Pair Correlation Approximation Research Articles

Generalized chemical model for plasmas with application to the ionization potential depression

On the basis of the generalized Poisson–Boltzmann equation derived from the Bogolyubov chain of equations for the equilibrium distribution functions in the pair correlation approximation, a general expression is proposed for the Helmholtz free energy of a system that contains any number of components and whose particles interact via arbitrary potentials. This opens up an extraordinary opportunity to simultaneously treat a whole range of physical effects including partial ionization, quantum effects of diffraction and electron degeneracy, short- and long-range interactions of charged particles with neutrals, finite size effects, etc. It is shown that all medium constituents are tied together in a single screening matrix, whose determinant and trace determine the excess contribution to the free energy. The approach developed is then applied to the problem of the ionization potential depression (IPD) leading to quite simple analytical expressions, which turn out to be useful for various practical purposes. In particular, for a single ionization from the neutral state the IPD is shown to significantly depend on the ionization degree such that it consists of the difference of charged and neutral contributions for a fully ionized plasma and turns non-zero for an almost neutral medium. On the other hand, for a multiple ionization process finite size effects of atoms and ions are demonstrated to be of great importance and accounted for in order to achieve good agreement with experimental data on the IPD under warm dense matter conditions.

Relating composition, structural order, entropy and transport in multi-component molten salts

Molecular dynamics simulations of the LiF-BeF(2) molten salt mixture are used to establish relationships between composition, structural order, entropy, and transport properties of multi-component ionic liquids. A sharp rise in tetrahedral order associated with formation of the fluoroberyllate network occurs for compositions with BeF(2) concentrations greater than that of the Li(2)BeF(4)-BeF(2) eutectic. The excess entropy of the liquid in this regime, within the pair correlation approximation, is strongly correlated with the local tetrahedral order. The different degree of participation of beryllium, fluorine, and lithium ions in the cooperative dynamics of the fluoroberyllate network can be related to the degree of deviation from Rosenfeld-type excess entropy scaling, with the lithium ions remaining essentially unaffected by the liquid state network. We demonstrate that the deviations from Nernst-Einstein and Stokes-Einstein behaviour emerge only in temperature-composition regimes where tetrahedral order strongly correlates with the pair entropy. Implications for understanding structure-property relationships in other ionic liquids, such as molten salts, oxide melts, and RTILs are considered.

Self-consistent chemical model of partially ionized plasmas

A simple renormalization theory of plasma particle interactions is proposed. It primarily stems from generic properties of equilibrium distribution functions and allows one to obtain the so-called generalized Poisson-Boltzmann equation for an effective interaction potential of two chosen particles in the presence of a third one. The same equation is then strictly derived from the Bogolyubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy for equilibrium distribution functions in the pair correlation approximation. This enables one to construct a self-consistent chemical model of partially ionized plasmas, correctly accounting for the close interrelation of charged and neutral components thereof. Minimization of the system free energy provides ionization equilibrium and, thus, permits one to study the plasma composition in a wide range of its parameters. Unlike standard chemical models, the proposed one allows one to study the system correlation functions and thereby to obtain an equation of state which agrees well with exact results of quantum-mechanical activity expansions. It is shown that the plasma and neutral components are strongly interrelated, which results in the short-range order formation in the corresponding subsystem. The mathematical form of the results obtained enables one to both firmly establish this fact and to determine a characteristic length of the structure formation. Since the cornerstone of the proposed self-consistent chemical model of partially ionized plasmas is an effective pairwise interaction potential, it immediately provides quite an efficient calculation scheme not only for thermodynamical functions but for transport coefficients as well.

