bluuebunny/crossref_metadata_2025 huggingface dataset:
Theory of dissociative and nondissociative adsorption and desorption
Authors: Kreuzer H. J. , Payne S. H. , Drozdowski A. , Menzel D.
Published: July 2002

Based on nonequilibrium thermodynamics we formulate a general theory of the kinetics of adsorption, desorption, and dissociation of gases at surfaces. We begin with a concise formulation of dissociation equilibrium at surfaces and then derive the kinetic equations for adsorption, desorption, and dissociation. For the explicit calculations we employ a lattice gas model for homonuclear molecules with both atoms and molecules present on the surface. Lateral interactions between all species are accounted for. In a series of model calculations we discuss equilibrium properties, such as heats of adsorption, and examine the role of dissociation dis-equilibrium on the time evolution of an adsorbate during temperature programmed desorption. The further effect of (attractive or repulsive) lateral interactions on the kinetics is elucidated in further model calculations. As a realistic example we apply the theory to oxygen on Pt(111).
Monolayer adsorption of nonrandom mixtures
Authors: Hocker T. , Aranovich G. L. , Donohue M. D.
Published: July 2002

A model for monomers on a lattice is presented based on local density calculations that were first proposed by Ono and Kondo in 1947 and recently generalized by Aranovich, Donohue, and co-workers. The model allows one to describe the adsorption behavior of molecules at a surface (or interface), and the phase behavior of adsorbed molecules, as well as of molecules in the bulk on the basis of short-range ordering in two and three dimensions. While there are prior lattice theories that predict nonrandom behavior for arbitrary lattice coordination numbers, the derivation of adsorption models from these theories is usually based on ideal fluid behavior in the bulk. However, the new adsorption model presented here is consistent in that molecular behavior in the bulk as well as in the adsorbed surface layer is based on identical assumptions. This is accomplished by calculating the total free energy of the system; the corresponding adsorption model follows through minimization of the free energy. This procedure is also used for deriving a new adsorption equation based on the quasi-chemical approximation to the Ising problem. Results from this equation are very similar to those obtained from the equation based on Ono–Kondo theory. When compared with lattice Monte Carlo computer simulations, the new adsorption models based on nonrandom mixing consistently show better agreement than those based on random behavior. For simplicity, the discussion of results is restricted to single-component systems. However, the new adsorption model based on Ono–Kondo theory is applicable to systems of arbitrary numbers of components without introducing any further assumptions.
Quantum fluid dynamics in the Lagrangian representation and applications to photodissociation problems
Authors: Mayor Fernando Sales , Askar Attila , Rabitz Herschel A.
Published: July 2002

This paper considers the practical utility of quantum fluid dynamics (QFD) whereby the time-dependent Schrödinger’s equation is transformed to observing the dynamics of an equivalent “gas continuum.” The density and velocity of this equivalent gas continuum are respectively the probability density and the gradient of the phase of the wave function. The numerical implementation of the QFD equations is carried out within the Lagrangian approach, which transforms the solution of Schrödinger’s equation into following the trajectories of a set of mass points, i.e., subparticles, obtained by discretization of the continuum equations. The quantum dynamics of the subparticles which arise in the present formalism through numerical discretization are coupled by the density and the quantum potential. Numerical illustrations are performed for photodissociation of NOCl and NO2 treated as two-dimensional models. The dissociation cross sections σ(ω) are evaluated in the dramatically short CPU times of 33 s for NOCl and 40 s for NO2 on a Pentium-200 MHz PC machine. The computational efficiency comes from a combination of (a) the QFD representation dealing with the near monotonic amplitude and phase as dependent variables, (b) the Lagrangian description concentrating the computation effort at all times into regions of highest probability as an optimal adaptive grid, and (c) the use of an explicit time integrator whereby the computational effort grows only linearly with the number of discrete points.
Diffusion and evaporation kinetics of large islands and vacancies on surfaces
Authors: Lo Alan , Skodje Rex T.
Published: July 2002

The diffusion and evaporation kinetics of two-dimensional islands and vacancy islands on surfaces are studied over a wide range of island sizes. These kinetic processes are central in surface phenomena such as thin film coarsening, island aggregation, and coalescence on surfaces. Several studies have utilized scaling theories to infer the atomic level mechanisms responsible for the kinetics of island diffusion and evaporation. Using a dynamic Monte Carlo model, we study a model system where two-dimensional islands diffuse via an evaporation-condensation mechanism on a face-centered-cubic (100) surface. We examine the diffusion (evaporation) kinetics for isolated islands as a function of the island’s size in the range of 100 to 100 000 atoms. The diffusion coefficient and the island evaporation rate exhibit a power law scaling of the island size. We find crossover behavior in the scaling exponents between the regime of intermediate sized islands (between 100 and 1000 atoms) and large islands (greater than 1000 atoms). At high coverages, we also examine these quantities for vacancy islands. We find that intermediate island sizes exhibit unusual scaling behavior.
The electronic structure and chemical bonding of hypermetallic Al5C by ab initio calculations and anion photoelectron spectroscopy
Authors: Boldyrev Alexander I. , Simons Jack , Li Xi , Wang Lai-Sheng
Published: July 2002

