Effective interactions between concentration fluctuations and charge transfer in chemically ordering liquid alloys

Summary The correlations between long-wavelength fluctuations of concentration in a liquid binary alloy are determined by a balance between an elastic-strain free energy and an Ornstein-Zernike effective interaction. The latter is extracted from thermodynamic data in the case of the Li−Pb system, which is well known to chemically order with stoichiometric composition corresponding to Li₄Pb. Strong attractive interactions between concentration fluctuations near the composition of chemical ordering originate from electronic charge transfer, which is estimated from the electron-ion partial structure factors as functions of composition in the liquid alloy. In honour of Prof. Fausto Fumi on the occasion of his retirement from teaching.     

Electron theory of long-wavelength concentration fluctuations in liquid metal alloys

Summary It is shown that long-wavelength concentration fluctuations in a binary liquid metal alloy are determined by a pair interchange free energyw, which is exactly given by the sum of an elastic strain term and of the concentration-concentration direct correlation function. The latter is evaluated in an alloy of homovalent components by electron screening theory in the pseudopotential approach of Shaw and Harrison and shown to be entirely determined by nonlocal terms reflecting charge transfer to the more electronegative alloy component. Numerical calculations for the liquid Na−K alloy show strong cancellation between the two contributions tow at all concentrations, in qualitative agreement with experiment.     

From mixing-demixing to condensation-evaporation phase transition in binary liquids

Summary Binary-fluid mixtures show first-order phase transition phenomena which are either classified as mixing-demixing (phase separation), or as condensation-evaporation. The localization of the transition lines, the characterization of the new phases, and the analysis of the parameters which force model systems to choose one of the two transition mechanisms is the aim of this study. We performed both parallel-molecular-dynamics simulations and integral-equation theory calculations on binary mixtures of Lennard-Jones particles. By fixing the composition and by varying the interaction strength, we found a continuous change between the two kinds of transition mechanisms. Theoretical and simulation results are compared with each other and a quantitative agreement i8s found. However, the simultation analysis appears to be more promising since, in contrast to the integral-equation theory in which the spinodal lines can only be approched, information on the microscopic structure of the new phases can be obtained. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copenello, Italy, July 4–8, 1994.     

Linear-response theory for partly quenched systems

Summary The matrix of linear density response functions is constructed within density functional theory for a monatomic fluid adsorbed in a quenched material. The structural Ornstein-Zernike relations obtained by Given and Stell with the replica method are regained in the appropriate limit. The usefulness of the present reformulation of their theory is illustrated by deriving from it the free-energy functional and the structural closure relations in the hypernetted-chain approximation. The extension to dynamical properties of partly quenched systems is indicated.     

High-frequency sum rules for classical one-component plasma in a magnetic field

A high-frequency sum-rule expansion is derived for all elements of a classical plasma dielectric tensor in the presence of an external magnetic field, ₄ ¹³ is found to be the only coefficient of ^–4 that has no correlational and finite-radiation-temperature contributions. The finite-radiation-temperature effect results in an upward renormalization of the frequencies of the modes; it also leads to either reduction of the negative correlational effect on the positive thermal dispersion or, together with correlation, enhancement of the positive thermal dispersion for finitek, depending on the direction of propagation. Further, for the extraordinary mode, the finite-radiation-temperature effect increases the positive refractive dispersion for finitek.     

Decay of correlations in classical fluids with long-range forces

We show with simple arguments that, as a consequence of the Poisson equation, the correlations of a charged system at equilibrium decay faster than any inverse power, if they are integrable and monotonous at infinity. For all other longrange systems (with potential(x)b¦x¦^–s , ¦x¦ , 0v,s} 2), the decay is bounded below by an inverse power.Partially supported by the Swiss National Foundation for Scientific Research.     

Interactions and correlations of particulate inclusions in a columnar phase

We calculate the elastic-field-mediated interaction between macroscopic particles in a columnar hexagonal phase. The interaction is found to be long-ranged and non-central, with both attractive and repulsive parts. We show how the interaction modifies the particle correlations and the column fluctuations. We also calculate the interaction of particles with the topological defects of the columnar phase. The particle-defect interaction reduces the mobility of the defects. Received 14 March 2002 and Received in final form 13 August 2002 RID="a" ID="a"e-mail: rjoy@physics.iisc.ernet.in     

Decay of correlations in classical lattice models at high temperature

In classical statistical mechanical lattice models with many body potentials of finite or infinite range and arbitrary spin it is shown that the truncated pair correlation function decays in the same weighted summability sense as the potential, at high temperature.Research partially supported by the National Science Foundation under Grant MCS 78-00680     

Decay of correlations in surface models

A convergent low-temperature expansion for a variety of models of twodimensional surfaces is presented. It yields existence of the thermodynamic limit for the pressure and correlation functions as well as analyticity inz =e ^– In addition, the estimates give exponential decay of truncated correlations, which proves the existence of a gap in the spectrum of the transfer matrix below the ground state eigenvalue. Two particular examples included in the general framework are the solid-on-solid and discrete Gaussian models.Supported in part by the National Science Foundation under grant No. PHY 79-16812.     

