On the isothermal density derivative ofG(r) and a new theory of the pair correlation function of hard spheres

A new representation is obtained for the isothermal density derivative ofg(r). It explicitly exhibits the contributions of potential energy terms that are not pairwise additive. Consideration of a previously known result shows that one has to be rather cautious when using it to obtain information on the triplet correlation function from the well-known relation between this function andg/, due to large cancellations which take place at high density. By integrating with respect to density the new representation forg/, after a suitable closure has been introduced, we obtain an augmented Percus-Yevick equation for hard spheres which has full thermodynamic consistency. The equation of state and the cavity functiony(r) are very accurate at low density and considerably improve PY at medium density, so that this appears to be a useful new approach to the theory of fluids, but it is necessary to improve the closure in order to treat a dense fluid.This paper is dedicated to Jerry Percus on the occasion of his 65th birthday.     

Direct correlation function of the hard-sphere fluid

Two analytic approximations for the direct correlation function of a hard-sphere fluid are considered. The first follows from a generalization of the Percus–Yevick result in d dimensions, whereas the second arises in the Rational Function Approximation (RFA) method. Both approximations require the equation of state of the hard-sphere fluid as input. The results, derived after use of the Carnahan–Starling and the Padé 4 Ripoll, MS and Tejero, CF. 1995. Molec. Phys., 85: 423[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar],3 Wertheim, MS. 1963. Phys. Rev. Lett., 10: 321 J. Math. Phys. 5, 643 (1964); E. Thiele, J. Chem. Phys. 39, 474 (1963).[Crossref], [Web of Science ®] , [Google Scholar] equations of state in both approaches, are compared with simulation data. The comparison shows that the first approximation is rather accurate in the region inside the core, but inherits the limitation of the Percus–Yevick theory for distances beyond the hard-sphere diameter. On the other hand, the results of the RFA method are also accurate inside the core and capture well the initial part of the tail beyond the hard-sphere diameter, but fail to account for the subsequent oscillations observed in the simulations. Other merits and limitations of the two approaches are reported.     

Exact expressions for row correlation functions in the isotropicd=2 ising model

We present exact explicit expressions for the row spin-spin correlation functions _{00 n}0 in the isotropicd= 2 Ising model, in terms of elliptic integrals, forn 5. We also give a general structural formula for _{00 n}0.     

Perturbative solution to order βɛ of the Percus-Yevick equation for triangular well potential forn=2

The radial distribution function for a fluid in which the molecules interactvia a triangular well potential is considered. Expanding the radial distribution function in pwoers of βɛ, where ɛ is the depth of the potential andβ=1/k _BT the first-order terms are calculated analytically using the Percus-Yevick theory in the Baxter’s formulation. The first-order terms in the direct correlation functionc(r) are also calculated. The first- and second-order terms in the free energy obtained from the energy equation of state are calculated and compared with other calculations. An erratum to this article is available at .     

Series representation of the Percus-Yevick pair correlation function g(r) of a hard-sphere fluid

An explicit expression for g(r) is derived using contour integration in K space: poles, occurring at complex K values as a result of disordering in the fluid state, give rise to damped oscillations whose asymptotic form accords with experiment.     

The incoherent scattering function and related correlation functions in hard sphere fluids at short times

For a classical fluid of hard spheres and hard disks exact expressions for all densities and wave vectors are derived for the coefficients oft ⁿ in the short-time expansion of the incoherent intermediate scattering function (n = 0, 1,..., 4) and the velocity correlation function (n=0,1,2). Similarly, we obtain the coefficient of the leading term in the short-time behavior of the cumulants of the displacements. Furthermore,S(k, ) has a high-frequency tail ^–4, characteristic for the hard-sphere fluid, which leads to a modification of the standard sum rules. We present estimates for the frequency range, in which this tail may be observed in neutron scattering off noble gases. The results are also compared with Enskog's theory and molecular dynamics calculations.     

On the calculation of equilibrium time correlation functions in hard-sphere fluids

We discuss in detail techniques that have been used to determine single-particle equilibrium time correlation functions in a hard-sphere fluid on the basis of kinetic theory. The accuracy of various procedures is assessed.On leave from Interuniversitair Reactor Instituut, Delft, The Netherlands.     

Convergent expansions for asymptotically degenerate inverse correlation lengths of classical lattice spin systems

We obtain convergent expansions for the inverse correlation length associated with various spin-spin correlation functions for some weakly coupled multicomponent classical lattice spin systems. In terms of the lattice quantum field theory associated with the models the expansions provide a convergent perturbation theory for particle masses which are asymptotically degenerate in the limit of zero coupling.Reseach partially supported by CNPq, Brazil.     

The direct correlation function of a one-dimensional Ising model

The strictly finite range of the direct correlation function for a homogeneous nearest neughbor Ising chain is shown to persist in the presence of arbitrary site-dependent coupling constants and an arbitrary external field. A method is developed to examine the range of the direct correlation function for many-neighbor interactions. It is found from numerical examples that, in general, third-neighbor and higher interactions induce long-range direct correlations, as does the presence of a field in the second-neighbor case.     

