Showing papers on "Correlation function (statistical mechanics) published in 1976"

The structure of the liquid–vapor interface

Abstract: A formal derivation is presented for the equilibrium relation between the singlet density in a fluid and the direct correlation function and for the equivalent relation involving the pair number density. It is shown that this relation is equivalent to the macroscopic condition for hydrostatic equilibrium when the singlet density varies sufficiently slowly to permit the introduction of local thermodynamics. Some aspects of the usage of this in the determination of the singlet density in the liquid–vapor transition region are discussed.

Proposal for the measurement of the resonant Stark effect by photon correlation techniques

Abstract: The second-order correlation function for light scattered at resonance from a two-level atom is calculated The measurement of intensity correlations employing either homodyne or heterodyne techniques provides a novel approach for the extraction of linewidth and splitting frequencies

Correlation of turbulent trailing vortex decay data

Abstract: A correlation function, derived on the basis of self similar variable eddy viscosity decay, is introduced and utilized to correlate aircraft trailing vortex velocity data from ground and flight experiments. The correlation function collapses maximum tangential velocity data from scale model and flight tests to a single curve. The resulting curve clearly shows both the inviscid plateau and the downstream decay regions. A comparison between experimental data and numerical solution shows closer agreement with the variable eddy viscosity solution than the constant viscosity analytical solution.

Real-time measurement of surface roughness by correlation of speckle patterns

Abstract: In a previous article we have shown that the two speckle patterns produced from the same rough surface illuminated by two coherent plane waves under two different angles of incidence are correlated. The correlation depends on the surface roughness. In this paper a method is described where the rough surface is illuminated simultaneously by the two plane waves. The ensemble-averaged coherence function, that is, the correlation function, of the scattered field is measured by using a two-waves interferometer. This affords a real-time measurement of the surface roughness in the range of large roughness (σ > λ). The theoretical calculations have been performed for a normally distributed surface. The experimental results are in good agreement with theory. We describe the optical arrangement of an instrument based on this principle.

Solution of Ornstein-Zernike equation for wall-particle distribution function

Abstract: The Ornstein-Zernike (OZ) equation is considered for the wall-particle distribution functiong0(x) in the case of a flat, impenetrable wall atx = 0 and a fluid of hard-core particles whose centers are constrained by the wall to occupy the semiinfinite spacex >σ/2, whereσ is the particle diameter. A solution is given in terms of the wall-particle direct correlation function c0(x) forx >σ/2, the bulk-fluid direct correlation function cB(t), and pB, the average bulk density. Explicit formulas for the contact surface density, total excess surface density, and the Laplace transform of the fluid density near the wall are given. For mean spherical type approximations, c0(x) forx >σ/2 and cB(t) are both prescribed functions; for this case, a closed-form solution is obtained. An example is discussed and additional equations that enable one to go beyond the approximations considered above are introduced.

Generalized mean spherical approximation for hard spheres

Abstract: The mean spherical approximation for molecules with a hard core has been solved [1], for the case where the direct correlation function is, outside the core, of the form of a Yukawa function. Despite recent simplifications, this solution is implicit and rather complex and, as a result, there are few numerical results. If the parameters, K and z, of this Yukawa tail are adjusted to give the known pressure and compressibility of a fluid of hard spheres, this solution can be used to obtain a generalized mean spherical approximation (GMSA) for the direct correlation function and the radial distribution function (RDF) of the hard-sphere fluid. Numerical results for K, z, and the RDF of the hard-sphere fluid are obtained. The GMSA RDF is found to be in excellent agreement with the simulation values. In addition, it is observed that for this system at high densities (the region of greatest interest) z is large and K is small. This fact is used to obtain a simple and explicit approximation to the full solution. T...

A molecular theory of interfacial phenomena in multicomponent systems

Abstract: The van der Waals theory of surface tensions is generalized to multicomponent systems. The local free energy density consists of a ’’local equilibrium’’ free energy (i.e., equilibrium free energy of a uniform mixture having species densities equal to the local species densities) plus a quadratic form in the gradients of the species densities. The coefficients in this quadratic form depend on the local species densities through the density dependence of the second moment of the local multicomponent direct correlation function. The requirement that the free energy be a minimum yields a system of partial differential equations (one for each component). A particular linear combination of the differential equations is the condition for mechanical equilibrium. It can be interpreted as a microscopic statement of the multicomponent Young–Laplace equation for the pressure variation across a curved interface. For two component systems the theory is a generalization of the treatment of Cahn and Hilliard in that it allows for pressure variations. If the local pressure fluctuations are suppressed, the differential equation for the concentration is very similar to theirs, except that the total density may vary across the interface. Similarly, when the theory is applied to liquid–vapor equilibrium in a binary system, the differential equation for the total number density reduces to that of a single component system when the local chemical potential difference (μ=μ1−μ2) is held constant.

The spin correlation functions of a semi-infinite Heisenberg ferromagnet

Abstract: Results are derived for the dynamic correlation functions between a pair of spin operators at any two sites within a semi-infinite Heisenberg ferromagnet at low temperatures, T<

Spatial coherence of light scattered by media with large correlation length of refractive index fluctuations

Abstract: The effect of a large spatial correlation in a scattering medium on the spatial coherence of the scattered field is presented. Theoretical curves are calculated for a specific form of the correlation function of the dielectric susceptibility. It is shown that when the spot size of the incoming coherent light is of the same order as the correlation length of fluctuations a sudden increase in the spatial coherence of the scattered light occurs. The method is applied to the study of the correlation length in a liquid crystal cell under a dc electric field.

