL;DR: In this article, the authors used stimulated echoes to investigate the reorientational mechanism in the selectively deuterated glass-former glycerol, C3D5(OH)3 about 15 K above its calorimetric glass temperature.
Abstract: The method of stimulated echoes was used to investigate the reorientational mechanism in the selectively deuterated glass-former glycerol, C3D5(OH)3 about 15 K above its calorimetric glass temperature. The reorientation process is fully isotropic. This enables an accurate determination of the decay constant, T1Q, of the quadrupolar spin order in the regime of ultraslow motion. The knowledge of this time constant has made it possible to reliably determine the rotational correlation function. The experimentally obtained evolution time-dependent correlation functions are compared with those from a simulation procedure involving a distribution of molecular jump angles. It is found that in glycerol small angles in the 2°–3° range dominate. They are accompanied by a small, but significant, fraction of larger jump angles.
90 citations
TL;DR: In this article, the exact structure factor (speckle pattern) during phase separation in a sodium borosilicate glass was measured using intensity fluctuation spectroscopy with a coherent x-ray beam.
Abstract: We report observations of the dynamics of the exact structure factor (speckle pattern) during phase separation in a sodium borosilicate glass, measured using intensity fluctuation spectroscopy with a coherent x-ray beam. Nonequilibrium fluctuations in the structure factor are analyzed using a two-time correlation function to extract the time-dependent and wave-number-dependent correlation time. The behavior of the correlation time is in agreement with a scaling law previously found in simulations. {copyright} {ital 1998} {ital The American Physical Society }
88 citations
06 Jul 1998
TL;DR: In this article, the authors describe the theory of determination of small deformation tensors by means of the method, availing of statistical properties of the speckle field in an optically free space geometry or in a near image field.
Abstract: This paper describes the theory of determination of small deformation tensor by means of the method, availing of statistical properties of the speckle field in an optically free space geometry or in a near image field. The small deformation tensor and a correlation function are briefly mentioned, and the main emphasis is aimed on theoretical derivation of the relationship between the correlation function of two speckle intensities, being recorded before and after deformation. This results in the relationship theoretically enabling a determination of all components of the small deformation tensor by means of a relatively simple optical arrangement in connection with computer and linear CCD detectors. Further, a compilation of all completed experimental results are briefly mentioned. An accuracy and sensitivity of this measurement methods are analyzed by theory of errors. As it flows from theory, the exact results at stress deformation, body displacement and rotation depend in crucially upon the geometrical arrangement of the optical system. The emphasis on the analysis of accuracy and sensitivity of individual geometrical parameters of assembly are given, with the aim to find an optimized geometry of experimental arrangement. The feasibility of an easy realization in practice and most importantly achieving satisfactory results of measurements are the important criteria. The conclusion presents some results obtained at concrete measurement with proposed experimental assembly.
80 citations
TL;DR: In this paper, the exact amplitude for the asymptotic correlation function in the Heisenberg antiferromagnetic chain was determined and the behaviour of the correlation functions for small xxz anisotropy and the form of finite-size corrections to the correlation function were also analysed.
Abstract: The exact amplitude for the asymptotic correlation function in the Heisenberg antiferromagnetic chain is determined: The behaviour of the correlation functions for small xxz anisotropy and the form of finite-size corrections to the correlation function are also analysed.
76 citations
TL;DR: In this article, the Ehrlich-Schwoebel effect, diffusion along the step edge, as well as elastic interactions between steps have been incorporated into the equilibrium theory for a train of steps and the analysis is based on a nonlocal Langevin equation derived from the Burton-Carbrera-Frank model.
