One-particle Correlation Functions Research Articles

Structure of an inhomogeneous fluid mixture: A new weighted density-functional theory within a perturbative approach

A simple density-functional approach is developed for an inhomogeneous fluid mixture where the functional Taylor expansion of the perturbative approach has been used along with a nonperturbative weighted density prescription. The functional Taylor expansion of the one-particle direct correlation function (DCF) of the inhomogeneous fluid mixture is truncated at second order in density inhomogeneity and the effect of various higher-order terms is taken into account by evaluating the third-order DCF at an weighted density obtained by using a suitable weight function which obeys certain conditions in the homogeneous limit. The proposed approach uses the two-particle DCFs of the corresponding uniform fluid mixture and their various density derivatives as inputs. The calculated numerical results for the density and concentration profiles of hard sphere mixtures near hard walls for different set of bulk parameters are shown to be in very good agreement with the available simulation data.

Structure of electric double layers: A self-consistent weighted-density-functional approach

A self-consistent weighted-density-functional approach is developed for the structure of electric double layer using the restricted primitive model which corresponds to charged hard sphere ions and a continuum solvent. The one-particle correlation function of this inhomogeneous system is evaluated using suitably averaged weighted densities for the short range hard sphere as well as the long range electrical components. The hard-sphere contribution is evaluated by making use of the universality of the density functionals and the correlation function of the uniform hard sphere fluid obtained through the integral equation theory with an accurate closure relation whereas mean spherical approximation is employed for the electrical contribution. Numerical results on the ionic density profile and the mean electrostatic potential near the electrode surface at several surface charge densities are found to show very good agreement with the available simulation results.

Incommensurate and superconducting phases in an exactly solvable model

An integrable lattice model of strongly interacted electrons with nearest-neighbor and next-nearest-neighbor hoppings is proposed and investigated. The exact ground-state phase diagram is calculated as a function of an on-site interaction, a value of the hopping integral between next-nearest-neighbor lattice sites and a band filling (the nearest-neighbor hopping integral is chosen equal to unity). The model describes incommensurate and superconducting phases which are realized simultaneously in a definite region of interaction parameters and a band filling. The long-distance asymptotics of the density-density and one-particle correlation functions are calculated in the incommensurate phase.

Analysis of one-and two-particle spectra at RHIC based on a hydrodynamical model

We calculate the one-particle hadronic spectra and correlation functions of pions based on a hydrodynamical model. Parameters in the model are so chosen that the one-particle spectra reproduce experimental results of √s= 130 AGeV Au + Au collisions at RHIC. Based on the numerical solution, we discuss the space-time evolution of the fluid. Two-pion correlation functions are also discussed. Our numerical solution suggests the formation of the quark-gluon plasma with large volume and low net baryon density.

Density functional theory of inhomogeneous fluid mixture based on bridge function

A simple density functional theory is proposed for an inhomogeneous fluid mixture by approximating its one-particle correlation function in terms of the second-order direct correlation functions and the bridge function of the corresponding homogeneous system. The theory is applied to predict the structure of a binary hard sphere mixture as well as Lennard-Jones fluid mixture near a hard wall, and the calculated density profiles for both the components are shown to agree quite well with the corresponding computer simulation results for both the systems. This theory for an inhomogeneous fluid mixture is further applied to homogeneous hard sphere mixture as well as Lennard-Jones fluid mixture and the calculated radial distribution functions are found to compare quite well with the same obtained through integral equation theory of fluid mixture.

Density Functional Theory for the Nonspecific Binding of Salt to Polyelectrolytes: Thermodynamic Properties

The thermodynamics of the nonspecific binding of salt to a polyelectrolyte molecule is studied using a density functional approach. The polyelectrolyte molecule is modeled as an infinite, inflexible, and impenetrable charged cylinder and the counterions and co-ions are modeled as charged hard spheres of equal diameter. The density functional theory is based on a hybrid approach where the hard-sphere contribution to the one-particle correlation function is evaluated nonperturbatively and the ionic contribution to the one-particle correlation function is evaluated perturbatively. The advantage of the approach is that analytical expressions are available for all the correlation functions. The calculated single ion preferential interaction coefficients, excess free energy, and activity coefficients show a nonmonotonic variation as a function of polyion charge in the presence of divalent ions. These properties display considerable departure from the predictions of the nonlinear Poisson-Boltzmann (NLPB) equation, with qualitative differences in some cases, which may be attributed to correlation effects neglected in the NLPB theory.

Structure of electric double layers: A simple weighted density functional approach

A simple weighted density functional approach 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. The approach is designed in such a way, that the calculation of the weight function is decoupled from the weighted density. 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. The corresponding results for the nonprimitive molecular solvent model provide insight into the layering effect and the charge inversion phenomena.

