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Showing papers on "Correlation function (statistical mechanics) published in 1993"


Journal ArticleDOI
TL;DR: In this article, an epi-illuminated microscope configuration for use in fluorescence correlation spectroscopy in bulk solutions has been analyzed and conditions for achieving quasi-cylindrical sample shape have been derived.
Abstract: An epi-illuminated microscope configuration for use in fluorescence correlation spectroscopy in bulk solutions has been analyzed. For determining the effective sample dimensions the spatial distribution of the molecule detection efficiency has been computed and conditions for achieving quasi-cylindrical sample shape have been derived. Model experiments on translational diffusion of rhodamine 6G have been carried out using strong focusing of the laser beam, small pinhole size and an avalanche photodiode in single photon counting mode as the detector. A considerable decrease in background light intensity and measurement time has been observed. The background light is 40 times weaker than the fluorescence signal from one molecule of Rh6G, and the correlation function with signal-to-noise ratio of 150 can be collected in 1 second. The effect of the shape of the sample volume on the autocorrelation function has been discussed.

1,021 citations


Journal ArticleDOI
TL;DR: Theoretical expressions for the height-height correlation function of self-affine fractal surfaces are discussed in comparison with scanning tunneling microscopy, correlation and surface-width data obtained from rough silver and gold films.
Abstract: Theoretical expressions for the height-height correlation function of self-affine fractal surfaces are discussed in comparison with scanning tunneling microscopy, correlation and surface-width data obtained from rough silver and gold films. Fourier transformations are used to compare with equilibrium phenomena, and lead to a correlation model with an associated roughness spectrum of analytic form.

280 citations


Journal ArticleDOI
TL;DR: In this article, the relaxational dynamics for local spin autocorrelations of the sphericalp-spin interaction spin-glass model is studied in the mean field limit, where the dynamics is ergodic and similar to the behaviour in known liquid-glass transition models.
Abstract: The relaxational dynamics for local spin autocorrelations of the sphericalp-spin interaction spin-glass model is studied in the mean field limit. In the high temperature and high external field regime, the dynamics is ergodic and similar to the behaviour in known liquid-glass transition models. In the static limit, we recover the replica symmetric solution for the long time correlation. This phase becomes unstable on a critical line in the (T, h) plane, where critical slowing down is observed with a cross-over to power law decay of the correlation function ∝t−ν, with an exponent ν varying along the critical line. For low temperatures and low fields, ergodicity in phase space is broken. For small fields the transition is discontinuous, and approaching this transition from above, two long time scales are seen to emerge. This dynamical transition lies at a somewhat higher temperature than the one obtained within replica theory. For larger fields the transition becomes continuous at some tricritical point. The low temperature phase with broken ergodicity is studied within a modified equilibrium theory and alternatively for adiabatic cooling across the transition line. This latter scheme yields rather detailed insight into the formation and structure of the ergodic components.

238 citations


Journal ArticleDOI
TL;DR: In this paper, the Fisher-Widom (FW) line was introduced to define the divergence point between pure exponential from exponentially damped oscillatory decay of the radial distribution function g(r) at a liquid-vapour interface.
Abstract: Recent work has highlighted the existence of a unified theory for the asymptotic decay of the density profile ρ(r) of an inhomogeneous fluid and of the bulk radial distribution function g(r). For a given short-ranged interatomic potential ρ(r) decays into bulk in the same fashion as g(r), i.e. with the same exponential decay length (α0/-1) and, for sufficiently high bulk density (ρb) and/or temperature (T), oscillatory wavelength (2π/α1). The quantities α0 and α1 are determined by a linear stability analysis of the bulk fluid; they depend on only the bulk direct correlation function. In this paper we reintroduce the concept of the Fisher-Widom (FW) line. This line was originally introduced, in say the (ρb, T plane, as that which separates pure exponential from exponentially damped oscillatory decay of g(r). We explore the relevance of the FW line for the form of the density profile at a liquid-vapour interface. Using a weighted density approximation (WDA) density functional theory we locate the FW line fo...

