Modal theory for the two-frequency mutual coherence function in random media: general theory and plane wave solution: II

Abstract

In a previous publication (part I) it has been shown that for an arbitrary statistically isotropic and homogeneous medium the parabolic equation for the two-frequency mutual coherence function can be separated and thereby expressed as a superposition of modes. A parameterization based on the longitudinal part of this representation has also been treated. This paper explores the transverse structure and parameterization of the field solution by employing dimensional, variational and the modified WKB procedures for solving the eigenfunction/eigenvalue problem. General expressions are derived first for a general structure function and then specialized for a power-law structure function with emphasis on quadratic and Kolmogorov media.     

Modal theory for the two-frequency mutual coherence function in random media: point source

The recently introduced modal expansion representation for the two-frequency mutual coherence function is applied here to the solution of a point-source field in a random medium. This approach reduces the solution for any structure function to an eigenvalue problem for an ordinary differential equation. For the initial point source it is shown here that the modal expansion yields a result similar to that for the initial plane wave, modified by a spherical free-space phase which contains a weighted coordinate that does not interact with the medium. Having established these general characteristics, special attention is paid to power-law media and, in particular, to a quadratic medium, for which a new exact solution is derived. Via a collective summation of this new modal solution, we rederive the alternative exact solution which exists in the literature. We also discuss the new parameterization implied by the new modal solution.     

On the theory of Thomson self-oscillatory systems

A nonlinear mechanism of the effect of broadband fluctuations on oscillations in a Thomson self-oscillator has been revealed. The correlation function for oscillations, which takes into account all appreciable effects in the second approximation, has been obtained for the first time. A new method has been developed for analyzing steady-state synchronous oscillations in a generator forming a part of the phase-synchronization system; linearized equations of steady-state synchronous oscillations, which take into account the effect of broadband noise, have been developed for the first time. An example of calculation of a complex phase-synchronization system is considered, in which the possibility of synthesizing highly effective systems with the help of the proposed methods of analysis is illustrated. The diffusion coefficients of the phase are estimated.     

Three-loop corrections in a covariant effective field theory

Chiral effective field theories have been used with success in the study of nuclear structure. It is of interest to systematically improve these energy functionals (particularly that of quantum hadrodynamics) through the inclusion of many-body correlations. One possible source of improvement is the loop expansion. Using the techniques of Infrared Regularization, the short-range, local dynamics at each order in the loops is absorbed into the parameterization of the underlying effective Lagrangian. The remaining nonlocal, exchange correlations must be calculated explicitly. Given that the interactions of quantum hadrodynamics are relatively soft, the loop expansion may be manageable or even perturbative in nuclear matter. This work investigates the role played by the three-loop contributions to the loop expansion for quantum hadrodynamics.     

Theoretical study on the band structure and optical properties of 4H-SiC

We have studied the band structure and optical properties of 4H-SiC by using a full potential linearized augmented plane waves (FPLAPW) method. The density of states (DOS) and band structure are presented. The imaginary part of the dielectric function has been obtained directly from the band structure calculation. With band gap correction, the real part of the dielectric function has been derived from the imaginary part by the Kramers－Kronig (KK) dispersion relationship. The values of reflectivity for normal incidence as a function of photon energy have also been calculated. We found the theoretical results are in good agreement with the experimental data.     

Neutrino oscillations from supersymmetry without R-parity—its implications on the flavor structure of the theory

We discuss here some flavor structure aspects of the complete theory of supersymmetry without R-parity addressed from the perspective of fitting neutrino oscillation data based on the recent Super-Kamiokande result. The single-VEV parameterization of supersymmetry without R-parity is first reviewed, illustrating some important features not generally appreciated. For the flavor structure discussions, a naive, flavor-model-independent, analysis is presented, from which a few interesting things can be learned.     

Modal theory for the two-frequency mutual coherence function in random media: beam waves

Pulse propagation in a random medium is mainly determined by the two-frequency mutual coherence function which satisfies the parabolic equation. It has recently been shown that this equation can be solved by separation of variables, thereby reducing the solution for any structure function to the solution of ordinary differential equations. In this paper, the method is applied for a beam-wave excitation in a random medium. The exact solution for a quadratic medium is derived. For non-quadratic power-law media an analytical expression at equal positions is presented.     