Diffusion in crystals with traps: A simple phenomenological model

Abstract: We present a phenomenological model describing the trapping and release of mobile defects at random inhomogeneities. The traps are characterized by two parameters, the capture radiusRt, describing the range of the interaction and the binding energyEb describing the escape. We give an integral representation of the correlation function of the mobile particles in the presence of traps. For large distances the correlation function can be described by a simple diffusional process with an effective diffusion constant. Finally we discuss the neutron scattering by mobile defects resulting from this trapping model.

Pair correlation function of dense electrolyte system: Restricted primitive model

Abstract: The solution of the Ornstein–Zernike equation with core condition, and direct correlation function of Yukawa form is analyzed to give analytic expressions of pair correlation functions for dense electrolyte system. A method for seimempirical determination of Yukawa parameters is proposed. Agreement of the correlation functions with Monte Carlo calculations is good.

Higher-order correlation functions of the planar Ising model II

Abstract: A method of calculating the asymptotic behaviour of the higher-order correlation functions for large distances is proposed for the planar Ising model in the absence of a magnetic field. The three-point correlation functions composed of a spin operator or of energy-density operators are considered. The asymptotic behaviour of the correlation functions for distances R ⪢ R c (where R c is the correlation radius) is determined. It is shown that the asymptotic behaviour of the correlation functions for large distances does not depend on the choice of operators. The asymptotic behaviour of the correlation functions in which two operators are relatively close to one another is considered near the critical point. The results which we obtained are compared with the predictions of the scaling laws and operator algebra.

Analysis of noises in photocurrent time‐correlation spectroscopy of scattered light

Abstract: A covariance function, VN (τ,σ), is introduced for the analysis of noises in photocurrent time‐correlation spectroscopy of scattered light. Its explicit forms under various measuring conditions are given and the characteristics and magnitudes of the noises are investigated. The distortion of a correlation function caused by the truncation of both upper and lower frequency ranges is examined. The reason for the absence of the so‐called aliasing error in a Gaussian‐photocurrent correlation measurement is given.

Spin correlations in a spin-polarized electron liquid

Abstract: The longitudinal charge-magnetization response functions of an electron liquid in a spin-polarized state are analysed by an equation of motion approach making explicit connection with the Mori memory function theory of the dynamic behaviour of a many-body system. Thermodynamic relations are derived for the response, which are appropriate extensions of known sum rules for the paramagnetic state, and a self-consistent scheme for the evaluation of spin correlations is indicated. Contact with the transport properties is also established, and in particular the inverse spin diffusion coefficient is related to the up-down correlation function in a state of magnetization drift. An explicit evaluation of the latter for the paramagnetic state at smallr s expression the Landau up-down transition probability through a Fermi-sphere integral involving the static dielectric function.

Second-Order Statistical Moments of a Surface Scatter Channel with Multiple Wave Direction and Dispersion

Abstract: Underwater acoustic communications channels involving surface reflection usually exhibit extensive time and frequency spreading. The phenomenon was studied in a recent paper [5] and the scattering function of the channel was obtained for large Rayleigh parameters using a Fresnel-corrected geometric optics model and a simple onedimensional surface correlation function. It was found that while extensive time spreading and Doppler were indeed predicted by this model, the Doppler shift and time delay were strongly correlated so that the scattering function had the form of a very narrow parabolic ridge. The problem considered in this paper is the extent to which this phenomenon persists when more realistic correlation-function models, dispersion, and small Rayleigh parameters are considered. It is found that the general form of the scattering function is not very much affected by fairly gross changes in the assumed surface statistics, and that substantial correlation between time delay and Doppler can be expected as long as the surface is not completely isotropic. The effect is also observed in a modified form with a small Rayleigh-parameter model, but since this model also features a strong coherent component it may be of less practical significance.

Time Correlation Function in the One-Dimensional Heisenberg System at High Temperatures

Abstract: :Vfoment:-; in the two-time spin-pair correlation function are evaluated up to 16-th order for the one-dimensional Heisenberg system with S=l/:2 at infinite temperature. The method of evaluatiOn, with a u:-;eful recurrence formula is reporter!. The current methods of treating the correlation function together with a newly proposed one are examined for both the :-;patially-Fourier-transformed correlation function and the auto-correlation function.

Functional approach to nonlinear stochastic processes. Application to a single-mode laser

Abstract: We introduce a generalized version of the Volterra-Wiener functional expansion is introduced. Its fruitfulness in the treatment of nonlinear stochastic processes is shown. As an application in a simple way the statistical properties of the single-mode laser radiation both in the steady state and in the transient regime are derived. Besides deriving already known results with good accuracy, the transient correlation function for the photon number is given for the first time. (AIP)

Predicted Critical Correlation Function for Three-Dimensional Phase Transitions

Abstract: A new approximant is proposed for the critical correlation function $g(y)$ of $y=k\ensuremath{\xi}$, where $\ensuremath{\xi}$ is the correlation length and $k$ the wave number of an order-parameter fluctuation. The approach involves truncating the spectral function associated with the three-term Fisher-Langer approximant in a manner suggested by the requirement of a three-particle threshold. The resulting $g(y)$ is accurate to better than 0.03% everywhere for the two-dimensional Ising model. Results for the three-dimensional case are consistent with $\ensuremath{\epsilon}$-expansion and high-temperature series results.

Transverse current correlations in simple liquids

Abstract: An approximate expression for the memory function associated with transverse current correlations have been evaluated for models both of liquid rubidium and liquid argon. Results for the frequency spectrum of the current correlation function are also presented for a range of wavenumbers and compared, where possible, with those obtained from computer simulation studies. From the memory function an expression for the shear viscosity coefficient may be derived, but the values obtained for the latter near the melting points of the liquids are of the order of 40% smaller than the experimentally determined values.