191 citations


Journal ArticleDOI
TL;DR: Inflationary models predict a definite, model-independent, angular dependence for the three-point correlation function of ΔT/T at large angles (≥ 1°) as mentioned in this paper.
Abstract: Inflationary models predict a definite, model-independent, angular dependence for the three-point correlation function of ΔT/T at large angles (≥1°) which we calculate. The overall amplitude is model dependent and generically unobservably small, but may be large in some specific models. We compare our results with other models of non-Gaussian fluctuations

188 citations



Journal ArticleDOI
TL;DR: In this article, the authors presented a model for a one-dimensional anisotropic exclusion process describing particles moving deterministically on a ring of length L with a single defect, across which they move with probability 0 ⌽p ⩽ 1.
Abstract: We present a model for a one-dimensional anisotropic exclusion process describing particles moving deterministically on a ring of lengthL with a single defect, across which they move with probability 0 ⩽p ⩽ 1. This model is equivalent to a two-dimensional, six-vertex model in an extreme anisotropic limit with a defect line interpolating between open and periodic boundary conditions. We solve this model with a Bethe ansatz generalized to this kind of boundary condition. We discuss in detail the steady state and derive exact expressions for the currentj, the density profilen(x), and the two-point density correlation function. In the thermodynamic limitL → ∞ the phase diagram shows three phases, a low-density phase, a coexistence phase, and a high-density phase related to the low-density phase by a particle-hole symmetry. In the low-density phase the density profile decays exponentially with the distance from the boundary to its bulk value on a length scale ξ. On the phase transition line ξ diverges and the currentj approaches its critical valuej c = p as a power law,j c − j ∞ ξ−1/2. In the coexistence phase the widthδ of the interface between the high-density region and the low-density region is proportional toL 1/2 if the densityρ f 1/2 andδ=0 independent ofL ifρ = 1/2. The (connected) two-point correlation function turns out to be of a scaling form with a space-dependent amplitude n(x1, x2) =A(x2)A Ke−r/ξ withr = x 2 −x 1 and a critical exponent κ = 0.

130 citations


Journal ArticleDOI
TL;DR: In this article, the authors consider the effect of hydrodynamic interactions between a particle and the surrounding fluid on the light scattering and derive an expression for the temporal autocorrelation function of the intensity fluctuations of the scattered light.
Abstract: We discuss the entension of dynamic light scattering to very strongly scattering media, where the propagation of light is described by the diffusion approximation, allowing the distribution of the light paths to be determined. The temporal evolution of the length of each of these paths, due to the dynamics of the scattering medium, is calculated, and an expression for the temporal autocorrelation function of the intensity fluctuations of the scattered light is obtained. This relates the measured decay of the autocor-relation function to the dynamics of the medium. This technique is called diffusing wave spectroscopy (DWS). To extend its utility, we consider the consequences of interactions between the scattering particles on the light scattering. To illustrate its applications, we consider several examples of new physics that can be investigated using DWS. We study the transient nature of hydrodynamic interactions between a particle and the surrounding fluid. We are able to probe the decay of the velocity correlation function of the particles, and we demonstrate its algebraic decay, with a t−3/2 time dependence. We also show that the time-dependent self diffusion coefficient exhibits an unexpected scaling behavior, whereby all the data, from samples of different volume fractions, can be scaled onto a single curve. Finally, we discuss the applications of DWS to the study of the dynamics of foams, and show how it can be used to probe the rearrangement of the bubbles within the foam as they coarsen.

121 citations


Journal ArticleDOI
TL;DR: In this article, space and time dependent correlation functions in the Heisenberg XX0 chain (in the transverse magnetic field) are expressed in terms of Fredholm determinants of linear integral operators.
Abstract: Space and time dependent correlation functions in the Heisenberg XX0 chain (in the transverse magnetic field) are expressed in terms of Fredholm determinants of linear integral operators. This is done in order to evaluate asymptotics of these correlations, which we shall do in next paper.

119 citations


Journal ArticleDOI
TL;DR: In this paper, the influence of barrier crossing processes on the positional time correlation function is studied. But the memory function of this correlation function was evaluated for a 2-4 potential as a function of the barrier height using the Mori continued fraction expansion and an equivalent but more efficient matrix formulation.
Abstract: The one‐variable Smoluchowski equation is used to study the influence of barrier crossing processes on the positional time correlation function. The memory function of this correlation function is evaluated for a 2–4 potential as a function of the barrier height using the Mori continued fraction expansion and an equivalent but more efficient matrix formulation. Higher orders in the expansions are required to obtain numerical convergence as the barrier height increases. An exact integral solution for the correlation time is derived and is compared with the approximations. A biexponential approximation, which describes the independent motion in a potential well and the transition between wells, is found to be very accurate for high barriers. Numerical simulations provide checks on the approximations to the correlation function for a barrier height of 2 kBT. The possibility of including the influence of more rapid barrier crossing processes into the many variable Smoluchowski description of long time polymer...

107 citations


Journal ArticleDOI
TL;DR: It is shown that the non-ideal mixing of lipid species due to mismatch in the hydrophobic lengths leads to a progressively increasing local ordering as the chain-length difference is increased and a pronounced local structure is found to persist deep inside the fluid phase of the mixture.