The chemical structure and bonding of the hypermetallic Al5C and Al5C− species have been studied by photoelectron spectroscopy and ab initio calculations. Both Al5C (C2v, 2A1) and Al5C− (C2v, 1A1) are found to have planar structures that can be related to that of the planar square Al4C− by adding one Al+ ion or one Al atom to an edge of the square. The planarity of Al5C and Al5C− can be explained in terms of the structure of their highest occupied molecular orbitals which are ligand five-center one- or two-electron bonding MO, respectively, similar to the orbital responsible for the planarity of Al4C−. Four peaks were observed in the photoelectron spectra of Al5C− with vertical binding energies of 2.67, 2.91, 3.19, and 4.14 eV which compare well with the 2.68, 2.96, 3.27, and 4.35 eV calculated by the Green function method [OVGF/6-311+G(2df )]. The excellent agreement between the calculated and experimental electron affinity and excitation energies allow us to completely elucidate the geometrical and electronic structures of Al5C− and suggest the most likely structure for the Al5C molecule.
The ordered and orientationally disordered crystalline phases of the flexible C4F8 molecule
Authors: Gamba Z. , Powell B. M.
Published: July 2002

There is ample experimental evidence for the existence of several crystalline phases of C4F8, although they still have been not clearly identified. In this paper we report a series of molecular dynamics (MD) simulations using a partially flexible molecular model, which takes into account the mixing of the low frequency intramolecular modes and lattice modes. The calculations are carried out at constant pressure and constant temperature and the algorithm employed allows for volume and symmetry changes of the MD sample as a function of thermodynamic variables. Although several stable crystalline phases are found, their number is still less than determined by experiments.
Electron-ion recombination in dense rare gases: Energy diffusion theory vs simulation
Authors: Wojcik Mariusz , Tachiya M.
Published: July 2002

An analytical method using the concept of diffusion in energy space is applied to calculate the electron-ion recombination rate constant and the electron escape probability in dense gaseous argon and krypton. The results are compared with the respective data obtained from computer simulations. The discrepancies between the two methods are found to be relatively small. The applicability of the energy diffusion approach is discussed.
Angle resolved photoelectron spectroscopy of O2(a1Δg) with synchrotron radiation
Authors: Beeching L. , De Fanis A. , Dyke J. M. , Gamblin S. D. , Hooper N. , Morris A. , West J. B.
Published: July 2002

Angular distribution of photoelectrons for the photoionization processes O2+(X 2Πg,v+=0–3)+e−←O2(a1Δg)+hν has been studied at the photon energy of 21.22 eV and in the photon energy range 13.8–15.2 eV where the cross-sections for these processes show strong enhancement due to the presence of resonant transitions to a Rydberg state (C 2Φu,3sσg)p 1Φu. It has been found that the plot of the asymmetry parameter, β, against photon energy shows structure at energies corresponding to O2(p 1Φuv′)←O2(a 1Δgv″=0) excitations. The O2+(X 2Πg,v+)←O2(a 1Δg,v″=0) ionizations have also been investigated in the photon energy range 18.0–19.2 eV, where the presence of unassigned resonances was observed in earlier photoelectron spectroscopic work. In this energy range the plot of asymmetry parameter against photon energy also shows resonant structure. Suggestions for the excited states associated with these resonances have been made on the basis of constant-ionic-state spectra recorded at different angles.
Critical localization of confined phonons in finite size admonolayers
Authors: Pouthier V. , Girardet C.
Published: July 2002

The renormalization group theory is applied to the determination of localized phonons in a finite size two dimensional monolayer. The fixed-point equation defines the critical values of the adsorbate-substrate force constants leading to the occurrence of localized modes. The transformation equation near the fixed point gives scaling laws and critical exponents which characterize the asymptotic behavior of the localization length of the phonons.
Structures and stability of CO layers on the MgO(001) surface
Authors: Sallabi A. K. , Jack D. B.
Published: July 2002

