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Showing papers on "Correlation function (statistical mechanics) published in 1970"


Journal ArticleDOI
TL;DR: In this article, the dielectric correlation function in glasses is calculated and the assumption of short correlation length for normal modes breaks the momentum selection rules and leads to expressions for the first-order Raman-scattering intensity in terms of the density-of-state functions and known frequency-dependent amplitudes.
Abstract: We present a calculation of the dielectric correlation function in glasses showing how the assumption of short correlation length for normal modes breaks the momentum selection rules and leads to expressions for the first-order Raman-scattering intensity in terms of the density-of-states functions and known frequency-dependent amplitudes

971 citations


Journal ArticleDOI
TL;DR: In this article, the asymptotic time behavior of the velocity autocorrelation function and of the kinetic parts of the correlation functions for the shear viscosity and the heat conductivity is derived.
Abstract: The asymptotic time behavior of the velocity autocorrelation function and of the kinetic parts of the correlation functions for the shear viscosity and the heat conductivity is derived. The results are expressed in terms of the transport coefficients and the specific heats and are valid for all densities.

296 citations



Journal ArticleDOI
TL;DR: In this article, the memory functions for the velocity, angular-momentum, and dipolar autocorrelation functions from a series of molecular-dynamics studies of liquid carbon monoxide are examined.
Abstract: The memory functions for the velocity, angular-momentum, and dipolar autocorrelation functions from a series of molecular-dynamics studies of liquid carbon monoxide are examined. The velocity and angular-momentum memory functions decay initially almost to zero in a Gaussian fashion. However, their long-time behavior has a much slower time dependence. The dipolar memory function from a simulation using a strong noncentral potential is approximately this system's angular-momentum autocorrelation function. Approximate velocity and angular-momentum correlation functions are generated from approximate memory functions and the results are compared to experiment. Gaussian memories based on the second and fourth moments of the corresponding autocorrelation functions give the best agreement with experiment. However, none of the approximate memories examined adequately represents the long-time behavior of the experimental memories. The static atomic radial distribution functions are given and are shown to depend upon the strength of the orientational parts of the pair potential used in the dynamics calculations. The non-Gaussian characteristics of the Van Hove self-correlation functions are examined and shown to depend on the potential and number of particles used in the dynamics calculations. The intermediate scattering function and its memory are also examined.

130 citations


Journal ArticleDOI
TL;DR: In this article, an integral equation for the pair correlation function, coupling the individual ion range with the deposited energy, was established to determine the damage caused by all those ions that come to rest at a specific penetration depth.
Abstract: Simple depth distribution functions of ion bombardment damage predict the spatial extension of the cumulative damage caused by a beam of ions. Correlation functions need to be considered when more detailed information is desirable, such as the average size or depth of individual damage clusters, the average location of an ion within its damage cluster, and the fluctuations of these quantities. In this paper we establish an integral equation for the pair correlation function, coupling the individual ion range with the deposited energy. This pair correlation function determines the damage caused by all those ions that come to rest at a specific penetration depth. Solutions of the integral equation are found by standard methods. Explicit results are presented for elastic scattering governed by power cross sections. The depth distribution of damage clusters turns out to be significantly narrower than the gross damage distribution at all mass ratios except for M 1 ≪ M 2, and the size distribution appe...

57 citations


Journal ArticleDOI
TL;DR: The static properties of the dielectric response function for an electron liquid, obtained previously by one of the authors, is investigated in this article, where it is shown that the resulting pair correlation function has the correct long-range and short-range behaviors so that the correlation energy calculated therefrom reproduces the known exact values to the order of e2, when an expansion with respect to the plasma parameter E is carried out.
Abstract: The static properties of the dielectric response function for an electron liquid, obtained previously by one of the authors, is investigated. It is shown that the resulting pair corre­ lation function has the correct long-range and short-range behaviors so that the correlation energy calculated therefrom reproduces the known exact values to the order of e2, when an expansion with respect to the plasma parameter E is carried out. The compressibility sum rule is satisfied to the order of e2 ln E. It is found that within the accuracy stated above the short-range behavior of the pair correlation function is not ,sensitive to the form of the ternary correlation function.