Journal ArticleDOI
TL;DR: Three mathematically acceptable, alternate forms for the height-height correlation function are investigated, to explore their impact on the analysis of diffuse x-ray-reflectivity data.
Abstract: Height-height correlations for self-affine surfaces with finite horizontal cutoffs are generally modeled by exponential forms. Three mathematically acceptable, alternate forms for the height-height correlation function are investigated, to explore their impact on the analysis of diffuse x-ray-reflectivity data. The appropriateness of these functions to actual physical samples is explored through comparison with x-ray-reflectivity and scanning-tunneling-microscopy data recorded on known self-affine surfaces.

Journal ArticleDOI
TL;DR: The ground state wave function for the spin-1/2 quantum antiferromagnet on a 36-site kagome$iaa--- structure is found by numerical diagonalization as discussed by the authors.
Abstract: The ground-state wave function for the spin-1/2 quantum antiferromagnet on a 36-site kagome$iaa--- structure is found by numerical diagonalization. Spin-spin correlations and spin gaps indicate that the ground state of this system does not possess magnetic order. The spin-Peierls order is studied using a four-spin correlation function. The short-range structure in this correlation function is found to be consistent with a simple dimer-liquid model. The spin-Peierls order, if it exists, must be quite small.

Journal ArticleDOI
TL;DR: In this article, a nonlinearity of electromagnetic field vibrations described by q -oscillators is shown to produce an essential dependence of second order correlation functions on the intensity and deformation of the Planck distribution.

Journal ArticleDOI
Abstract: This letter describes results of a cross-correlation between the 170 GHz partial-sky survey, made with a 3.8 deg beam balloon-borne instrument, and the COBE DMR 'Fit Technique' reduced galaxy all-sky map with a beam of 7 deg. The strong correlation between the data sets implies that the observed structure is consistent with thermal variations in a 2.7 K emitter. A chi-square analysis applied to the correlation function rules out the assumption that there is no structure in either of the two maps. A second test shows that if the DMR map has structure but the 170 GHz map does not, the probability of obtaining the observed correlation is small. Further analyses support the assumption that both maps have structure and that the 170 GHz-DMR cross-correlation is consistent with the analogous DMR correlation function. Maps containing various combinations of noise and Harrison-Zel'dovich power spectra are simulated and correlated to reinforce the result. The correlation provides compelling evidence that both instruments have observed fluctuations consistent with anisotropies in the cosmic microwave background.

Journal ArticleDOI
TL;DR: The exact dynamical magnetic structure factor S(Q, E) in the ground state of a one-dimensional S=1/2 antiferromagnet with gapless free S= 1/2 spinon excitations is calculated using the Haldane-Shastry model with inverse-square exchange.
Abstract: We calculate the exact dynamical magnetic structure factor S(Q, E) in the ground state of a one-dimensional S=1/2 antiferromagnet with gapless free S=1/2 spinon excitations, the Haldane-Shastry model with inverse-square exchange, which is in the same low-energy universality class as Bethe's nearest-neighbor exchange model. Only two-spinon excited states contribute, and S(Q, E)is found to be a very simple integral over these states

Journal ArticleDOI
TL;DR: In this paper, a three-dimensional Lagrangian model for the motion of particles in turbulent flows has been established, and the computed results are compared with the experimental data for the particle dispersion, velocity correlations and velocity decay.

Journal ArticleDOI
01 Dec 1993-EPL
TL;DR: In this article, the Wolf-Villain model for growing surfaces is investigated using the height-height correlation function and the structure factor, and a modified scaling law is introduced which may describe quite generally the crossover behaviour in models of this kind.
Abstract: The Wolf-Villain model for growing surfaces is investigated using the height-height correlation function and the structure factor. Both functions show an unusual scaling behaviour that can be attributed to the time dependence of the average step size and is characterized by a new exponent. A modified scaling law is introduced which may describe quite generally the crossover behaviour in models of this kind. It leads to a very different classification of the model than has been inferred from the exponents obtained by measuring the width of the surface as a function of time and system size.