Abstract: The equilibrium theory for a train of steps is revisited The analysis is based on a nonlocal Langevin equation derived from the Burton-Carbrera-Frank model The Ehrlich-Schwoebel effect, diffusion along the step edge, as well as elastic interactions between steps have been incorporated We discuss several static correlation functions and give an improved estimate for the terrace width distribution By exploiting the dispersion relation, the time dependence of the step fluctuations has been calculated In the limit of well separated length scales there are several time intervals where the temporal step correlation function follows a power law with one of the exponents 1/2, 1/3, or 1/4 In the opposite situation, neither power laws nor simple scaling behaviors are obtained We provide precise conditions on which regime must be expected in a given real situation Moreover, it is shown that different physical mechanisms can give rise to the same exponent This study is thus crucial for the discrimination between various physical regimes in a real experiment The range of validity of the approximation and the crossover times are discussed for steps on Si(111)
74 citations
TL;DR: In this article, the authors present results of several MHD simulations that address this issue using both two-and-one-half dimensional and three-dimensional compressible models and a wide variety of initial states and plasma parameters.
Abstract: Spacecraft observations of magnetic field fluctuations in the solar wind reveals a “Maltese Cross” pattern in the two-dimensional correlation function measurements of solar wind fluctuations [Matthaeus et al., 1990]. This pattern suggests the presence of two components: fluctuations with their (Fourier) wave vector approximately parallel to the ambient magnetic field (e.g., slab turbulence) and fluctuations with their (Fourier) wave vector approximately perpendicular to the ambient magnetic field (e.g., quasi two-dimensional turbulence). To date, the appearance of such a pattern has never been reproduced from numerical simulation studies. Here we present results of several MHD simulations that address this issue using both two-and-one-half dimensional and three-dimensional compressible models and a wide variety of initial states and plasma parameters. Slab turbulence and quasi two-dimensional turbulence appear in various runs; however, their simultaneous appearance is difficult to achieve and seems to rely upon their separate existence in the initial data. In contrast, the presence of transverse pressure-balanced magnetic structures causes slab turbulence to evolve in such a manner that a two-component correlation function emerges through time averaging. We suggest that the Maltese Cross and similar observations may be a consequence of either the initial data or of averaging over different parcels of solar wind.
TL;DR: In this paper, the exact amplitude for the asymptotic correlation function in the S = 1/2 Heisenberg antiferromagnetic chain was determined, and the behavior of the correlation functions for small xxz anisotropy and the form of finite-size corrections to the correlation function was analyzed.
Abstract: The exact amplitude for the asymptotic correlation function in the S=1/2 Heisenberg antiferromagnetic chain is determined: goes to (-1)^r delta^{ab}(ln r)^{1/2}/[(2 pi)^{3/2}r]. The behaviour of the correlation functions for small xxz anisotropy and the form of finite-size corrections to the correlation function are also analysed.
TL;DR: In this paper, a general expression for gloss within the scalar Kirchhoff's theory is derived in terms of the detector collecting angle, and two statistical parameters that characterize the surface roughness.
Abstract: A general expression for gloss within the scalar Kirchhoff 's theory is de- rived in terms of the detector collecting angle, and two statistical parameters that characterize the surface roughness. Analytical expressions for gloss are derived for an exponential and a Gaussian correlation function, and numerical results for these and other quasi-exponential correlation functions are presented. It is shown that the inco- herent contribution to gloss is significant in common polymeric surfaces. The latter implies that surface height correlations cannot be neglected in the evaluation of gloss. It is also shown that for a correlation function with a single characteristic length, gloss scales with the correlation length Lc in the same way as with the detector collecting angle. This fact can be used to determine Lc with a glossmeter, and an experimental method to achieve this is proposed. q 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1321-1334, 1998
TL;DR: In this article, the effects of the phase fluctuations of the order parameter on the stability of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states are examined in exactly two-dimensional (2D) type-II superconductors with cylindrically symmetric Fermi surface on the basis of a generalized Ginzburg-Landau theory.