42 citations


Journal ArticleDOI
TL;DR: In this paper, the scattering of light by a two-dimensional spherulite of radius R is calculated when there is disorder of optic axis orientation with respect to the radius.
Abstract: The scattering of light by a two-dimensional spherulite of radius R is calculated when there is disorder of optic axis orientation with respect to the radius. Special cases are considered when (1) the disorder occurs in the radial direction only, (2) the disorder occurs in the angular direction only, (3) there is combined radial and angular disorder, and (4) the optic axis makes a constant angle with the radius but there is disorder in the twist angle about the axis. In all of these calculations, a correlation function for disorder is defined and the scattering pattern depends on the ratio of the associated correlation distance to the size of the spherulite. With decreasing correlation distance, the azimuthal dependence of the scattering becomes less and there is a change in the variation of scattered intensity with scattering angles in a manner dependent upon the type of disorder.

41 citations


Journal ArticleDOI
01 Oct 1970
TL;DR: In this paper, measurements of the Raman effect on single crystal ferromagnetic CdCr2Se4 and CcCr2S4 as a function of temperature were reported.
Abstract: Measurements are reported of the Raman effect on single crystal ferromagnetic CdCr2Se4 and CdCr2S4 as a function of temperature. The lines observed at 158 cm−1, 172 cm−1 and 241 cm−1 for CdCr2Se4 and 257 cm−1, 281 cm−1 and 396 cm−1 for CdCr2S4 have been identified as due toГ12+,Г25+ andГ1+ phonons, respectively. Certain lines ofГ1+ orГ25+ symmetry, observed in both materials, show a temperature dependence of the intensity which resembles the behaviour of the spin correlation function. Some of these lines also exhibit a symmetry change at the Curie point. A group theoretical analysis of the eigenvectors of the Raman active modes is given. The results are interpreted in terms of a model proposed by Baltensperger which involves the ion position dependence of the magnetic exchange interaction in order to couple spin system and phonons. The weak frequency shift of the lines, which occurs predominantly in the ordered state, is interpreted in terms of the same model.

41 citations


Journal ArticleDOI
TL;DR: In this paper, a theory of dielectric relaxation is presented which is based on using an interpolation function to represent a classical correlation function which is analytic at the origin and becomes exponential at sufficiently long times.
Abstract: A theory of dielectric relaxation is presented which is based on using an interpolation function to represent a classical correlation function which is analytic at the origin and becomes exponential at sufficiently long times. The Fourier transform of this interpolation function is a relatively simple analytical function of frequency which has the Debye character at low frequencies but decreases essentially exponentially in the high‐frequency wing. The parameters in the correlation function are discussed in terms of relaxation due to reorientational diffusion. Our model predicts practically the same absorption in the microwave region and somewhat more absorption in the far‐infrared region as theories of dielectric relaxation which include the effect of rotational inertia, but in agreement with experiment predicts very much smaller absorption in the infrared region.

32 citations


Journal ArticleDOI
TL;DR: In this paper, the proton and fluorine spin relaxation time T1 has been measured in CH4, CF4, CHF3, and CH3F gases at low densities.
Abstract: The proton and fluorine spin relaxation time T1 has been measured in CH4, CF4, CHF3, and CH3F gases at low densities. By measuring the dependence of T1 on density near the characteristic T1 minimum, new information has been obtained on the spin–rotation interaction coupling constants in CF4, CHF3, and CH3F. The CH4 system was used to test the validity of this method since the spin–rotation coupling constants are accurately known for CH4. The correlation function for the spin–rotation interaction was found to be exponential within experimental error for all of the molecules studied. In the analysis of the experimental data, the effects of the dipolar interactions and of nuclear spin symmetry considerations were completely neglected. The validity of these approximations is discussed in the Appendix.