Journal Article
TL;DR: In this paper, the Malthus-Verhulst stochastic model is studied in the presence of multiplicative noise by means of a simple approximation scheme valid outside the critical region and exact asymptotic expansion at the critical point.
Abstract: We study the nonlinear relaxation in the presence of multiplicative noise by means of a simple approximation scheme valid outside the critical region and exact asymptotic expansion at the critical point. The theory is developed in the Malthus-Verhulst stochastic model case. We find nonmonotonic growth of fluctuations during the transient. At the critical point we study the statistical properties of the finite time average of the original process. We obtain an exact result for the generating function exhibiting scaling asymptotic behavior at the critical point. We deduce also an asymptotic sum rule for the n-times correlation function of the original process and the asymptotic expression of the two-times correlation function

Journal ArticleDOI
TL;DR: In this article, a special class of correlation models based on so-called spatial autoregressive processes is critically examined, and it is shown that models of this type are not positive definite on the meteorological relevant spaces.
Abstract: The method of optimal interpolation, which is widely used in meteorological data assimilation, relies very much on good approximations of spatial correlation functions. Therefore, many models for such functions have been developed. These models should fulfill certain mathematical constraints; particularly, they should be positive-definite functions. For the classes of homogeneous and isotropic processes, the positivity property and its consequences are reviewed. A special class of correlation models based on so-called spatial autoregressive processes is critically examined. It is shown that models of this type are not positive definite on the meteorological relevant spaces. Some other models taken from the literature are shown to lack this property also. Three strategies to obtain models that have the appropriate mathematical properties are outlined.

Journal ArticleDOI
TL;DR: In this article, the authors used statistical and topological quantities to test the COBE-DMR first year sky maps against the hypothesis that the observed temperature fluctuations reflect Gaussian initial density perturbations with random phases.
Abstract: We use statistical and topological quantities to test the COBE-DMR first year sky maps against the hypothesis that the observed temperature fluctuations reflect Gaussian initial density perturbations with random phases Recent papers discuss specific quantities as discriminators between Gaussian and non-Gaussian behavior, but the treatment of instrumental noise on the data is largely ignored The presence of noise in the data biases many statistical quantities in a manner dependent on both the noise properties and the unknown CMB temperature field Appropriate weighting schemes can minimize this effect, but it cannot be completely eliminated Analytic expressions are presented for these biases, and Monte Carlo simulations used to assess the best strategy for determining cosmologically interesting information from noisy data The genus is a robust discriminator that can be used to estimate the power law quadrupole-normalized amplitude independently of the 2-point correlation function The genus of the DMR data are consistent with Gaussian initial fluctuations with Q_rms = 157 +/- 22 - (66 +/- 03)(n - 1) uK where n is the power law index Fitting the rms temperature variations at various smoothing angles gives Q_rms = 132 +/- 25 uK and n = 17 +03 -06 While consistent with Gaussian fluctuations, the first year data are only sufficient to rule out strongly non-Gaussian distributions of fluctuations

Journal ArticleDOI
TL;DR: In this paper, two-and three-pulse photon echo signals are calculated for various model systems and the use of an experimental solvation correlation function as the solvent fluctuation correlation function leads to two conclusions: inertial solvent motion plays a major role in the electronic dephasing process.
Abstract: Two‐ and three‐pulse photon echo signals are calculated for various model systems. The use of an experimental solvation correlation function as the solvent fluctuation correlation function leads to two conclusions. First, inertial solvent motion plays a major role in the electronic dephasing process. Second, simple models such as Markovian or exponential models for the solvent fluctuation correlation function may not provide an adequate description of the echo signal. The real and imaginary parts of the echo response, which may be measured via heterodyne detected stimulated photon echoes, are compared with conventional photon echo signals.

Journal ArticleDOI
TL;DR: This work studies the photon correlations between the output of two spectral filters set within the fluorescence triplet of a two-state atom, finding positive (bunching) correlations arise when the two filters are set at the same frequency, and also when they are positioned symmetrically at opposite sides of the driving frequency.
Abstract: We study the photon correlations between the output of two spectral filters set within the fluorescence triplet of a two-state atom. The time uncertainty arising from the spectral resolution of the filters implies a possible interference between opposite orders of emission, contributing to the same detection order. Furthermore, the fluorescent emission is a quantum-mechanical process, and successive emissions in different components do not commute. The correlation functions are affected both by the memory time of the filters and by the noncommutativity of successive emissions. When the two filter bandwidths are larger than the widths of the components, this only modifies the short-time behavior of the correlation functions between two photons from different spectral components. For narrow filters, the entire correlation function is dominated by memory-time effects. Positive (bunching) correlations arise when the two filters are set at the same frequency, and also when they are positioned symmetrically at opposite sides of the driving frequency.

