Direct correlation functions and bridge functions in additive hard-sphere mixtures

A method to obtain (approximate) analytical expressions for the radial distribution functions in a multicomponent mixture of additive hard spheres that was recently introduced is used to obtain the direct correlation functions and bridge functions in these systems. This method, which yields results practically equivalent to the generalized mean spherical approximation and includes thermodynamic consistency, is an alternative to the usual integral equation approaches and requires as input only the contact values of the radial distribution functions and the isothermal compressibility. Calculations of the bridge functions for a binary mixture using the Boublik-Mansoori-Carnahan-Starling-Leland equation of state are compared to parallel results obtained from the solution of the Percus-Yevick equation. We find that the conjecture recently proposed by Guzman and del Rio (1998, 98, Molec. Phys., 95, 645), stating that the zeros of the bridge functions occur approximately at the same value of the shifted distance for all pairs of interactions, is at odds with our results. Moreover, in the case of disparate sizes, even the Percus-Yevick bridge functions do not have this property. It is also found that the bridge functions are not necessarily non-positive.     

Structure functions

Structure functions are a measure of the partonic structure of hadrons, which is important for any process which involves colliding hadrons. They are a key ingredient for deriving partons distributions in nucleons. In recent years dramatic progress has been made in the understanding of the nucleon structure and the precision of its partonic content, due to vast theoretical progress, and the availability of new high precision measurements. This review gives an overview on present structure functions and related data, and on the most recent techniques used to extract parton distribution functions to describe the structure of the proton. Special attention is given to the determination of the uncertainties on the parton distributions.     

Localized wannier functions

Wannier functions constructed from k.p Bloch functions for a crystal with inversion symmetry are shown to have minimal width and to be real and symmetrical (or antisymmetrical) about their center. Therefore, at least for non-degenerate bands, they are exponentially decreasing functions.     

Approximate Wannier functions

We present a method for constructing approximate Wannier functions from finite sets of Bloch functions specified at special points in the Brillouin zone.     

Structure functions at HERA

HERA provides the key facility for the measurement of proton structure functions. Formalism and methods are outlined for the measurement and interpretation of inclusive structure functions, including the use of polarised e ^± beams. The measurement of charm, beauty and photon structure functions is discussed, together with special runs at low proton energy for measurement of the longitudinal structure function. Finally, the functions accessed using polarised beams on polarised targets are indicated.     

Hierarchical wave functions revisited

We study the hierarchical wave functions on a sphere and on a torus. We simplify some wave functions on a sphere or a torus using the analytic properties of wave functions. The open question, the construction of the wave function for quasielectron excitations on a torus, is also solved in this paper.     

Graphical functions in parametric space

Graphical functions are positive functions on the punctured complex plane \({\mathbb C}{\setminus }\{0,1\}\) which arise in quantum field theory. We generalize a parametric integral representation for graphical functions due to Lam, Lebrun and Nakanishi, which implies the real analyticity of graphical functions. Moreover, we prove a formula that relates graphical functions of planar dual graphs.     

Numerical calculation of localized (Wannier) functions from ab-initio Hartree-Fock wave functions

The Fourier transformation necessary to obtain localized (Wannier) functions from delocalized ab-initio crystal Hartree-Fock (Bloch) functions is carried out for the one-dimensional models of solids. Combinations of Wannier functions from different bands lead to even more localized functions in close analogy to localization in molecules.     

Causal functions in general relativity

Using the notion of size or volume of future or past of an event, causal functions are defined on a space-time and their behavior is examined in certain space-time models. These functions are then employed to obtain a unified characterization of causality conditions on a spacetime in terms of their simple functional properties like one-oneness, monotonicity, etc. and limiting behavior of these functions along timelike curves. Causal or ideal points boundary of space-time has also been characterized and classified using these causal functions.     

Kinetic Green's functions

It is shown that the theory of kinetic Green's functions coincides completely with the theory of vacuum Green's functions after the choice of the operatorO ^?1 in its overall part. An expression for the energy of the system is obtained directly in terms of the mass operators. An equation is given that is a generalization of the Boltzmann equation and has the same mathematical structure.     

Distribution functions and green's functions

A unitary transformation is indicated which makes it possible when computing a partially traced density matrix to use the method of two-time quantum Green's functions. For systems in strong nonequilibrium, an integral equation is found which describes both the initial and kinetic stages of relaxation of the density matrix of a subsystem from any initial distribution.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 77–81, May, 1978.I am very grateful to V. L. Bonch-Bruevich for his constant attention.     