Study of ground states of <Superscript>3,4,6</Superscript>He nuclides by Feynman’s continual integrals method

The energy and the square modulus of the wave function for the ground states of helium nuclides ^3,4,6He has been calculated by Feynman’s continual integrals method. A new parameterization of the shell model for light nuclei is proposed.     

Regge behaviour of structure functions and evolution of gluon structure function upto next-to-leading order at low-x

Evolution of gluon structure function from Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations upto next-to-leading order at low-x is presented assuming the Regge behaviour of structure functions. We compare our results of gluon structure function with GRV 98 global parameterization and show the compatibility of Regge behaviour of structure functions with PQCD.     

Multiphase density functional theory parameterization of the interatomic potential for silver and gold

The ground state energies of Ag and Au in the face-centered cubic (FCC), body-centeredcubic (BCC), simple cubic (SC) and the hypothetical diamond-like phase, and dimer werecalculated as a function of bond length using density functional theory (DFT). Theseenergies were then used to parameterize the many-body Gupta potential for Ag and Au. Wepropose a new parameterization scheme that adopts coordination dependence of theparameters using the well-known Tersoff potential as its starting point. Thisparameterization, over several phases of Ag and Au, was performed to guaranteetransferability of the potentials and to make them appropriate for studies of relatednanostructures. Depending on the structure, the energetics of the surface atoms play acrucial role in determining the details of the nanostructure. The accuracy of theparameters was tested by performing a 2?ns MD simulation of a cluster of 55 Ag?atoms – awell studied cluster of Ag, the most stable structure being the icosahedral one. Withinthis time scale, the initial FCC lattice was found to transform to the icosahedralstructure at room temperature. The new set of parameters for Ag was then used in atemperature dependent atom-by-atom deposition of Ag nanoclusters of up to 1000 atoms. Wefind a deposition temperature of 500?±?50?K where low energy clusters are generated,suggesting an optimal annealing temperature of 500?K for Ag cluster synthesis. Surfaceenergies were also calculated via a 3 ns MD simulation.     

Towards a gravitation theory in Berwald-Finsler space

Finsler geometry is a natural and fundamental generalization of Riemann geometry. The Finsler structure depends on both coordinates and velocities. It is defined as a function on tangent bundle of a manifold. We use the Bianchi identities satisfied by the Chern curvature to set up a gravitation theory in Berwald-Finsler space. The geometric part of the gravitational field equation is nonsymmetric in general. This indicates that the local Lorentz invariance is violated.     

Towards a gravitation theory in Berwald-Finsler space

Finsler geometry is a natural and fundamental generalization of Riemann geometry. The Finsler structure depends on both coordinates and velocities. It is defined as a function on tangent bundle of a manifold. We use the Bianchi identities satisfied by the Chern curvature to set up a gravitation theory in Berwald-Finsler space. The geometric part of the gravitational field equation is nonsymmetric in general. This indicates that the local Lorentz invariance is violated.     

Width of the equilibrium charge distribution of heavy ions in solid and gaseous media

Based on an analysis of the experimental data on the charge distributions of ions in gases and solids, the analytical parameterization of the width of the charge distribution as a function of the energy, the average equilibrium ion charge, ion nuclear charge, and nuclear charge of target atom has been obtained. The proposed relations are applicable in a broad energy range and describe the existing experimental data satisfactorily.     

Monte Carlo simulation in the theory of wave propagation in random media: II. Scintillation index, second and fourth moments

The purpose of this article (comprising parts I and II) is to develop and test the approach of combining a path-integral technique and a complex-valued Monte Carlo method to calculate the highest moments of the Green function of the stochastic wave equation for media with random small-scale inhomogeneities against the background of large-scale inhomogeneities. In part II calculations of the second and fourth moments of the Green function and the scintillation index have been performed for 1D and 2D cases in the framework of three models: a model of the stochastic wave equation and models of parabolic and Markov approximations. The finiteness of the correlation radius of inhomogeneities has been shown to be the reason for the significant difference between the Markov approximation and the other two. The results obtained prove that the applicability of the parabolic approximation (without the Markov approximation) is much wider than might be expected. A comparison has been made showing good agreement with reliable results for 1D media. The Monte Carlo results have exhibited the singularities existing at the localization centres and forming exponential decay of the second moment from distances of about one wavelength. The unexpected sharp oscillations interrupting the exponential decay of the Green function moments have been obtained at distances from the localization centre of several tens of times the average distance between scatterers. The effect of weak large-scale inhomogeneities on the behaviour of the second moment has also been investigated.     