30 citations


Journal ArticleDOI
TL;DR: For an axially symmetric overall diffusion with internal rotation about one and two axes correlation functions of a second rank spherical tensor are calculated in this paper, where the results comprise all the solutions of the pertinent problem as given so far and allow the extension of the theory to a wider field of application.
Abstract: By use of Green's functions for the diffusional motion a very concise formulation and computation of correlation functions is possible. For an axially symmetric overall diffusion with internal rotation about one and two axes correlation functions of a second rank spherical tensor are calculated. The results comprise all the solutions of the pertinent problem as given so far and allow the extension of the theory to a wider field of application


Journal ArticleDOI
TL;DR: In this paper, the absorption rates of bound 1s and 2p pions in some light nuclei have been investigated on the basis of a shell model picture modified by short range nucleonnucleon correlations.
Abstract: The absorption rates of bound 1s and 2p pions in some light nuclei have been investigated on the basis of a shell model picture modified by short range nucleonnucleon correlations. It turns out that the total absorption rate, the missing energy spectra and the single neutron energy spectra depend sensitively on the details of the correlation functions. The results of the present analysis indicate that one can obtain informations on the short range correlations from pion absorption experiments.

Journal ArticleDOI
TL;DR: In this article, the effect of pair correlations can rigorously be taken into account in both the equilibrium and nonequilibrium theory, and the system of a fully ionized gas combined to a half-space by a perfectly reflecting boundary is discussed.
Abstract: The system of a fully ionized gas combined to a half‐space by a perfectly reflecting boundary is discussed. It is shown how the effect of pair correlations can rigorously be taken into account in both the equilibrium and nonequilibrium theory.

Journal ArticleDOI
TL;DR: In this paper, the frequency dependence of these transport functions becomes significant at high frequencies, i.e., when approaches cc-1, where c is the collision time, and should be essentially responsible for the departure from classical hydrodynamics.
Abstract: The general expression for the transport coefficients at finite frequency is given by the spectral function of the autocorrelation of the flux corresponding to the transport phenomenon considered. Because the explicit analytical solution of such a correlation function involves the whole many-body problem for strongly coupled systems, appeal must be made to a model in order to derive the explicit frequency dependence of the transport functions. In the first part of this paper, we calculate these functions analytically [i.e., the diffusion D(), the viscosities S() and B(), and the thermal conductivity ()] from the generalized Berne-Boon-Rice model. The frequency dependence of these transport functions becomes significant at high frequencies, i.e., when approaches cc-1, where c is the collision time, and should be essentially responsible for the departure from classical hydrodynamics. This is shown in Sec. II of this paper, where we present a calculation of the spectral distribution of the light scattered from thermal fluctuations in simple fluids. When the transport functions are introduced in the hydrodynamic equations to replace the usual constant transport coefficients, the spectrum of the scattered light is modified significantly, to second order in k2, where is essentially a linear function of the transport functions. The second-order spectrum obtained here is in agreement with previous results, but it is shown that the main effect arises from the frequency dependence of the transport functions, which was ignored in previous work. These effects induce a small but significant negative dispersion in the first-sound velocity. This prediction is in qualitative agreement with the recent light scattering experiments by Fleury and Boon on liquid argon, which were initially interpreted as a possible experimental observation of the frequency dependence of the transport functions in simple liquids. © 1970 The American Physical Society.

Journal ArticleDOI
TL;DR: In this article, two techniques for obtaining information about the intensity correlation function of an optical field, from measurements of photoelectric counting distributions, are described, based on double differentiation of the second factorial moment with respect to the counting time.
Abstract: Two techniques are described for obtaining information about the intensity correlation function of an optical field, from measurements of photoelectric counting distributions. The first method is based on double differentiation of the second factorial moment with respect to the counting time. It requires very accurate data, but is shown to be quite feasible, and yields the intensity-correlation function explicitly. The second procedure is less sensitive to inaccuracies and allows the correlation time and certain other parameters to be determined from the factorial moments. In addition, it yields some information about the general form of the correlation function, but no explicit function. The procedures are illustrated and compared by application to photoelectric counting measurements of a laser far below the threshold of oscillation.

