Showing papers on "Correlation function (statistical mechanics) published in 1985"

Free-energy density functional for hard spheres

Abstract: A free-energy density functional for a system of hard spheres is derived on a semiempirical basis. It is constructed to reproduce the thermodynamics and direct correlation function of a homogeneous fluid and then is tested in two highly inhomogeneous situations: the hard-wall--hard-sphere interface and the hard-sphere solid. The results are very good in both cases, showing that this density-functional model may be used with advantage in the study of the hard-sphere model by itself, or used as a reference system in a perturbative analysis.

ARMA Representation of Random Processes

Abstract: Auto-regressive moving-average (ARMA) models of the same order for AR and MA components are used for the characterization and simulation of stationary Gaussian multivariate random processes with zero mean. The coefficient matrices of the ARMA models are determined so that the simulated process will have the prescribed correlation function matrix. To accomplish this, the two-stage least squares method is used. The ARMA representation thus established permits one, in principle, to generate sample functions of infinite length and with such a speed and computational mode that even real time generations of the sample functions can be easily achieved. The numerical example indicates that the sample functions generated by the method presented herein reproduce the prescribed correlation function matrix extremely well despite the fact that these sample functions are all very long. This is seen from the closeness between the analytically prescribed auto- and cross-correlation functions and the corresponding sample correlations computed from the generated sample functions.

Some aspects of light scattering from a randomly rough metal surface

Abstract: Two problems involving the interaction of a volume electromagnetic wave with a randomly rough metal surface are studied. In the first part a recently constructed theory of the resonant nonspecular scattering of light from a randomly rough metal surface is fitted to experimental data in a way that permits the extraction of the two-dimensional Fourier transform g(k∥) of the two-point correlation function of the surface profile function from the experimental results. It is found that the resulting correlation function can have its first maximum away from k∥ = 0 and decays to zero with increasing k∥ in a nonmonotonic fashion. This form for g(k∥) has been obtained in recent, independent, experimental determinations of this function. In the second part the scattering of p-polarized light from a randomly rough grating is studied in a case in which the plane of incidence is normal to the grooves of the grating. A diagrammatic method that self-consistently takes into account the diagrams responsible for localization phenomena in other contexts is used in this analysis. It is shown that the contribution from these diagrams gives rise to an enhanced scattered intensity in the antispecular direction. As a by-product of this calculation, the localization of surface polaritons by surface roughness is demonstrated and their localization length is determined.

Hydrodynamic theory of the glass transition.

Abstract: Les equations de l'hydrodynamique pour un fluide compressible simple, en incluant non-linearites et fluctuations thermiques, indiquent une transformation par un etat vitreux pour des densites suffisamment hauts et des temperatures suffisamment basses. Comportement des viscosites, vitesses du son et fonctions de correlation au voisinage de la transformation

Correlation functions in the capillary wave model of the liquid–vapor interface

Abstract: We study the capillary wave model of the liquid–vapor interface and derive expressions valid in arbitrary dimensions for the density profile and the density–density pair correlation function. The latter is inverted to give an explicit expression for the direct correlation function. We examine the effects of long wavelength density fluctuations on these functions in dimensions d<3 and discuss the applicability of the model to a real liquid–vapor system.

Dynamics of wormlike chains

Abstract: Dynamique de polymere sans ecoulement, en solution diluee, a l'aide du modele de Kratky Porod

Correlation functions for the Heisenberg XXZ-antiferromagnet

Abstract: The general method for calculation of correlation functions in integrable quantum models has been given in papers [1, 2]. The correlation function of the third components of local spins for the Heisenberg one-dimensionalXXZ-antiferromagnet is calculated in this paper. The answer is a series which gives, in particular, an improved version of the usual perturbative expansion in the anisotropy parameter. The remarkable property of the series obtained is that the long-distance asymptotics of the correlator is given already by the first term. The arguments are given in favour of the convergence of the series.

Low-frequency current noise with a 1/ f spectrum in solids

Abstract: The problem of low-frequency current noise with a 1/f spectrum in solids (flicker noise) is reviewed. The fundamental general properties of this noise are described: frequency-dependence of the spectral density, time-dependence of the correlation function, form of the distribution function of the fluctuations, dependence of the spectral density on the potential applied to the specimen, anisotropy of the fluctuations of the resistivity tensor, correlation length of the fluctuations, dependence of the noise on the dimensions of the specimen and on the concentration of current carriers, the empirical Hooge relationship, etc. A model of 1/f noise is presented and discussed that associates its spectrum with the presence in solids of an extensive hierarchy of relaxation times. Concrete models of systems having an exponentially broad spectrum of relaxation times are described (the McWhorter model, two-level tunneling systems, the disordered Ising kinetic model). The theory and experimental data on current noise caused by temperature fluctuations are analyzed. The problem is treated of surface noise in semiconductors and 1/f noise in metal films.

Generalized moment expansion for Brownian relaxation processes

Abstract: The generalized moment expansion has previously only been used to provide an effective algorithm for the approximation of the time dependence of observables connected with reactive Brownian processes. We extend this algorithm to describe the relaxation of observables in nonreactive processes. The wide applicability of the method is demonstrated for various examples: equilibrium correlation functions like autocorrelation functions and dynamic structure factors, particle number correlation functions monitoring diffusive redistribution, and barrier crossing problems.