Journal ArticleDOI
TL;DR: It is shown that the presence of a macroscopic groove does not require higher-order nonlinearities but is a consequence of the fact that the roughness exponent a≥1 for these models, which implies anomalous behavior for the scaling of the height-difference correlation function G(x)= which is explicitly calculated for the linear diffusion equation with noise in d=2 and 3 dimensions.
Abstract: The existence of a grooved phase in linear and nonlinear models of surface growth with horizontal diffusion is studied in d=2 and 3 dimensions. We show that the presence of a macroscopic groove, i.e., an instability towards the creation of large slopes and the existence of a diverging persistence length in the steady state, does not require higher-order nonlinearities but is a consequence of the fact that the roughness exponent a≥1 for these models. This implies anomalous behavior for the scaling of the height-difference correlation function G(x)= which is explicitly calculated for the linear diffusion equation with noise in d=2 and 3 dimensions. The results of numerical simulations of continuum equations and discrete models are also presented and compared with relevant models

Journal ArticleDOI
TL;DR: The present results allow us to confirm the validity of spin-wave theory up to temperatures of 0.5 T c and to predict the phase-transition temperature according to an Ising-like model with a renormalized exchange constant.
Abstract: Using a classical Monte Carlo simulation on the two-dimensional Heisenberg model with exchange anisotropy, we have obtained reliable results for several properties: spontaneous magnetization, total energy, self-correlation, susceptibility, and correlation functions. An improved algorithm has been used in order to eliminate artifacts in such quantities below the critical temperature. The present results allow us to confirm the validity of spin-wave theory up to temperatures of 0.5 T c and, simultaneously, to predict the phase-transition temperature according to an Ising-like model with a renormalized exchange constant

Journal ArticleDOI
TL;DR: In this article, a theoretical study of the time-dependent correlation function of multiply scattered light in laminar and stationary flow is presented, which is sensitive to the root mean square of velocity gradients weighted by the cloud of diffusive light paths.
Abstract: A theoretical study of the time-dependent correlation function of the multiply scattered light in laminar and stationary flow is presented. We study an inhomogeneous system of flow, i.e. when the strain tensor σ ij ( r ) depends on the space variables. Since in such flows the dephasing of light is space dependent, we introduce the useful function of the local density distribution of diffusion paths. We show that the time-dependent correlation function C1(t) of the scattered field is sensitive to the root mean square of velocity gradients weighted by the cloud of diffusive light paths. We establish a general formulation of C1(t) for laminar and stationary flow in the weak scattering limit kl ⪢ 1. The effects of the dimension of the inhomogeneous system and of the boundary conditions are also discussed. These results are applied to the cases of an infinitely thin and continuous sheet of vorticity, of a Rankine vortex, and of a Gaussian shaped velocity gradient.


Journal ArticleDOI
TL;DR: In this paper, the doubly differential cross-section for weak inelastic scattering of waves or particles by manybody systems is derived in Born approximation and expressed in terms of the dynamic structure factor according to van Hove.
Abstract: The doubly differential cross-section for weak inelastic scattering of waves or particles by manybody systems is derived in Born approximation and expressed in terms of the dynamic structure factor according to van Hove. The application of this very general scheme to scattering of neutrons, x-rays and high-energy electrons is discussed briefly. The dynamic structure factor, which is the space and time Fourier transform of the density-density correlation function, is a property of the manybody system independent of the external probe and carries information on the excitation spectrum of the system. The relation of the electronic structure factor to the density-density response function defined in linear-response theory is shown using the fluctuation-dissipation theorem

Journal ArticleDOI
TL;DR: In this article, a weighted density functional theory was developed for inhomogeneous ionic fluids and applied to the structure of the electric double layer using the restricted primitive model where the ions are considered to be charged hard spheres of equal diameter.
Abstract: A weighted-density-functional theory is developed for inhomogeneous ionic fluids and applied to the structure of the electric double layer using the restricted primitive model where the ions are considered to be charged hard spheres of equal diameter. The formalism is nonperturbative with both hard-sphere and electrical contributions to the one-particle correlation function evaluated through a suitably averaged weighted density, the only input being the second-order direct correlation functions of the corresponding uniform system. Numerical results on the ionic density profile and the mean electrostatic potential near a hard wall at several surface charge densities are shown to compare well with available simulation results.

Journal Article
TL;DR: A weighted-density-functional theory is developed for inhomogeneous ionic fluids and applied to the structure of the electric double layer using the restricted primitive model where the ions are considered to be charged hard spheres of equal diameter.
Abstract: A weighted-density-functional theory is developed for inhomogeneous ionic fluids and applied to the structure of the electric double layer using the restricted primitive model where the ions are considered to be charged hard spheres of equal diameter. The formalism is nonperturbative with both hard-sphere and electrical contributions to the one-particle correlation function evaluated through a suitably averaged weighted density, the only input being the second-order direct correlation functions of the corresponding uniform system. Numerical results on the ionic density profile and the mean electrostatic potential near a hard wall at several surface charge densities are shown to compare well with available simulation results