Assessing thermodynamic-dynamic relationships for waterlike liquids

Here we investigate a family of isotropic waterlike glass-forming liquids, in which each thermodynamic state point corresponds to a different potential energy surface which is prescribed to reproduce the g(OO)(r;T,rho) of the reference TIP4P-Ew water model potential. Although each isotropic potential is simulated separately, together the family of isotropic potentials displays anomalous dynamics with density and fragile diffusivity with temperature. By removing a common energy landscape, and therefore expected thermodynamic trends with temperature within a single potential, we can more rigorously evaluate whether various entropic measures used in popular phenomenological thermodynamic theories can quantitatively predict the diffusivity or viscosity. We find that the Adam-Gibbs relation between diffusion (or viscosity) and the temperature scaled configurational entropy, S(c), is a poor predictor of fragility trends and density anomalies when necessary anharmonic corrections are added. By contrast the Dzugutov scaling relationship that uses the pair correlation approximation to S(excess) approximately S(2) provides excellent agreement for diffusion anomalies and for fragile dynamics for weakly supercooled states for the family of isotropic potentials, within a single isotropic potential, and for the TIP4P-Ew model, but deviates strongly in all three cases at more deeply supercooled temperatures. By studying the microscopic dynamics at these low temperatures, we find an increased heterogeneity in the mobility of particle populations reflected in a highly non-Gaussian distribution of particle displacements, even at very long time scales. We conclude that after the onset of dynamical heterogeneity, new consideration of higher structural correlations and/or more complex connectivity paths between basins through barriers appear to be critical for the formulation of a predictive theory for dynamics.

Quantum many-body theory of qubit decoherence in a finite-size spin bath

Decoherence of a center spin or qubit in a spin bath is essentially determined by the many-body bath evolution. We develop a cluster-correlation expansion (CCE) theory for the spin-bath dynamics relevant to the qubit decoherence problem. A cluster-correlation term is recursively defined as the evolution of a group of bath spins divided by the cluster correlations of all the subgroups. This correlation accounts for the authentic (nonfactorizable) collective excitations within a given group. The bath propagator is the product of all possible cluster correlation terms. For a finite-time evolution as in the qubit decoherence problem, a convergent result can be obtained by truncating the expansion up to a certain cluster size. The two-spin cluster truncation of the CCE corresponds to the pair-correlation approximation developed previously [W. Yao et al., Phys. Rev. B 74, 195301 (2006)]. In terms of the standard linked cluster expansion, a cluster-correlation term is the infinite summation of all the connected diagrams with all and only the spins in the group flip-flopped, and thus the expansion is exact whenever convergence occurs. When the individual contribution of each higher-order correlation term to the decoherence is small (while all the terms combined in product could still contribute substantially), as the usual case for relatively large baths, where the decoherence could complete well within the bath spin flip-flop time, the CCE coincides with the cluster expansion [W. M. Witzel and S. Das Sarma, Phys. Rev. B 74, 035322 (2006)]. For small baths, however, the qubit decoherence may not complete within the bath spin flip-flop time scale and thus individual higher-order cluster correlations could become significant. In such cases, only the CCE converges to the exact coherent dynamics of multispin clusters. We check the accuracy of the CCE in an exactly solvable spin-chain model.

Estimating the entropy of liquids from atom–atom radial distribution functions: silica, beryllium fluoride and water

Molecular dynamics simulations of water, liquid beryllium fluoride and silica melt are used to study the accuracy with which the entropy of ionic and molecular liquids can be estimated from atom–atom radial distribution function data. The pair correlation entropy is demonstrated to be sufficiently accurate that the density–temperature regime of anomalous behaviour as well as the strength of the entropy anomaly can be predicted reliably for both ionic melts as well as different rigid-body pair potentials for water. Errors in the total thermodynamic entropy for ionic melts due to the pair correlation approximation are of the order of 10% or less for most state points, but can be significantly larger in the anomalous regime at very low temperatures. In the case of water, the rigid-body constraints result in larger errors in the pair correlation approximation, between 20 and 30%, for most state points. Comparison of the excess entropy, S e, of ionic melts with the pair correlation entropy, S 2, shows that the temperature dependence of S e is well described by T −2/5 scaling across both the normal and anomalous regimes, unlike in the case of S 2. The residual multiparticle entropy, ΔS = S e − S 2, shows a strong negative correlation with tetrahedral order in the anomalous regime.

Waterlike hierarchy of anomalies in a continuous spherical shouldered potential

We investigate by molecular dynamics simulations a continuous isotropic core-softened potential with attractive well in three dimensions, introduced by Franzese [J. Mol. Liq. 136, 267 (2007)], that displays liquid-liquid coexistence with a critical point and waterlike density anomaly. Besides the thermodynamic anomalies, here we find diffusion and structural anomalies. The anomalies, not observed in the discrete version of this model, occur with the same hierarchy that characterizes water. We discuss the differences in the anomalous behavior of the continuous and the discrete model in the framework of the excess entropy, calculated within the pair correlation approximation.