A molecular dynamics study of liquid chloroform

Abstract: Molecular Dynamics simulations of liquid chloroform with 200 molecules in the basic cube have been performed at 295 and 325 K. The interactions were described by a rigid five-site model with (12/6) Lennard-Jones spheres and partial charges at the atom positions. At room temperature four simulation runs have been carried out. Three of them differ in the method with which the Coulomb forces have been truncated at the cut off distance. For the fourth one the charges have been removed in order to study their influence on the MD results. The intermolecular structure functions have been calculated from the simulation and are found in good agreement with results from an x-ray measurement and with four out of five structure functions from neutron diffraction studies with isotopic substitution. Strong disagreement between simulation and experiment exists, however, for the six atom-atom radial distribution functions. The origin of this discrepancy is traced back to the difference in one of the five neutron structure functions (CH37Cl3); because of the consistency of the simulation results with each other and with the other experimental data, it can be attributed to uncertainties of the neutron scattering experiment. It is also shown that the expansion of the molecular pair correlation function in terms of spherical harmonics does not converge rapidly enough for the calculation of the first five so called g-coefficients with a sufficient degree of reliability from five neutron diffraction measurements. The self-diffusion coefficients have been calculated for 295 and 324 K, respectively, and found in good agreement with experimental results. Rotational diffusion coefficients, the spectral densities of hindered translations and of the librations are reported. Various reorientational correlation functions have been calculated, which reproduce satisfactorily the corresponding experimental results. The MD calculations show clearly that the description of the dielectric relaxation needs a multi-particle correlation function, whereas the far infrared absorption is due to single-particle motion.

Diffusive and jump description of hindered motions

Abstract: Site jump models are often used to interpret spectroscopic effects of molecular motions occurring in the presence of potential wells. Continuous diffusion equations, albeit complex to handle, are expected to give a more detailed picture of the dynamics and to provide molecular interpretation of the kinetic parameters. In the paper we show how the results of random walk models can be recovered from the correct solutions of the diffusion equations. To this purpose, two routes are followed. First, a procedure is developed for the exact calculation of the time integral of pertinent correlation functions, to be compared with the time constant for the kinetic process of interest. Secondly, the asymptotic solutions of the diffusion equations, valid in the limit of high potential gradients, are used to derive ‘localized functions’, which lead quite naturally to master equations for jumps among discrete sites. Rotational diffusion in uniaxial liquid crystals, translational motions across smectic layers, hindered i...

Effects of entanglements on the single-chain motion of polymer molecules in melt samples observed by neutron scattering

Abstract: The motion of single molecules of polytetrahydrofuran in melt samples of deuterated polytetrahydrofuran has been observed using high-resolution quasi-elastic neutron scattering (the neutron spin-echo technique). Comparison of results for two systems in which the matrix of deuterated molecules surrounding the observed molecules is either well above or well below the entanglement molecular weight shows clearly the effects of molecular entanglements on the observed correlation functions. The form of these correlation functions agrees with the theoretically predicted behaviour for entangled systems and allows a value for the average distance between entanglements of 30 A to be extracted.

Correlation functions and correlation times for models with multiplicative white noise

Abstract: Correlation functions and correlation times for the Stratonovich and Verhulst model are investigated. By transforming the Fourier transform of the corresponding Fokker-Planck equation into a tridiagonal vector recurrence relation, the Fourier transform of the correlation function and the correlation time are expressed in terms of matrix continued fractions or by similar iterations and are thus obtained numerically. By using the inverse Fourier transform, the correlation function itself is calculated. Furthermore an analytic expression in terms of an integral is obtained for the correlation time, which is evaluated exactly in the Verhulst model and asymptotically for large and weak noise strength in the Stratonovich model. A Pade expansion approximating the correlation time for all noise strength is also given.

Kinetic Ising model for polymer dynamics. II. Generalized transition rates and the Williams–Watts nonexponential function

Abstract: We continue our study [J. Chem. Phys. 79, 1955 (1983)] of the one‐ dimensional kinetic Ising model to investigate cooperative dynamics in amorphous polymers. In this paper we consider the most general single spin‐flip model. The spin–spin correlation function is calculated approximately using continued fractions. We find that the Williams–Watts empirical function φ(t)=exp[−(t/τ)β] with 1/2≤β≤1 provides a good fit to this correlation function. The results are interpreted in terms of the dynamics of domain wall defects in which the two fundamental processes are defect migration and defect creation and annihilation. This suggests possible microscopic mechanisms for relaxation in solid amorphous polymers.

Canonical Stochastic Quantization

Abstract: On propose une quantification stochastique canonique en introduisant l'equation de Langevin d'impulsion π(x,t). On obtient la methode de moyenne de Gibbs comme une consequence de cette quantification stochastique canonique

Exact one‐dimensional pair correlation functions of a monolayer/substrate system

Abstract: We have derived an exact expression for the one‐dimensional atomic pair correlation function of the combined overlayer and substrate system in the very first stages of epitaxy. The overlayer can have an arbitrary island size distribution. This pair correlation function is then used to evaluate the widths and shapes of low‐energy (or high‐energy) electron diffraction intensity profiles. Several model calculations have been computed and the diffraction profiles resemble the recent molecular beam epitaxy measurements of Si/Si(111) and W/W(110) systems reported by Henzler and co‐workers.

Motion in a double-well potential with additive colored Gaussian noise

Abstract: The overdamped motion of particles in the double-well potential−ax2/2+bx4/4 with additive exponentially correlated noise is investigated. By solving an appropriate two-variable Fokker-Planck equation in terms of matrix continued fractions, stationary distribution functions in one and two variables as well as eigenvalues and correlation functions are obtained.

Energy-density correlation functions in the two-dimensional Ising model with a line defect.

Abstract: On considere le modele d'Ising a 2 dimensions sur un reseau rectangulaire avec une ligne de forces de couplage horizontales changee