Abstract: Effects of the phase fluctuations of the order parameter on the stability of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states are examined in exactly two-dimensional (2D) type-II superconductors with cylindrically symmetric Fermi surface on the basis of a generalized Ginzburg-Landau theory. It is found that for the FFLO states with oscillations in a single direction, not only the long-range order but also quasi-long-range order (QLRO), which is characterized by a power law decay of the order parameter correlation function, is suppressed by the phase fluctuations at any finite temperatures. On the other hand, for the FFLO states with order parameter structures such as triangular and square lattices, it is shown that the QLRO is possible as the uniform BCS state. Systems with anisotropy in the Fermi surface and pairing are also discussed.
TL;DR: In this article, the authors developed a method of optimized discretization for imaging the relative source from two particle correlation functions, where the source resolution depends on the relative particle separation and is adjusted to available data and their errors.
Abstract: We develop the new method of optimized discretization for imaging the relative source from two particle correlation functions In this method, the source resolution depends on the relative particle separation and is adjusted to available data and their errors We test the method by restoring assumed pp sources and then apply the method to pp and IMF data In reactions below 100 MeV/nucleon, significant portions of the sources extend to large distances (r > 20 fm) The results from the imaging show the inadequacy of common Gaussian source-parametrizations We establish a simple relation between the height of the pp correlation function and the source value at short distances, and between the height and the proton freeze-out phase-space density
TL;DR: In this article, a generic correlation function was proposed to quantify the spatial correlation of single-particle displacements in liquids and amorphous systems, and they evaluated this function using computer simulations of an equilibrium glass-forming liquid, and showed that the displacements of particles are spatially correlated over a range that grows with decreasing temperature as the glass transition is approached.
Abstract: We dene a generic correlation function that quanties the spatial correlation of single-particle displacements in liquids and amorphous systems. We evaluate this function using computer simulations of an equilibrium glass-forming liquid, and show that the displacements of particles are spatially correlated over a range that grows with decreasing temperature as the glass transition is approached. c 1998 Elsevier Science B.V. All rights reserved.
TL;DR: In this article, the authors present an analysis of the 2-point correlation function of the X-ray Brightest Abell-type Cluster sample (XBACs; Ebeling et al. 1998) and of the cosmological constraints that it provides.
Abstract: We present an analysis of the 2-point correlation function, of the X-ray Brightest Abell-type Cluster sample (XBACs; Ebeling et al. 1998) and of the cosmological constraints that it provides. If \xi(r) is modelled as a power-law, we find r_0=26.0 +/- 4.5 Mpc/h and \gamma=2.0 +/-0.4, with errors corresponding to 2\sigma uncertainties. Only a marginal increase of the correlation amplitude is found as the flux limit is increased from 5x10^{-12} cgs to 12x10^{-12} cgs, thus indicating a weak dependence of the correlation amplitude on the cluster X-ray luminosity. Furthermore, we present a method to predict correlation functions for flux-limited X-ray cluster samples from cosmological models. The method is based on the analytical recipe by Mo & White (1996) and on an empirical approach to convert cluster fluxes into masses. We use a maximum-likelihood method to place constraints on the model parameter space. We find that the shape parameter of the power spectrum lies in the 2\sigma range 0.05<\Gamma<0.20. As for the amplitude of the power-spectrum, we find \sigma_8 in the range 0.4-0.8 for \Omega_0=1 and 0.8-2.0 for \Omega_0=0.3. This result is in agreement with, although less constraining than, results based on the local cluster abundance.
TL;DR: In this article, effective spin S chains are realized by ferromagnetically coupling n=2S antiferromagnetic spin chains with S = 1/2 and the temperature dependence of the uniform susceptibility, the staggered susceptibility, and the static structure factor peak intensity are computed down to very low temperatures.