Decay of correlations in spin systems

We investigate the decay of initial correlations in a spin system where each spin relaxes independently by an intramolecular mechanism. The equation of motion for the spin density matrix is assumed to be the Redfield equation, which is of the form of a quantum mechanical master equation. Our analysis of this problem is based on the techniques of Shuler, Oppenheim, and coworkers, who have studied the decay of correlations in systems which can be described by classical stochastic master equations. We find that the off-diagonal elements of the reduced spin density matrices approach their equilibrium values faster than the diagonal elements. The Ursell functions, which are a measure of the correlations in the system, decay to their zero equilibrium values faster than the spin density matrix except for the furthest off-diagonal elements. Far off-diagonal matrix elements of the spin density matrix approach equilibrium at the same rate as the Ursell functions, which is the important difference between the quantum mechanical model studied here and the classical models studied earlier.Supported in part by the National Science Foundation.     

Quantum and classical correlations in a classical dephasing environment

We calculate the non-Markovian dynamics of quantum correlations, including entanglement and discord, and classical correlation in a two-qubit system with Ornstein-Uhlenbeck noise and discuss the relations in these correlations. It?s found that the initial-state parameters and the non-Markovian properties play an important role in these dynamics behaviors.     

Band structure and atomic sum rules for X-ray dichroism

Corrections to the atomic orbital sum rule for circular magnetic X-ray dichroism in solids are derived using orthonormal LMTOs as a single-particle basis for electron band states. Received 4 September 2000     

Use and misuse of QCD sum rules,factorization and related topics

The purpose of this paper is twofold. First, we are prompted by some recent publications to reply to the criticism of the QCD sum-rules approach contained therein. Hopefully, some of the discussion is of wider interest. In particular, we point out that the multi-gluon operators unlike the multi-quark ones, relevant to the sum rules, do not factorize at large N_c. This implies that the masterfield, even if it is found, will be of no immediate help in evaluating the quarkonium spectrum. Second, we derive new sum rules for light quarks which are sensitive to the mean intensity of the gluon field in the vacuum (the so-called gluon condensate, or 〈vac|G²|vac〉). New sum rules confirm the standard value of 〈vac|G²|vac〉. Some casual remarks on the π⁰ transitions into two virtual photons, π⁰ → γ^*γ^*, are also presented. Finally, we enumerate (in sect. 7) basic points of the sum-rule approach and discuss, im brief, the unsolved problems.     

Decay of correlations in one and two dimensions

An exposition of some methods of proving exponential (stretched exponential) decay of correlations is given. One-dimensional strictly hyperbolic and quadratic maps and two-dimensional piecewise smooth, uniformly hyperbolic maps are considered. The emphasis is on the fundamental constructions of the Markov sieve method due to Bunimovich-Chernov-Sinai and those of Liverani's Hilbert metric method.     

Decay of correlations in a chaotic measure-preserving transformation

For a chaotic, area-preserving map on the torus, we study the decay of correlations in detail. Taking as observables the square-integrable functions, we find examples of decay rates which are algebraic, exponential, and faster than exponential. For correlations that decay exponentially the rate is sensitive to the choice of function. The implications for numerical experiments of this nonuniformity in the decay are discussed.     

Decay of correlations. IV. Necessary and sufficient conditions for a rapid decay of correlations

We considerN-particle systems whose probability distributions obey the master equation. For these systems, we derive the necessary and sufficient conditions under which the reducedn-particle (n) probabilities also obey master equations and under which the Ursell functions decay to their equilibrium values faster than the probability distributions. These conditions impose restrictions on the form of the transition rate matrix and thus on the form of its eigenfunctions. We first consider systems in which the eigenfunctions of theN-particle transition rate matrix are completely factorized and demonstrate that for such systems, the reduced probabilities obey master equations and the Ursell functions decay rapidly if certain additional conditions are imposed. As an example of such a system, we discuss a random walk ofN pairwise interacting walkers. We then demonstrate that for systems whoseN-particle transition matrix can be written as a sum of one-particle, two-particle, etc. contributions, and for which the reduced probabilities obey master equations, the reduced master equations become, in the thermodynamic limit, those for independent particles, which have been discussed by us previously. As an example of suchN-particle systems, we discuss the relaxation of a gas of interacting harmonic oscillators.Supported in part (grants to D.B. and K.E.S.) by the Advanced Research Projects Agency of the Department of Defense as monitored by the U.S. Office of Naval Research under Contract N00014-69-A-0200-6018, and in part (grant to I.O.) by the National Science Foundation.     

A GMSA calculation of the radial distribution functions of molten RbCl

Summary The generalized mean spherical approximation (GMSA) for a fluid of charged hard spheres of equal diameters is used for calculating the radial distribution functions of molten RbCl. The results are compared to neutron diffraction data and a good overall agreement is found between the experimental and the theoreticalg _ij (r). Further application of this same approach to the case of ionic melts with ionic species of different diameters is discussed. Work supported in part by Comitato Regionale Ricerche Nucleari and Struttura della Materia (CRRNSM), Sicily, Italy.