CONTROL OF ELECTRON SPIN DECOHERENCE IN MESOSCOPIC NUCLEAR SPIN BATHS

The electron spin decoherence by nuclear spins in semiconductor quantum dots is caused by quantum entanglement between the electron and the nuclei. The many-body dynamics problem of the interacting nuclear spins can be solved with the pair-correlation approximation which treats the nuclear spin flip-flops as mutually independent. The nuclear spin dynamics can be controlled by simply flipping the electron spin so that the electron is disentangled from the nuclei and hence its lost coherence is restored.

Ionic melts with waterlike anomalies: Thermodynamic properties of liquid BeF2

Thermodynamic properties of liquid beryllium difluoride (BeF(2)) are studied using canonical ensemble molecular dynamics simulations of the transferable rigid ion model potential. The negative slope of the locus of points of maximum density in the temperature-pressure plane is mapped out. The excess entropy, computed within the pair correlation approximation, is found to show an anomalous increase with isothermal compression at low temperatures which will lead to diffusional as well as structural anomalies resembling those in water. The anomalous behavior of the entropy is largely connected with the behavior of the Be-F pair correlation function. The internal energy shows a T(35) temperature dependence. The pair correlation entropy shows a T(-25) temperature dependence only at high densities and temperatures. The correlation plots between internal energy and the pair correlation entropy for isothermal compression show the characteristic features expected of network-forming liquids with waterlike anomalies. The tagged particle potential energy distributions are shown to have a multimodal form at low temperatures and densities similar to those seen in other liquids with three-dimensional tetrahedral networks, such as water and silica.

Control of electron spin decoherence caused by electron–nuclear spin dynamics in a quantum dot

Control of electron spin decoherence in contact with a mesoscopic bath of many interacting nuclear spins in an InAs quantum dot is studied by solving the coupled quantum dynamics. The nuclear spin bath, because of its bifurcated evolution predicated on the electron spin up or down state, measures the which-state information of the electron spin and hence diminishes its coherence. The many-body dynamics of the nuclear spin bath is solved with a pair-correlation approximation. In the relevant timescale, nuclear pair-wise flip–flops, as elementary excitations in the mesoscopic bath, can be mapped into the precession of non-interacting pseudo-spins. Such mapping provides a geometrical picture for understanding the decoherence and for devising control schemes. A close examination of nuclear bath dynamics reveals a wealth of phenomena and new possibilities of controlling the electron spin decoherence. For example, when the electron spin is flipped by a π-pulse at τ, its coherence will partially recover at as a consequence of quantum disentanglement from the mesoscopic bath. In contrast to the re-focusing of inhomogeneously broadened phases by conventional spin-echoes, the disentanglement is realized through shepherding quantum evolution of the bath state via control of the quantum object. A concatenated construction of pulse sequences can eliminate the decoherence with arbitrary accuracy, with the nuclear–nuclear spin interaction strength acting as the controlling small parameter.

Entropy, diffusivity, and structural order in liquids with waterlike anomalies

The excess entropy, defined as the difference between the entropies of the liquid and the ideal gas under identical density and temperature conditions, is studied as a function of density and temperature for liquid silica and a two-scale ramp potential, both of which are known to possess waterlike liquid state anomalies. The excess entropy for both systems is evaluated using a fairly accurate pair correlation approximation. The connection between the excess entropy and the density and diffusional anomalies is demonstrated. Using the pair correlation approximation to the excess entropy, it can be shown that if the energetically favorable local geometries in the low and high density limits have different symmetries, then a structurally anomalous regime can be defined in terms of orientational and translational order parameters, as in the case of silica and the two-scale ramp system but not for the one-scale ramp liquid. Within the category of liquids with waterlike anomalies, we show that the relationship between the macroscopic entropy and internal energy is sufficient to distinguish between those with local anisotropy and consequent open packings at low densities and those with isotropic interactions but multiple length scales. Since it is straightforward to evaluate the pair correlation entropy and internal energy from simulations or experimental data, such plots should provide a convenient means to diagnose the existence as well as type of anomalous behavior in a range of liquids, including ionic and intermetallic melts and complex fluids with ultrasoft repulsions.