Abstract: Antiferromagnetic Heisenberg spin chains with various spin values (S=1/2,1,3/2,2,5/2) are studied numerically with the quantum Monte-Carlo method. Effective spin S chains are realized by ferromagnetically coupling n=2S antiferromagnetic spin chains with S=1/2. The temperature dependence of the uniform susceptibility, the staggered susceptibility, and the static structure factor peak intensity are computed down to very low temperatures, . The correlation length at each temperature is deduced from numerical measurements of the instantaneous spin-spin correlation function. At high temperatures, very good agreement with exact results for the classical spin chain is obtained independent of the value of S. For the S=2 chain which has a gap , the correlation length and the uniform susceptibility in the temperature range are well predicted by the semi-classical theory of Damle and Sachdev.
TL;DR: In this paper, a transfer matrix method was developed to compute exactly the spin-spin correlation functions for Bethe lattice Ising model and Blume-Emery-Griths (BEG) model in the external magnetic field h and for any temperature T. The correlation length ξ(T,h) obtained from the spin correlation function shows interesting scaling and divergent behavior as h→0 and T approaches the critical temperature Tc.
Abstract: We develop a transfer matrix method to compute exactly the spin–spin correlation functions for Bethe lattice Ising model and Blume–Emery–Griffiths (BEG) model in the external magnetic field h and for any temperature T. The correlation length ξ(T,h) obtained from the spin–spin correlation function shows interesting scaling and divergent behavior as h→0 and T approaches the critical temperature Tc.
TL;DR: In this article, statistical properties of energy levels and eigenfunctions in a ballistic system with diffusive surface scattering are investigated and the two-level correlation function, the level number variance, the correlation function of wavefunction intensities, and the inverse participation ratio are calculated.
Abstract: Statistical properties of energy levels and eigenfunctions in a ballistic system with diffusive surface scattering are investigated. The two-level correlation function, the level number variance, the correlation function of wavefunction intensities, and the inverse participation ratio are calculated.
TL;DR: In particular, this paper showed that even large quasar surveys are likely to reside in the "sparse sampling" regime for correlation function measurements, so that the statistical fluctuations in measurements are simply the Poisson fluctuations in the observed numbers of pairs.
Abstract: The non-Euclidean geometry of spacetime induces an anisotropy in the apparent correlation function of high-redshift objects, such as quasars, if redshifts and angles are converted to distances in "naive" Euclidean fashion. The degree of angular distortion depends on cosmological parameters, especially on the cosmological constant Λ, so this effect can constrain Λ independent of any assumptions about the evolution of luminosities, sizes, or clustering. We examine the prospects for distinguishing between low-density (Ω0 = 0.1-0.4) cosmological models with flat and open space geometry using the large quasar samples anticipated from the Two Degree Field Survey (2dF) and the Sloan Digital Sky Survey (SDSS). Along the way, we derive a number of results that are useful for studies of the quasar correlation function. In particular, we show that even these large quasar surveys are likely to reside in the "sparse sampling" regime for correlation function measurements, so that the statistical fluctuations in measurements are simply the Poisson fluctuations in the observed numbers of pairs. As a result, (1) one can devise a simple maximum likelihood scheme for estimating clustering parameters, (2) one can generate Monte Carlo realizations of correlation function measurements without specifying high-order correlation functions or creating artificial quasar distributions, and (3) for a fixed number of quasars, a deeper survey over a smaller area has greater statistical power than a shallow, large-area survey. If the quasar correlation length is equal to the value implied by recent (quite uncertain) estimates, then the 2dF and SDSS samples can provide clear discrimination between flat and open geometries for Ω0 ≤ 0.2 but only marginal discrimination for Ω0 = 0.4. Clear discrimination is possible for Ω0 = 0.4 if the true quasar correlation length is a factor of 2 larger, and a high-density survey of 30,000 quasars in 200 deg2 would provide clear discrimination even for the lower correlation length. Detection of quasar clustering anisotropy would confirm the cosmological spacetime curvature that is a fundamental prediction of general relativity.
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TL;DR: Olshanski and Borodin this paper studied the correlation functions for point stochastic processes in terms of multivariate hypergeometric functions and showed that the lifted correlation functions are given by a determinantal formula involving a kernel.