Balance functions at RHIC

The balance function is based on the principle that charge is locally conserved when particles are pair produced. Balance functions have been measured for all charged pairs, identified pion pairs, and identified charged kaon pairs in Au+Au collisions at $\sqrt {s_{NN} } = 200$ GeV and p+p collisions at $\sqrt {s_{NN} } = 200$ GeV at the Relativistic Heavy Ion Collider using STAR. Balance functions for all charged particles from Au+Au scale smoothly with centrality to the p+p value. Balance functions for charged particles and pions are narrower in central collisions than in peripheral collisions consistent with trends predicted by models incorporating the concept of late hadronization. Balance functions for kaon pairs represent a strangeness balance. Balance functions for kaons are narrower than those for pion pairs and may show less dependence on centrality.     

Technique for "tuning" vocal tract area functions based on acoustic sensitivity functions

A technique for modifying vocal tract area functions is developed by using sum and difference combinations of acoustic sensitivity functions to perturb an initial vocal tract configuration. First, sensitivity functions [e.g., Fant and Pauli, Proc. Speech Comm. Sem. 74, 1975] are calculated for a given area function, at its specific formant frequencies. The sensitivity functions are then multiplied by scaling coefficients that are determined from the difference between a desired set of formant frequencies and those supported by the current area function. The scaled sensitivity functions are then summed together to generate a perturbation of the area function. This produces a new area function whose associated formant frequencies are closer to the desired values than the previous one. This process is repeated iteratively until the coefficients are equal to zero or are below a threshold value.     

Pressure-dependent partition functions

It is shown that the partition functions relating to statistical ensembles can be classified as cumulative, distributive or differential with regard to any of the extensive thermodynamic variables. The Laplace transforms involved in the general formulation of transformed partition functions, when extensive parameters are replaced by their conjugate intensive variables, are two-sided and appear in different forms according to the classification mentioned.

The petit partition function at constant pressure can be defined for both classical and quantal systems as a Stieltjes integral or dimensionless Laplace transform over the volume-dependent partition function. This expression contains no arbitrary external parameters and satisfies all the conditions formulated by Münster; it can be interpreted as the ratio of two partition functions, the one relating jointly to the system and a macroscopic boundary, and the second to the boundary alone.

It is known that the constant pressure grand partition function as defined by Guggenheim diverges for all thermodynamically compatible values of its independent variables. It is shown that the Gibbs-Duhem relation, and hence all the statistical properties of the system, except its size, can be derived by differentiating the reciprocal of this, or a similarly defined, function, not its logarithm as with other partition functions.

The mathematical differences arising out of the various proposed definitions are illustrated in a number of simple examples.     

Quantum mechanics without wave functions

The phase space formulation of quantum mechanics is based on the use of quasidistribution functions. This technique was pioneered by Wigner, whose distribution function is perhaps the most commonly used of the large variety that we find discussed in the literature. Here we address the question of how one can obtain distribution functions and hence do quantum mechanics without the use of wave functions.     

Quantum fields presentation and generating functions of symplectic Schur functions and symplectic universal characters

This paper is concerned with construction of quantum fields presentation and generating functions of symplectic Schur functions and symplectic universal characters. The boson-fermion correspondence for these symmetric functions have been presented. In virtue of quantum fields, we derive a series of infinite order nonlinear integrable equations, namely, universal character hierarchy, symplectic KP hierarchy and symplectic universal character hierarchy, respectively. In addition, the solutions of these integrable systems have been discussed.     

Two-particle Green's functions in non-equilibrium matter

The method of the derivation of two-particle Green's functions in non-equilibrium matter is developed. The closed set of equations for the vertex functions and also for the two-particle Green's functions is obtained by means of the summation of the series of irreducible diagrams. The solution of such equations completely defines the two-particle Green's functions in matter.     

Two-particle Green's functions in non-equilibrium matter

The method of derivation of two-particle Green's functions in the non-equilibrium matter has been developed. The closed set of equations for the vertex functions, as well as for the two-particle Green's functions, is obtained by means of the summation of the series of indecomposable diagrams. The solution of such equations completely determines the two-particle Green's functions in the matter.     

Approximation of Green's functions

Special symmetries of the Green's functions of a non-relativistic many fermion-system and conservation laws, expressible by hermitian generators, are formulated as relations for a Green's function operator. Approximations for the Green's functions, defined as partial summations of the perturbation expansion, and consistent with the symmetries and conservation laws are presented.