Quantum spin-{3 \over 2} models on the Cayley tree - optimum ground state approach

We present a class of optimum ground states for quantum spin- models on the Cayley tree with coordination number 3. The interaction is restricted to nearest neighbours and contains 5 continuous parameters. For all values of these parameters the Hamiltonian has parity invariance, spin-flip invariance, and rotational symmetry in the xy-plane of spin space. The global ground states are constructed in terms of a 1-parametric vertex state model, which is a direct generalization of the well-known matrix product ground state approach. By using recursion relations and the transfer matrix technique we derive exact analytical expressions for local fluctuations and longitudinal and transversal two-point correlation functions. Received 1 March 1999     

Search for singlet-triplet bistability or biradicaloid properties in polycyclic conjugated hydrocarbons: a valence-bond analysis

Two classes of molecules displaying singlet-triplet biradical bistability (i.e. species having significant biradicaloid properties) can be designed as follows. Alternant conjugated polycyclic hydrocarbons with numerous fixed double bonds (double bonds that remain unchanged in all its Kekulé resonance structures), a large number of Dewar resonance structures which measures the corresponding diradical resonance, and a small HOMO-LUMO band gap which measures the ease of thermal spin inversion are candidates for singlet triplet biradical bistability. Chichibabin's hydrocarbon ( 1 ) is an example. In addition, in the search for candidate molecules having singlet triplet bistability, one should also examine polycyclic conjugated systems having nonalternant induced spin frustration. Spin frustrated nonalternant polycyclic conjugated hydrocarbons will display singlet-triplet bistability (biradicaloid properties) and are generated from alternant valence-bond diradicals or Hückel molecular orbital diradicals having classical Kekulé structures by appropriate intramolecular joining of two starred or nonstarred positions with bonds, respectively.     

Quantum and classical correlations for a two-qubit X structure density matrix

We derive explicit expressions for quantum discord and classical correlation for an X structure density matrix. Based on the characteristics of the expressions, the quantum discord and the classical correlation are easily obtained and compared under different initial conditions using a novel analytical method. We explain the relationships among quantum discord, classical correlation, and entanglement, and further find that the quantum discord is not always larger than the entanglement measured by concurrence in a general two-qubit X state. The new method, which is different from previous approaches, has certain guiding significance for analysing quantum discord and classical correlation of a two-qubit X state, such as a mixed state.     

Correlated tracer diffusion in an ordered interface structure

In this paper, we postulate a simple two-dimensional structure that attempts to capture the character of many of the qualitative findings from computer simulations of diffusion paths in grain boundaries. We postulate two types of mechanism: those where single atom jumps occur and those where multiple atom jumps occur. We derive analytical expressions for the tracer correlation factors, including those correlation factors that appear in the analysis of the diffusion isotope effect. We also carry out Monte Carlo simulations of these correlation factors. We find very good agreement between the derived expressions for the correlation factors and the simulation results. We are able to show that, in the absence of knowledge about the kinetic energy factor ΔK, isotope effect experiments cannot differentiate between a simple atom-jump mechanism and multiple-atom-jump mechanism.     

Phase behavior of organic pollutants in supercritical water

Methods for analyzing, ranking, and predicting the global phase behavior and possible heterogeneous fluid equilibria in supercritical water-organic pollutant systems are discussed in terms of present-day conceptions of the global phase diagrams of binary mixtures. The phase equilibria of some classes of organic compounds (polycyclic aromatic hydrocarbons, polychlorinated biphenyls, polychlorinated dibenzodioxins and furans as well as some pesticides) in supercritical water are studied. Based on found correlations with the partition coefficient of organic substances in immiscible mixtures of octanol and water (K _OW ), we determine the binary interaction parameter k ₁₂ in a one-fluid mixture model. Analytical expressions for predicting the azeotropic states of binary mixtures are derived; the occurrence of azeotropic behavior in aqueous solutions of organic compounds is estimated. Results of calculations of phase equilibria and critical curves for earlier unstudied organic pollutants in supercritical water are described.     

Ground-state energy of a classical artificial molecule

We study the ground-state energy of a classical artificial molecule formed by two-dimensional clusters (artificial atoms) of N/2 charged particles separated by a distance d. For the small molecules of N = 2 and 4, we obtain analytical expressions for this energy. For the larger ones, we calculate the ground-state energy using molecular dynamics simulation for N up to 128. From our numerical results, we are able to find out a function to approximate the ground-state energy of the molecules covering the range from atoms to molecules for any inter-atom distance d and for particle number from N = 8 to 128 within a difference less than one percent from the MD data.     

The evolution of the cluster size distribution in a coagulation system

The coagulation equation with kernelK _ij =A+B(i+j)+C _ij and arbitrary initial conditions is studied analytically and a simple expression for the solution is found. For monodisperse initial conditions, we recover the known size distribution expressed in terms of a degeneracy factorN _k, which is determined by a recursion relation. For polydisperse initial conditions, a similar solution form is found, which includes a degeneracy factorN _kl, also determined by a recursion relation. The physical meaning ofN _kl and the recursion relation is given. A method to get explicit expressions forN _k andN _kl is illustrated. Finally, the pre-gel solution is given explicitly and a general method to get the post-gel solution is proposed.     