Abstract: We continue the study of the correlation functions for the point stochastic processes introduced in Part I (G.Olshanski, math.RT/9804086). We find an integral representation of all the correlation functions and their explicit expression in terms of multivariate hypergeometric functions. Then we define a modification (``lifting'') of the processes which results in a substantial simplification of the structure of the correlation functions. It turns out that the ``lifted'' correlation functions are given by a determinantal formula involving a kernel. The latter has the form (A(x)B(y)-B(x)A(y))/(x-y), where A and B are certain Whittaker functions. Such a form for correlation functions is well known in the random matrix theory and mathematical physics. Finally, we get some asymptotic formulas for the correlation functions which are employed in Part III (A.Borodin and G.Olshanski, math.RT/9804088).
TL;DR: In this paper, the scattering amplitude is calculated as a space-time integral over the scattering sample for an incident wave characterized by its correlation function, which results from the shaping of the wave field by the apparatus.
Abstract: We present scattering from many-body systems in a new light. In place of the usual van Hove treatment, (applicable to a wide range of scattering processes using both photons and massive particles) based on plane waves, we calculate the scattering amplitude as a space-time integral over the scattering sample for an incident wave characterized by its correlation function, which results from the shaping of the wave field by the apparatus. Instrument resolution effects, seen as due to the loss of correlation caused by the path differences in the different arms of the instrument, are automatically included and analytic forms of the resolution function for different instruments are obtained. Each element of the apparatus is associated with a correlation length (or time). These correlation lengths, determined by the dimensions of the apparatus, are generally much smaller than these dimensions and larger than the wavelength. As is well known, these are the conditions for the validity of geometrical optics so that the conventional treatment, where the scattering is calculated by the van Hove plane-wave approach and the trajectories through the instrument are treated classically, is usually valid. In the present approach analytic expressions for the correlation functions are obtained. The intersection of the moving correlation volumes (those regions where the correlation functions are significant) associated with the different elements of the apparatus determines the maximum correlation lengths (times) that can be observed in a sample, and hence, the momentum (energy) resolution of the measurement. This geometrical picture of moving correlation volumes derived by our technique shows how the interaction of the scatterer with the wave field shaped by the apparatus proceeds in space and time. Matching of the correlation volumes so as to maximize the intersection region yields a transparent, graphical method of instrument design.
TL;DR: In this article, the low temperature Monte Carlo dynamics of an ensemble of linear harmonic oscillators is studied and the authors observe some typical non-equilibrium features of glassy systems like activated-type behavior and aging in the correlation function and in the response function.
Abstract: The low temperature Monte Carlo dynamics of an ensemble of linear harmonic oscillators shows some entropic barriers related to the difficulty of finding the directions in configurational space which decrease the energy. This mechanism is enough to observe some typical non-equilibrium features of glassy systems like activated-type behavior and aging in the correlation function and in the response function. Due to the absence of interactions the model only displays a one-step relaxation process.
TL;DR: In this paper, the authors consider the one-dimensional delta-interacting electron gas in the case of infinite repulsion and derive differential equations which drive the correlation functions, which describe power law behavior and exponential decay as functions of temperature, magnetic field and chemical potential.
Abstract: We consider the one-dimensional delta-interacting electron gas in the case of infinite repulsion. We use determinant representations to study the long time, large distance asymptotics of correlation functions of local fields in the gas phase. We derive differential equations which drive the correlation functions. Using a related Riemann–Hilbert problem we obtain formulae for the asymptotics of the correlation functions, which are valid at all finite temperatures. At low temperatures these formulae lead to explicit asymptotic expressions for the correlation functions, which describe power law behavior and exponential decay as functions of temperature, magnetic field and chemical potential.
TL;DR: In this article, the density-density correlation function and structure factor were calculated from fluctuating hydrodynamics, and the theoretical predictions agree well with two-dimensional molecular-dynamics simulations.