Pb()O3-type Perovskites: Part I. Pair-correlation Theory of Order-disorder Phase Transition

The limitation of the long-range order parameter and the necessity of the short-range order parameter for the thermodynamic description of Pb()O3-type perovskites are discussed. Based on the discussion, a statistical thermodynamic model that takes into account the configuration of the neighboring B-site ions (B′ and B″ cations) was developed. A pair-correlation approximation was used in the calculation of the configurational entropy and the long-range coulombic interaction energy between the nearest B-site ions. The theoretical calculations using Pb(Sc1/2Ta1/2)O3 (PST) and Pb(Sc1/2Nb1/2)O3 (PSN) systems indicate that the short-range order parameter persists over a wide range of temperatures examined (0–1800 K) and that there possibly occur consecutive long-range order-disorder transitions in the configuration of B-site cations. The possibility of the existence of short-range ordering above the long-range order-disorder transition temperature was also examined using the annealed PSN specimen as a typical example of Pb()O3-type perovskites.

Green's-function approach to atomic many-body calculations with application to the ground state in alkali-metal atoms

In this paper we apply the single-particle Green's-function method to the atomic many-body perturbation theory. We present an all-order evaluation scheme for the proper self-energy operator based on the systematic use of Dyson's integral equations. The method is complete to third order in perturbation theory and, in addition, large classes of higher-order effects are included by solving the Dyson equations. Certain classes of many-body correlation effects beyond the pair-correlation approximation are included. The proposed method is tested by calculating the ground-state valence-electron binding energy for the alkali-metal atoms Li, Na, and K. Agreement with experimental results corresponds to an error in the correlation energy contribution of 3--4%. If certain three-particle effects, not evaluated in this work, are added, the agreement with experiments is, for sodium and potassium, approximately within 1% of the correlation energy.

Accurate calculations of transition probabilities, isotope shifts and hyperfine structures for some allowed - transitions in B I, C II and C I

Results from systematic multiconfiguration Hartree - Fock calculations of transition probabilities, isotope shifts and hyperfine structures of the - and - transitions in B I, the - transitions in C II and the - transition in C I are reported. Higher-order correlation effects beyond the pair-correlation approximation are shown to be important for the transition probabilities, and are included in large configuration interaction calculations. For all the transitions except one, the agreement between the length and velocity forms of the weighted oscillator strength is better than 0.4%. The present results are believed to be substantially more accurate than those of other theories.

The phase diagrams of an Ising spin-1 random site model for ternary alloy

A Blume-Emery-Griffths three components system in which one component is randomly distributed and the other two components are forming sublattice ordering is studied using the pair correlation approximation. The phase diagrams in different typical interaction energy regions are calculated and the crossover behavior of phase diagrams near the boundary line between the two interaction energy regions is also investigated.

Global analysis of phase states in a random-site model.

The global features of the random-site model of C IV atoms for the alloys (A III B V ) 1-x C 2x IV are determined using the pair-correlation approximation in the limit at the absolute zero of temperature. There are four different types of phase-state configurations for all combinations of nearest-neighbor interaction energies. The first type has a site percolation threshold at the critical composition x c of the order-disorder transition. The second type has a critical composition x c =1/6. The phase-state configuration on the boundary line between types 1 and 2 has critical composition x c =3/8

Magnetic susceptibility of diluted magnetic semiconductor alloys Cd1-xCoxS in the temperature range 40 mK

The magnetic susceptibility of ${\mathrm{Cd}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Co}}_{\mathit{x}}$S has been measured over the temperature range 40 mK\ensuremath{\le}T\ensuremath{\le}400 K for alloy compositions 0.0016\ensuremath{\le}x\ensuremath{\le}0.082. The value of the effective exchange integral was obtained from the susceptibility data using the pair-correlation approximation and the mean-field approach, yielding ${\mathit{J}}_{\mathrm{eff}}$/${\mathit{k}}_{\mathit{B}}$=-22\ifmmode\pm\else\textpm\fi{}4 K and -20\ifmmode\pm\else\textpm\fi{}4 K, respectively. The dependence of \ensuremath{\chi} on T indicates the presence of a small temperature-independent contribution, which has been found to be consistent with the prediction of the crystal-field model for a ${\mathrm{Co}}^{2+}$ ion in a wurtzite-structure lattice. Results of the crystal-field model, together with the pair-correlation approximation, were also successfully applied to describe the susceptibility anisotropy observed at very low temperatures.