Journal ArticleDOI
TL;DR: In this article, the statistical distribution of the number of photoelectrons emitted in a short time interval from a phototube illuminated by laser light scattered from a fluid is examined.
Abstract: The statistical distribution of the number of photoelectrons emitted in a short time interval from a phototube illuminated by laser light scattered from a fluid is examined. Moments of this distribution measure correlated scattering of photons and are related to density correlations of various orders in the fluid. It is pointed out that a measurement of the second moment will indicate whether corrections are needed to the usual interpretation of the scattered-light spectrum. Deviations of the higher moments from the value for uncorrelated scattering would allow measurement of the spatial dependence of multiparticle correlations. The strength of the correlated scattering contribution to the various moments is estimated near a critical point, where it is expected to be largest, using a scaling-law equation of state and available data for simple fluids. According to this estimate, measurement of these multi-particle correlations will be very difficult in a simple fluid. It is pointed out that it may be easier near the critical mixing point of a binary fluid.

Journal ArticleDOI
TL;DR: In this article, the fonction de correlation de Van Hove est calculee d'habitude sur la base d'arguments macroscopiques, and a justification rigoureuse a ces results is presented.

Journal ArticleDOI
TL;DR: In this paper, it was demonstrated that a small number of individual screens moving with different velocities may explain many of the observed asymmetric cross-correlation functions when the spaced receiver method of drift measurements is applied to reflections from the D- and E-regions.

Journal ArticleDOI
TL;DR: In this paper, photometric and photometric light scattering patterns from the cholesteryl esters are analyzed in terms of theories previously developed for the scattering from crystalline polymers.
Abstract: : Photographic and photometric light scattering patterns from the cholesteryl esters are analyzed in terms of theories previously developed for the scattering from crystalline polymers. The scattering is shown to primarily result from correlations in orientation of anisotropic elements. The solid state may exist in a negatively birefringent spherulitic form with a size dependent upon crystallization temperature, or may occur in the form of randomly correlated aggregates of crystals best characterized by a correlation function. Such random correlation persists through the smectic state. In the cholesteric state, there is a transition to disc-like non-random correlation with a correlation distance and non-randomness parameters dependent upon the ester, temperature, and thermal history. (Author)

Journal ArticleDOI
TL;DR: The connection between the correlation coefficients previously discussed by Kutzelnigg, del Re and Berthier and the correlation factors introduced by McWeeny is determined in this paper, where it is shown that for atoms S-staes the angular correlation coefficientτ is completely determined by the ι = 0 and 1 contributions of the expansion of the pair denstity π(Γ1.π2) in Legendre polynomials.

Journal ArticleDOI
TL;DR: In this paper, the shape of the correlation curves close to the resonance frequencies is shown to be a Lorentz curve and the equation describing their structure is obtained by summation of the perturbation theory series.
Abstract: Equations are derived for the correlation functions of a weakly turbulent plasma (both for decay and non-decay spectra). It is shown that the shape of the correlation curves close to the resonance frequencies is that of a Lorentz curve and the equation describing their structure is obtained by summation of the perturbation theory series. Estimates are given of the width of the correlation function of Langmuir pulsations.

Journal ArticleDOI
TL;DR: In this article, a two-dimensional surface displacement correlation function has been measured for low-divergence wind-blown waves in a laboratory tank and the measured phase and group velocities of the correlation function agreed with theoretical values for the peak frequency water-wave component when the measurements were transformed to coordinates that had the velocity of the surface (drift) current.
Abstract: A wind-blown water surface can be characterized in terms of a traveling correlation function in which the group and phase velocities are given by the values at the frequency of maximum spectral energy density. The two-dimensional (space and time) surface displacement correlation function has been measured for low-divergence wind-blown waves in a laboratory tank. The measured phase and group velocities of the correlation function agreed with theoretical values for the peak frequency water-wave component when the measurements were transformed to coordinates that had the velocity of the surface (drift) current. This description, which may be useful in the ocean as well, has recently been used to predict the temporal correlation of sound scattered from a model sea of known three-dimensional surface correlation function (Clay and Medwin, 1970).