Structure of binary hard-sphere mixtures near a hard wall: A simple weighted-density-functional approach

The structure of binary hard-sphere mixtures near a hard wall is studied using a density functional theory. The formalism is based on a simple weighted density approach for the one-particle correlation functions of the nonuniform system, and requires as input only the one- and two-particle direct correlation functions of the corresponding uniform system. The approach is designed in a way, where the weight function is decoupled from the weighted density. Numerical results on the density profiles are shown to compare well with available simulation data.

Density Functional Theory for the Distribution of Small Ions around Polyions

A density functional theory is presented for the distribution of charged hard spheres (model for salt) around an infinite, rigid, and impenetrable charged cylinder (model for DNA or tobacco mosaic virus). The theory is based on a weighted density approach where the hard-sphere contribution to the one-particle correlation function is evaluated nonperturbatively using a position dependent effective density, and the ionic part is obtained through a second-order functional Taylor expansion around a uniform fluid. The theory is in good agreement with Monte Carlo simulations for the density distribution of monovalent, divalent, and mixed salts. For axial charge densities corresponding to DNA, the hypernetted chain integral equation theory is not as accurate as the density functional theory, but both liquid state approaches are superior to the Poisson−Boltzmann theory. For higher axial charge densities the density functional theory predicts interesting charge inversion effects that are absent in the nonlinear Po...

Highly charged colloidal suspensions in planar slits

A simple density functional approximation, which is based both on the density functional Taylor series expansion of the one-particle direct correlation function (DCF) and on the exact contact value theorem for a structureless hard wall with infinity wall distance, has been developed to study the structural properties of a highly charged colloidal suspension and compared with the computer simulation. Two kinds of two-particle DCFs, which are the rescaled mean spherical approximation (RMSA) and the Rogers-Young (RY) closure relation, have been used to calculate the local concentration profiles of a highly charged colloidal suspension confined in charged silt walls as input. The calculated results show that for a structureless hard wall the present approximation is better than the hypernetted chain (HNC) functional approximation and describes well the structural properties of a confined colloidal suspension compared with the computer simulation. However, the agreement between the computer simulation and the theory for the density profiles deteriorates with increasing the wall-particle interaction.

Density functional approximations for confined classical fluids

A density functional approximation, which is based on both the density functional Taylor series expansion of the one-particle direct correlation function and the exact contact value theorem for a hard wall, has been proposed to study the structural properties of confined classical fluids. The approximation has been applied to calculate the density profiles of sticky hard-sphere fluids confined in structureless hard walls. The calculated density profiles have shown that the present approximation compares very well with the results from the computer simulation. Furthermore, a density functional perturbative approximation, which is based on both the weighted-density approximation for the repulsive part of potential and the present approximation for the attractive part of potential, has been developed to predict the density profiles of model fluids with the attractive part of potential and has been applied to calculate the density profiles of hard-sphere Yukawa fluids near a planar slit. The calculated results also show that the proposed perturbative approximation is a significant improvement upon those of the modified version of the Lovett-Mou-Buff-Wertheim, and compares very well with the computer simulation.

Thermodynamic perturbative approach for simple fluids: Structure of a confined square-well fluid

An approximation, which is based on both the weighted-density approximation (WDA) of Tarazona [Phys. Rev. A 31, 2672 (1985)] for the repulsive part of the model potential, and the density-functional approximation (CNPR) of Calleja et al. [Mol. Phys. 59, 973 (1991)] for the attractive part of the model potential, has been proposed to study the structural properties of simple fluids and is abbreviated as WDA-CNPR. The WDA-CNPR approximation can be considered as an extended Choudhury-Ghosh approximation, which is based on the density-functional expansion of a one-particle direct correlation function corresponding to the attractive part of the model potential. It has been applied to predict the density profiles of a confined square-well fluid, and compared with the computer simulation. The calculated results show that for the square-well fluid confined in planar slits the WDA-CNPR approximation is a significant improvement upon those of the Choudhury-Ghosh approximation, and compares well with the computer simulation. For the weak fluid-wall interaction a very good agreement between the results of theory and computer simulation are obtained, but the agreement deteriorates with the increase of the fluid-wall interaction.