Exact nonrelativistic expressions for the tensor for scattering of light by atoms

Exact nonrelativistic analytical expressions are derived for dipole two-photon transitions between arbitrary multiplets of the hydrogen atom and positive hydrogenlike ions. The result is expressed in terms of a single Gauss hypergeometric function and polynomials whose degrees increase linearly with the number of nodes of the bound states of the quantum system. The cross sections of elastic scattering of light by K-and L-shells of the hydrogen atom are given as an example. It is demonstrated that by expanding the discrete-spectrum wave functions in ultraspherical polynomials it is also possible to obtain analytical expressions of the cross sections of two-photon transitions between states described by the Simons model potential. The basis consisting of Chebyshev polynomials is shown to be the best expansion basis, and the coefficients of such an expansion are given for a broad range of parameters of the problem. Calculation of the polarizability of the 5S-state of the rubidium atom is chosen as an example. Finally, the results are compared with the experimental data and the theoretical results of other researchers. Zh. éksp. Teor. Fiz. 111, 816–830 (March 1997)     

Supersonic Jet Spectroscopy Coupled to Chromatography for Very High Resolution Chemical Analysis

Abstract

Much effort by a great many researchers has been put into improving existing analytical techniques or developing new methods for the analysis of complex samples such as biological specimens, environmental contaminants, and naturally occurring substances. A particular example is the interest that has been shown in developing methods for the detailed analysis of polycyclic aromatic hydrocarbons (PAH) 111, real samples of which can be viewed with only “slight exaggeration, in the words of Hayes and Small 121, as “containing infinitesimal amounts of an infinite number of species.” PAH (see Fig. l), many of which are carcinogenic, are ubiquitous, being produced both naturally and by man whenever organic substances are heated or burned; they make up the bulk of coals, heavy crude oils, and tars. Similar analytical problems are presented by biological and other samples, where it may be necessary to detect and sometimes follow the course of a trace substance in a complex matrix. In the case of PAH samples, detailed characterization is associated with discrimination among substitutional isomers [3] The complexity of such samples and the high molecular weight of the components has made detailed analysis difficult. Numerous isomers are possible, the number of which increases nearly exponentially with molecular weight. However, seemingly small differences in molecular structure, such as the skeletal position of a methyl group substituent, have been found to sharply affect genotoxic properties [4,5], and presumably also affect other chemical processes such as liquefaction, combustion, and soot formation.     

Energy contributions in magnetite nanoparticles: computation of magnetic phase diagram,theory, and simulation

In this study, we present a theoretical analysis of magnetization processes by considering energy contributions in magnetite fine particles. The focus is on the K _S-driven magnetic phase transition taking place between the low surface-anisotropy ferrimagnetic state and the hedgehog configuration obtained in the high surface-anisotropy limit. Analytical expressions of energy terms (exchange, magnetocrystalline anisotropy, surface-anisotropy) are presented and their magnitudes are computed for different particle sizes. Monte Carlo simulations were also carried out for comparison purposes. A core–shell model is implemented for simulating magnetite nanoparticles between 2 and 10 nm in diameter. Our simulation framework is based on a three-dimensional classical Heisenberg-like Hamiltonian with nearest magnetic neighbors interactions. It includes exchange coupling, cubic magnetocrystalline anisotropy for core ions, and single-ion site surface-anisotropy for those atoms belonging to the shell. The magnetic phase diagram and comparisons between analytical and numerical results are presented and discussed.     

Kurtosis parameter of truncated standard and elegant Laguerre–Gaussian beams propagating through ABCD optical systems

On the basis of the propagation equation of truncated standard and elegant Laguerre–Gaussian beams, the closed-form propagation expressions for the kurtosis parameter K of standard and elegant Laguerre–Gaussian beams passing through apertured optical systems are derived, it is shown that the kutosis parameter K of standard and elegant Laguerre–Gaussian beams depend on order p and index m of Laguerre polynomial, the beam-truncated parameter δ and the generalized Fresnel number F. Detailed numerical examples are given to illustrate the analytical results.     

Third-order diamagnetic susceptibilities of hydrogenlike atoms

We develop a method for calculating diamagnetic susceptibilities based on higher-order perturbation theory for the wave function and energy of the excited states of the hydrogen atom with degeneracy of arbitrary multiplicity. We derive analytical expressions for third-order matrix elements in the spherical states |nlm〉 with fixed principal quantum number n and magnetic quantum number m. The formulas for the susceptibilities of doubly degenerate levels are represented in the form of radical-fractional relationships containing polynomials in the principal quantum number. We establish the existence of a monotonic interdependence between the absolute values of susceptibilities of the first three orders. We also present the results of numerical calculations for the states with n⩽6 and m⩽3 mixed by the field. Finally, for Rydberg states with large n and small m we detect the existence of a discontinuity in the interdependence of the susceptibilities at the boundary between the doublet and equidistant parts of the spectrum of diamagnetic sublevels with opposite parities. Zh. éksp. Teor. Fiz. 116, 838–857 (September 1999)     