Specific heat of Cd1-xCoxS and Cd1-xCoxSe at low temperatures.

The specific heat of two diluted magnetic semiconductors, ${\mathrm{Cd}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Co}}_{\mathit{x}}$S and ${\mathrm{Cd}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Co}}_{\mathit{x}}$Se, both having the wurtzite structure, has been measured in the temperature range 0.4--4.0 K, and in various magnetic fields up to 2.8 T. In the dilute limit (x\ensuremath{\simeq}0.001), both materials exhibit broad maxima in the specific heat resulting from the zero-field splitting, 2D, of the ground orbital state of the ${\mathrm{Co}}^{2+}$ ion. From quantitative analysis we have obtained D/${\mathit{k}}_{\mathit{B}}$=0.97\ifmmode\pm\else\textpm\fi{}0.03 K for ${\mathrm{Cd}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Co}}_{\mathit{x}}$S, and D/${\mathit{k}}_{\mathit{B}}$=0.72\ifmmode\pm\else\textpm\fi{}0.03 K for ${\mathrm{Cd}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Co}}_{\mathit{x}}$Se. For larger concentrations x of ${\mathrm{Co}}^{2+}$ ions (x=0.0077), exchange interactions have to be included in the theoretical model. We have used the nearest-neighbor pair-correlation approximation (NNPA), with the distance dependence of the exchange integral given by ${\mathit{J}}_{\mathit{i}}$(${\mathit{R}}_{\mathit{i}}$)\ensuremath{\sim}(${\mathit{R}}_{\mathit{i}}$${)}^{\mathrm{\ensuremath{-}}\mathit{n}}$. This approximation describes the specific-heat data quite well in the present case. The best fit of the NNPA curve has been achieved for n=6.0\ifmmode\pm\else\textpm\fi{}1.0, which is very close to that for Mn-based diluted magnetic semiconductors.

Analysis of long-range magnetic interactions in diluted magnetic semiconductors (abstract)

Specific-heat, susceptibility, and high-field magnetization of a number of diluted magnetic semiconductors will be reported. These include Zn(Mn)Se, Zn(Mn)Te, [Zn(Mn)]3As2, [Cd(Mn)]3As2, with various Mn concentrations, ranging from above to far below the percolation limit. A paramagnetic to spin-glass transition has been observed in all compounds in the whole range of concentrations. The concentration dependence of the freezing temperature was found to be compatible with a radial dependence of the antiferromagnetic exchange interaction between Mn ions of the type J(R)∼R−n, with n ranging from 7 [Zn(Mn)Se, Zn(Mn)Te] to 4 in [Cd(Mn)]3As2. Calculations of C, χ, and M have been performed by means of an extended pair-correlation approximation, including both a nearest-neighbor and a long-range (J∼R−n) interaction, as indicated by the experimental results. A satisfactory simultaneous description of all data could be obtained, whereas no adjustment of the ‘‘statistical’’ distribution of the magnetic ions was necessary. We will report a similar analysis of the available data on other diluted magnetic semiconductors, such as Cd(Mn)Te, Cd(Mn)Se, Hg(Mn)Se, and Hg(Mn)Te. Also in these cases a fair theoretical description of the thermodynamic properties can be obtained, provided the long-range character of the exchange is taken into account.

Dynamics of a spin-1 model with the pair correlation

A spin-1 or three state system will undergo a first or second order phase transition depending on the ratio of coupling parameters α. Using the pair correlation approximation, the transition temperature is determined in order to establish the unstable, the metastable, as well as the stable regions of this cooperative system. The dynamics of the system is studied by means of the most probable path method and the flow lines and fixed points of the system are given for zero field. The choice of possible initial conditions is discussed. The role of the unstable points in the phase diagram, as separators between the stable and metastable points, is described, and they are computed for a number of cases.