The Nagaoka instability and off-diagonal superconductivity in the finite Hubbard lattice

The first strict evidence for time-reversal symmetry breaking and change in statistics of electrons in U(1) gauge field, induced by periodic boundary conditions is demonstrated for ld Hubbard model with U→ ∞. The exact ground state energy, eigenfunction and one-particle density correlation function are calculated for arbitrary number of electrons and lattice sites. The criteria for the stability of either the Nagaoka state or spontaneously broken superconducting state with off-diagonal long-range order are found. The theory predicts the existence of superconductivity and ferromagnetism for electrons in periodic lattices and mesoscopic rings. The electrons in lattices are shown to provide for the presence of parity-dependent paramagnetic and diamagnetic persistent currents in the ground state.

Superconductivity in the two-dimensional Hubbard model: One-particle correlation functions.

The one-particle correlation functions of a ${\mathit{d}}_{\mathit{x}}^{2}$-${\mathit{y}}^{2}$ superconducting state in the two-dimensional Hubbard model are investigated within the fluctuation-exchange approximation. This approximation has been previously applied to investigate properties of the Hubbard-model normal state, including incipient instabilities. Results are obtained for the wave vector and temperature dependence of the one-particle energy gap. A miximum gap ratio 2${\mathrm{\ensuremath{\Delta}}}_{\mathit{k}}^{\mathrm{max}}$(T=0)/${\mathit{k}}_{\mathit{B}}$${\mathit{T}}_{\mathit{c}}$ of order 10 is obtained for intermediate coupling strengths and electron densities near one per site. The potential appearance of spin excitons in two-particle response functions is discussed.

Solvation forces in ionic and neutral liquids: A density functional approach

The solvation forces between two planar charged surfaces in ionic solutions, corresponding to charged and neutral hard spheres representing the ions and the solvent, respectively, are studied here using a weighted density functional theory for inhomogeneous Coulomb systems developed by us recently. The hard sphere contributions to the one-particle correlation function are evaluated nonperturbatively using a position-dependent effective density, while the electrical contributions are obtained through a perturbative expansion around this weighted density. The calculated results on the solvation forces between two charged hard walls compare well with available simulation results for ionic systems. For a neutral system, the present results show good agreement with the experimentally observed oscillating forces for two mica surfaces in octamethylcyclotetrasiloxane. The present approach thus provides a direct route to the calculation of interaction energies between colloidal particles.

Quasi Fermi distribution and resonant tunneling of quasiparticles with fractional charges.

We study the resonant tunneling of quasiparticles (anyons) through an impurity between the edges of a fractional quantum Hall sample. These quasiparticles are anyons, but their equilibrium one-particle correlation functions are shown to have some quasi Fermi properties. The broken symmetry of many-particle states at the impurity yields a new selection rule for the resonant tunneling: The resonance is suppressed unless an integer number of electrons occupies the impurity. This rule allows an explanation of the scaling behavior observed in the mesoscopic fluctuations of the conductivity in the fractional quantum Hall effect.

The WZNW model at two loops

We study perturbatively the (conformal) WZNW model. At one loop we compute one-particle irreducible two- and three-point current correlation functions, both in the conventional version and in the classically equivalent, chiral, nonlocal, induced version of the model. At two loops we compute the two-point function and find that it vanishes (modulo infrared-induced logarithms). We use dimensional regularization and the R ∗ operation for removing infrared divergences. The outcome of the calculations is insensitive to the treatment of the ε μν tensor as a two-dimensional or d-dimensional object. Our results indicate that the one-particle irreducible current correlation functions constitute an effective action equal to the original WZNW action with the familiar level shift, k → k + h ̃ .

Weighted-density-functional theory of electrode-electrolyte interface: Beyond the primitive model.

A weighted-density-functional theory is developed for an inhomogeneous electrolyte solution near a planar charged electrode using a nonprimitive three-component model consisting of one neutral and two charged hard-sphere components representing the solvent and the ions, respectively. Both the hardsphere and electrical contributions to the one-particle correlation function are obtained nonperturbatively by evaluating the direct-correlation functions of the corresponding uniform system using appropriate effective densities. Numerical results on the density profiles of the ions and the solvent molecules and also the mean electrostatic potential near the electrode surface at several surface-charge densities are presented to obtain insight into the layering and charge-inversion phenomena occurring at the interface

Weighted-density-functional theory of nonuniform ionic fluids: Application to electric double layers

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.

Weighted-density-functional theory of nonuniform fluid mixtures: Application to the structure of binary hard-sphere mixtures near a hard wall.

A computationally practical density-functional theory of nonuniform fluid mixtures ``designed primarily for the study of interfacial phenomena'' is presented and applied to the structure of a binary hard-sphere mixture near a hard wall. The theory is based on a weighted-density approximation for the one-particle direct correlation functions of the nonuniform system, and requires as input only the one- and two-particle direct correlation functions of the corresponding uniform system. Numerical results for density and concentration profiles are presented and compared with available simulation data.