Analytical representation of the density derivative of the Percus–Yevick hard-sphere radial distribution function

ABSTRACT

Explicit analytical expressions are presented for the density derivative, ?g_HS(R; ρ)/?ρ, of the Percus–Yevick approximation to the hard-sphere radial distribution function for R ≤ 6σ, where σ is the hard-sphere diameter and ρ = (N/V)σ³ is the reduced density, where N is the number of particles and V is the volume. A FORTRAN program is provided for the implementation of these for R ≤ 6σ, which includes code for the calculation of g_HS(R; ρ) itself over this range. We also present and incorporate within the program code convenient analytical expressions for the numerical extrapolation of both quantities past R = 6σ. Our expressions are numerically tested against exact results.     

Local-field correction of the charged Bose condensate for two and three dimensions

The local-field correction for the dielectric function of the two-dimensional and of the three-dimensional Bose condensate is calculated within a sum-rule version of the Singwi et al. (Phys. Rev.176, 589 (1968)) approach. We derive analytical expressions for small and large wave numbers and give analytical expressions for the density dependence. We compare the results of the groundstate energy for the three-dimensional system with Monte-Carlo computations. In two dimensions a roton structure in the plasmon dispersion is found at low boson density. The plasmon density of states is calculated. A correlation induced charge-density-wave instability in layered structures of two-dimensional Bose gases is discussed.     

Recursive calculations for processes with n gluons

A method is presented in which multigluon processes are calculated recursively. The technique is explicitly developed for processes where only gluons are produced and processes where in addition to the gluons also a quark-antiquark pair with or without a vector boson or e⁺e⁻ pair are present. The recursion relations are used to derive rigorously amplitudes for certain configurations, where most of the gluons have the same helicities. This proves a number of conjectures in the literature. Also expressions for amplitudes with collinear or soft gluons are derived.     

Influence of heterogeneous chemical reactions on the slip velocity of an inhomogeneous multicomponent gaseous mixture

In constructing a theory of thermal diffusiophoresis of volatile aerosol particles it is necessary to have boundary conditions for the tangential velocity component which allow for the presence of heterogeneous chemical reactions. Conditions of this sort have been obtained by a number of authors [R. N. Gupta et al., Technical Papers, AIAA 22nd Aerospace Science Meeting, AIAA 19th Thermophysics Conference, New York (1985), pp. 465–490; D. V. Kul’ginov, Tech. Phys. 63, 940 (1993); A. V. Bogdanov et al., Preprint No. 1051, Fiz-Tekh. Inst. Akad. Nauk. SSSR, Leningrad (1986)]. The results of Gupta et al. are in the form of analytical expressions, but their computations actually used Maxwell’s method, which is of low accuracy. Kul’ginov et al. and Bogdanov et al. used the method of matched asymptotic expansions, which did not permit them to get simple analytical expressions. In the present paper the slip velocity is calculated by the Loyalka method. Analytical expressions are obtained for the slip coefficients, and the results of numerical calculations are presented. It is shown that in the presence of concentration gradients of the components of the gaseous mixture along the surface of an aerosol particle, the slip velocity can acquire new terms due to the change in the sticking coefficient along the catalytic surface. Expressions in final form are given for these terms. Zh. Tekh. Fiz. 67, 29–33 (May 1997)     

Statistical mechanics of red blood cell aggregation: The distribution of rouleaux in thermal equilibrium

When placed in suspension red blood cells adhere face-to-face and form long, cylindrical, and sometimes branched structures called rouleaux. We use methods developed in statistical mechanics to compute various statistical properties describing the size and shape of rouleaux in thermodynamic equilibrium. This leads to analytical expressions for (1) the average number of rouleaux consisting ofn cells and havingm branch points; (2) the average number of cells per rouleau; (3) the average number of branch points per rouleau; and (4) the number of rouleaux withn cells in a system containing a total ofN cells. We also derive asymptotic formulas that simplify these analytic expressions, and present numerical comparisons of the exact and asymptotic results.     

Ranges of low-energy heavy ions in beryllium, boron, carbon, and silicon

Based on a theory of the passage of low-energy, heavy ions through matter, simple analytical expressions are obtained for calculating the average projected ranges of the ions and the rms deviations of the projected ranges. The theoretical and experimental ranges of heavy ions with atomic numbers 29⩽Z ₁⩽83 in targets of Be, B, C, and Si are compared. The theory is found to be in good agreement with experiment. Zh. Tekh. Fiz. 68, 33–36 (September 1998)     

Renormalization Group Recursion Formulas and Flows of 2D O(N) Spin Models

Renormalization group recursion formulas for classical O(N) spin models in two dimensions are obtained. The main part of the recursion formulas is solved and yields the flows which are very close to those of the hierarchical model approximations of Dyson–Wilson type. Spontaneous mass generations also take place under our approximation.