Analytical approach to the current correlation function in dissipative two-state systems

Using the spin-boson model with coupling to Ohmic bath, an analytical approach is developed to study the dynamics of the current correlation function in dissipative two-state systems with the view of understanding the effects of environment and tunneling on the coherent oscillation and the long-time decay of the current correlation function in these systems. An analytic expression of current correlation function is obtained and the results agree very well with that of numerical simulations.      

Critical behavior of the correlation function of a coulombic fluid

An extension of the Ornstein-Zernike theory of critical scattering by a simple fluid to include a type of coulombic system is suggested. The relation between the oscillations of the charge distribution predicted by the second moment condition of Stillinger and Lovett in the restricted primitive model and the critical behavior of the correlation function is also discussed.This work was supported in part by a grant from the National Institutes of Health, GM 20800-03.Contribution No. 3100 from the Department of Chemistry, Indiana University.Supported by CONACYT (Mexico) and on leave from Universidad Autónoma de Puebla, Puebla, Mexico.     

纠缠双光子态关联函数的两种解法

介绍了量子光学中常见的双光子纠缠态关联函数的两种求法,第一种方法是利用产生湮没算符的对易关系来求解;第二种方法是应用"二次量子化"的方法来计算,这种方法不需要用对易关系,计算简便.     

The GMSA for a hard-sphere fluid revisited: evaluation of the Henderson-Blum approximation[*

The Generalized Mean Spherical Approximation for a hard-sphere fluid developed by Waisman [E. Waisman, Mol. Phys. 25, 45 (1973)] over forty years ago is revisited. The relatively recent [C. F. Tejero and M. López de Haro, Mol. Phys. 105, 2999 (2007)] completely analytical results for the direct correlation function of such approximation are used to assess the simplification introduced by Henderson and Blum [D. Henderson and L. Blum, Mol. Phys. 32, 1627 (1976)]. The conclusion is reached that such simplification is a rather valuable compromise between simplicity and accuracy.     

Simulation study of the effects of time delay on the correlation function of a bistable system with correlated noises

<正>The effects of time delay on the fluctuation properties of a bistable system are investigated by simulating its normalised correlation function C(s).Three cases including linear delay,cubic delay and global delay in the system are considered respectively.The simulation results indicate that the linear delay enhances the fluctuation of the system (reduces the stability of the system) while the cubic delay and global delay weaken it(enforce the stability of the system),and the effect of cubic delay is more pronounced than the linear delay and global delay.     

Coincidence theorem for the direct correlation function of hard-particle fluids

The Mayerf-function for purely hard particles of arbitrary shape satisfiesf ²(1, 2)=–f(1, 2). This relation can be introduced into the graphical expansion of the direct correlation functionc(1, 2) to obtain a graphical expression for the case of exact coincidence, in position and orientation, of two identical hard cores. The resulting expression forc(1, 1)+1 contains only graphsG fromc(1), the sum of irreducible graphs with one labeled point. Relative to its coefficient inc(1),G occurs inc(1, 1) with an additional factorR _c which is 1 for the leading graph in the expansion and of the form 2–2L(G) for all other graphs. HereL(G)=0, 1, 2,..., is a nonnegative integer. Topological analysis is used to derive an expression forL(G) in terms of the connectivity properties ofG.     

Source function extracted from single-event HBT correlation functions of hydrodynamical sources

We investigate the single-event two-pion correlation functions for the hydrodynamic particle-emitting sources with the fluctuating initial conditions generated by the Heavy Ion Jet Interaction Generator （HIJING）. Using a three-dimension fast Fourier transform （FFT）, we further extract the source functions from the single-event correlation functions. It is found that the inhomogeneity of the hydrodynamic sources with the fluctuating initial conditions lead to event-by-event fluctuations of the correlation functions and source functions.     

Simulation study of the two-time intensity correlation function of a two-mode laser system with both pump and quantum noises

This paper investigates the two-time intensity correlation function of a two-mode ring laser system subjected to both pump and quantum noises by stochastic simulation. It finds that the decay rate of the intensity correlation function of one mode gets faster with decreasing values of relevant parameters, i.e., the coupling constant ξ, the cross-correlation coefficient λ , the difference of the pump parameters Δa and the pump parameter a₁; however, its variations get complex in the other mode when relevant parameters are changed. The investigating results also show that the effects of the mode competition on intensity correlation function are obvious.     

Source function extracted from single-event HBT correlation functions of hydrodynamical sources

We investigate the single-event two-pion correlation functions for the hydrodynamic particle-emitting sources with the fluctuating initial conditions generated by the Heavy Ion Jet Interaction Generator (HIJING). Using a three-dimension fast Fourier transform (FFT), we further extract the source functions from the single-event correlation functions. It is found that the inhomogeneity of the hydrodynamic sources with the fluctuating initial conditions lead to event-by-event fluctuations of the correlation functions and source functions.     

The δ-function expansion of the modified two-particle Ursell function of a hard-sphere fluid

The expansion of the modified two-particle Ursell functionU(r) of a hardsphere quantal fluid is obtained in terms of a series of derivatives of δ-function. This expansion has been used to expand the second virial co-efficientB ₂ of the fluid. The expansion is correct up to the fourth power in thermal wavelength and the terms of the order of λ⁸ and λ⁴ in the first expa nsion are new.