Journal ArticleDOI
TL;DR: In this paper, a theory has been developed which relates the intensity of the non-specular scattering of X-rays from thin films to the correlation function for the local deviation of the dielectric constant of the film from its average value.
Abstract: A theory has been developed which relates the intensity of the non-specular scattering of X-rays from thin films to the correlation function for the local deviation of the dielectric constant of the film from its average value. The theory predicts the positions and intensities of the maxima and minima in the distribution of the non-specularly scattered radiation as well as the existence of the non-specular `anomalous surface reflection' first reported by Yoneda. The results of an experimental study with thin copper films were in good agreement with the theory.

Journal ArticleDOI
TL;DR: In this paper, a theory for examining the influence of spin-phonon interaction on the phonon dynamics in anharmonic crystals is developed for analyzing the role of the direct interaction between lattice vibrations with that of the indirect interaction via spins in the propagation and attenuation of sound as well as in the behaviour of thermodynamic quantities.
Abstract: In this paper, a theory is developed for examining the influence of the spin-phonon interaction on the phonon dynamics in anharmonic crystals. In contrast to a harmonic approximation such an approach allows for comparing the role of the direct interaction between lattice vibrations with that of the indirect interaction via spins in the propagation and attenuation of sound as well as in the behaviour of thermodynamic quantities. Explicit expressions are derived for the phonon self-energy using successively higher approximations obtained from a cumulant expansion of the density of interparticle distances. It is shown that even in the harmonic approximation the two-spin correlation function and the four-spin correlation function enter into the expression of the generalized dynamical matrix in deviation from previous results. The modification of this harmonic dynamical matrix due to the renormalization of the harmonic phonons and due to phonon-phonon scattering processes is given employing a “weak coupling” approximation between the localized spins and the interparticle-distance density of the crystal. The resemblance of the present approach to an earlier microscopic treatment of electronic contributions to phonon dynamics in anharmonic crystals is pointed out.

Journal ArticleDOI
Kensuke Tani1
TL;DR: In this article, the theory of neutron scattering from lattice vibrations is redeveloped from the first principles and the expression for the scattering cross section contains factors depending on the anharmonicity explicitly, in addition to the conventional results and recent results based on the phonon Green function.
Abstract: The theory of neutron scattering from lattice vibrations is redeveloped from the first principles. The expression for the scattering cross section contains factors depending on the anharmonicity explicitly, in addition to the conventional results and recent results based on the phonon Green function. Near the Curie temperature T c of displacive-type ferroelectrics a certain term in the factors depends anomalously on temperature because of softening of frequencies and becomes comparable to or even greater than the conventional term. A similar deviation near the magnetic critical point in discussed briefly. A general theory of phonons at arbitrary temperature is also developed using the correlation function method which includes the ordinary phonon theory as the limiting case of the absolute zero, and the dispersion of the Cochran mode is determined. A self-consistent method of determining the frequency of a photon is proposed.

Journal ArticleDOI
TL;DR: In this paper, two derivations of the three-body nonadditivity correction to the radial distribution function of a fluid are given, one based on the properties of n−particle correlation functions and the second based on statistical mechanical formulas relating to the equation of state.
Abstract: Two derivations of the three‐body nonadditivity correction to the radial distribution function of a fluid are given. The first employs only the properties of n‐particle correlation functions, and the second is based on statistical mechanical formulas relating to the equation of state. We obtain a new formula for the effective pair potential in the low‐density limit, valid through terms in the square of the density, assuming only that the nonadditive three‐body interaction is small. An extension of this formula to higher densities is obtained by replacing the exact triplet correlation function for low densities by the superposition approximation. Our results provide no grounds for supposing that the effective pair potential is linear in the density for either gases or liquids.

Journal ArticleDOI
TL;DR: In this paper, the effects of a vertical velocity component upon the conventional horizontal spaced receiver measurements are carefully analyzed and the correlation between multi-frequency scintillation records of a radio star is investigated.