Resonance properties from a coupled channel meson exchange model

In this talk, I present the results on the pole structure of pion-nucleon scattering in an analytic model based on meson exchange. The analytic properties of scattering amplitudes provide important informa-tion. Besides the cuts, the poles and zeros on the different Riemann sheets determine the global behavior of the amplitude on the physical axis. Pole positions and residues allow for a parameterization of resonances in a well-defined way, free of assumptions for the background and energy dependence of the resonance part. This is a necessary condition to relate resonance contributions in different reactions.     

Mayer function perturbation theory of effective interaction of charged colloids

In this paper, the effective interaction between charged colloids has been studied based on the standard Mayer function perturbation theory. With the formalism developed in this paper, the effective interaction as a function of Mayer functions and the correlation functions of the homogeneous microions is obtained. The asymptotic behaviour of the effective interaction at large distance is analysed in detail. It is found that at large distance the effective interaction is Yukawa like, provided the bare charge is replaced by the renormalised one. Exact expressions for the renormalised charge and the decay length as functions of the short-range part of the Mayer function and that of the correlation function of the homogeneous microions are obtained. With perturbation methods, it is easy to see how the effective interaction at large distance is affected by microion correlations and nonlinearity.     

An extended hydrodynamic theory for particle coarsening—I: Theory

The asymptotic hydrodynamic approach to the mathematical solution of the kinetics of particle coarsening (Ostwald ripening), first proposed by Lifshitz and Slyozov and Wagner, has been extended and generalized. The coarsening rate equations in dimensionless forms have been separated into asymptotically determinate and indeterminate parts. The generalized evaluation of the asymptotically indeterminate part allows the consideration of coarsening processes that are more complicated than those involving power law type kinetics considered in previous studies. Further, the extended theory allows the determination of particle size distribution function and averaged particle coarsening kinetics even in cases where different physical processes occur at different size regimes within the same distribution of particles.     

Electromagnetic emission from two-dimensional plasmons in a semiconductor-dielectric structure with metal grating: Rigorous theory

The spectrum of electromagnetic (EM) radiation from two-dimensional(2D) plasmons in a semiconductor-dielectric structure with metal grating has been calculated in a strict electromagnetic approach. It is shown that radiation frequency and linewidth vary over a broad range of magnitude as a function of the grating parameters. The radiative decay linewidth is found to be two orders of magnitude larger than expected from the perturbation theory. Comparison of the results with previously published experimental data on 2D plasmons in GaAs heterostructures makes us conclude that the main contribution to the experimental decay linewidth arises from dielectric losses in the layers of the structure.     

Energy transport by excitons: an application of Mori-Zwanzig theory

The problem of energy transport by excitons is studied by evaluating the memory function starting from the Hamiltonian of the exciton-phonon system and applying the Mori-Zwanzig projection formalism. We thus provide a microscopic derivation of the time-dependent memory function for exciton motion on a linear chain which in the literature has been introduced so far only phenomenologically.     

The foundation of quantum theory and noncommutative spectral theory: Part II

The present paper comprises Sects. 5–8 of a work which proposes an axiomatic approach to quantum mechanics in which the concept of a filter is the central primitive concept. Having layed down the foundations in the first part of this work (which appeared in the last issue of this journal and comprises Sects. 0–4), we arrived at a dual pair Y, M consisting of abase norm space Y and anorder unit space M, being in order and norm duality with respect to each other. This is precisely the setting of noncommutative spectral theory, a theory which has been developed during the late nineteen seventies by Alfsen and Shultz. ^(2,3) In this part we add to the four axioms (Axioms S, DP, R, SP) of Sect. 3 three further axioms (Axioms E, O, L). These axioms are suggested by the work of Alfsen and Shultz and enable us to derive the JB-algebra structure of quantum mechanics (cf. Theorem 8.9).