Abstract: The clustering instability in freely evolving granular fluids manifests itself in the density-density correlation function and structure factor. These functions are calculated from fluctuating hydrodynamics. As time increases, the structure factor of density fluctuations develops a maximum, which shifts to smaller wave numbers (growing correlation length). Furthermore, the inclusion of longitudinal velocity fluctuations changes long-range correlations in the flow field qualitatively and extends the validity of the theory for spatial velocity correlations to higher inelasticities. The theoretical predictions agree well with two-dimensional molecular-dynamics simulations.
TL;DR: In this paper, a manifestly rotational invariant formulation of the matrix product method valid for spin chains and ladders is presented, which can be applied to two-legged spin ladders with spins, 1 and and different magnetic structures labelled by the exchange coupling constants.
Abstract: We present a manifestly rotational invariant formulation of the matrix product method valid for spin chains and ladders. We apply it to two-legged spin ladders with spins , 1 and and different magnetic structures labelled by the exchange coupling constants, which can be ferromagnetic or antiferromagnetic along the legs and the rungs of the ladder. We compute ground-state energy densities, correlation lengths and string order parameters. We present numerical evidence of the duality properties of the three different nonferromagnetic spin ladders. We show that the long-range topological order characteristic of isolated spin 1 chains is broken by the interchain coupling. The string order correlation function decays exponentially with a finite correlation length that we compute. A physical picture of the spin 1 ladder is given in terms of a collection of resonating spin 1 chains. Finally, for ladders with spin equal to or greater than we define a class of AKLT states whose matrix product coefficients are given by 9-j symbols.
TL;DR: The view is put forward that, even if recent work disfavors the models with cosmic strings and global O(4) texture, causal scaling seed perturbations merit a more thorough and general analysis, which is initiated in this paper.
Abstract: In this work we present a partially new method to analyze fluctuations which are induced by causal scaling seeds. We show that the power spectra due to these kinds of seed perturbations are determined by five analytic functions, which we determine numerically for a special example. We put forward the view that, even if recent work disfavors the models with cosmic strings and global $O(4)$ texture, causal scaling seed perturbations merit a more thorough and general analysis, which we initiate in this paper.
TL;DR: In this article, the authors applied the complex phase method to obtain the analytical expressions for the coherence and correlation functions, which are then calculated numerically for the realistic models of the fluctuating ionosphere.
Abstract: This paper is devoted to the investigation of the two-frequency, two-position, time coherence function and the ionospheric scattering function describing the HF ionospheric fluctuating radio channel. The complex phase method is applied to obtain the analytical expressions for the coherence and correlation functions, which are then calculated numerically for the realistic models of the fluctuating ionosphere. The numerical Fourier transformation of the correlation function gives the ionospheric scattering function. The numerical results obtained lead to the conclusion that in the general case the large variability of shapes of the scattering function of the fluctuating ionosphere exists depending on the concrete conditions of propagation. In particular, the well-known delay-Doppler coupling can be more or less pronounced in different propagation conditions. We have shown that the presence of the coupling is exclusively due to the nonzero imaginary part of the correlation function of the scattered field, which means that this effect has a purely diffractional nature and cannot be obtained in the geometrical optics approximation.
TL;DR: In this paper, the core radius and the core fraction of pions were derived from the Bose-Einstein correlation functions from CERN experiment NA44 in the context of the core-halo model.
Abstract: Having first performed a Monte Carlo simulation to justify the analysis technique to be used, we then analyze the Bose-Einstein correlation functions from CERN experiment NA44 in the context of the core-halo model. Although experimental resolution and error bar distribution prevents a direct observation of the halo structure, the values for the core radius and the core fraction of pions can be obtained in a straight-forward manner. These are found to be independent of the structure of the correlation function at small relative momenta of Q pi + pi + X reaction at CERN SPS. As we find that the "model-independent" HBT radii yield results that are quantitatively as well as qualitatively unreliable for systems with long-lived resonances, we present their corrected form that applies for correlation functions with lambda(K) < 1.