Monte Carlo simulations of CO/MgO(001) show that below 41 K the CO molecules form a c(4×2) structure with six molecules per unit cell distributed into two kinds of adsorption sites: a perpendicular site and a tilted site (polar angle of 31°). Both sites are localized near Mg2+ ions. The occupancy of perpendicular sites to tilted sites occurs in the ratio of 1:2. At 41 K the c(4×2) phase undergoes a phase transition into a less dense, disordered phase accompanied by the expulsion of some molecules to form a partial second layer. The density of the remaining disordered layer is the same as for a p(3×2) phase and portions of the disordered layer show regions of short range ordering with either the c(4×2) or p(3×2) structures. The p(3×2) phase contains four molecules per unit cell and also consists of perpendicular and tilted sites, but in the ratio of 1:1. This structure was found to be stable up to 50 K after which the expulsion of some molecules and disordering of the layer occurred. A model to test the relative stability of these two phases by examining the difference in Gibbs free energy is constructed and shows that below 41 K the c(4×2) phase is the most stable but above 41 K the p(3×2) phase is the most stable. However, at low pressures the model suggests that the p(3×2) phase will not be observed and the layer will instead transform from the c(4×2) phase to a disordered phase at 41 K. This result reconciles the findings of low-energy electron diffraction (LEED) experiments [p(3×2) phase observed] with those of helium atom scattering (HAS) and polarization infrared spectroscopy (PIRS) experiments (disordered phase observed). It is proposed that the c(4×2)→p(3×2) transition is part of an infinite sequence of transitions involving (n×2)-type structures which, under suitable conditions of temperature and pressure, constitutes an example of the devil’s staircase phenomenon. Such a phenomenon has been suggested by previous LEED experiments.
Geometry dependent critical exponents at complete wetting
Authors: Rascón C. , Parry A. O.
Published: July 2002

We consider the complete wetting transition at nonplanar wall–fluid interfaces, where the height of the substrate varies as a power-law ∝|x|γ (with exponents 0⩽γ⩽1) in one direction (x). From a general scaling analysis, supported by numerical and analytical effective interfacial model calculations, we argue that such power-law wedges can alter the growth law describing the divergence of the interfacial height l0 (measured from the wedge bottom) and other length scales as the bulk saturation chemical potential is approached. For realistic experimental systems with dispersion forces, we predict that the complete wetting critical exponents are determined by γ for wedge shape with γ>1/2. For γ<1/2, the asymptotic growth of the film thickness should be similar to that found for planar systems. Nevertheless, crossover behavior due to the influence of the geometry is still observable in adsorption isotherms.
Analysis of the susceptibility minimum observed in 0.4Ca(NO3)2–0.6KNO3 by dielectric spectroscopy and light scattering
Authors: Casalini R. , Ngai K. L. , Roland C. M.
Published: July 2002

An intriguing feature of the relaxation of glass formers is the broad minimum in the dynamic susceptibility spectrum, lying intermediate between the high frequency vibrational absorption (or Boson peak) and the slower, temperature-dependent structural relaxation and diffusion. As first shown by Lunkenheimer et al. [Phys. Rev. Lett. 77, 318 (1996)], high frequency dielectric spectra can be accounted for by invoking a temperature-dependent, frequency-independent contribution (“constant loss”) to the loss spectrum. Herein, we analyze dielectric relaxation and light scattering data for 0.4Ca(NO3)2–0.6KNO3 (CKN), which exhibit broad minima at GHz to THz frequencies. Over a wide temperature range, the spectra can be accurately described by the additive superposition of a constant loss to the structural relaxation and the Boson peak. Moreover, the temperature dependence of the constant loss term is the same for the two spectroscopies. The behavior of the constant loss inferred from this analysis is minimally affected by the details of the fitting procedure, demonstrating the robustness of the method. We also show that dielectric relaxation data for a silver iodide–silver selenate glass conform to the predictions of mode coupling theory, even though a liquid state theory is not obviously applicable to a glassy ionic conductor. This underscores the value of alternative interpretations of the high frequency dynamics in glass-forming liquid, including contributions from a constant loss such as described herein.
Heterochirality in Langmuir monolayers and antiferromagnetic Blume–Emery–Griffiths model
Authors: Pelizzola A. , Pretti M. , Scalas E.
Published: July 2002

Chirality is quite a common property in organic molecules. Chiral molecules exist in two forms (called enantiomers) which cannot be superimposed by rotations and translations and may have very different biochemical properties. Experiments on Langmuir monolayers made up of chiral amphiphiles have shown that, in most cases, heterochiral interactions dominate, implying the formation of a racemic compound. It has been shown that a monolayer mixture of two enantiomers can be simply described by a two-dimensional (2-D) spin-1 lattice gas [Blume–Emery–Griffiths (BEG) model], where the heterochiral preference is represented by an effective antiferromagnetic coupling. By now just mean field calculations have been performed on this model. Here we present a revisitation of the tripod amphiphile model, proposed by Andelman and de Gennes [D. Andelman and P.-G. de Gennes, Compt. Rend. Acad. Sci. (Paris) 307, 233 (1988)], together with a rigorous proof of the heterochiral preference shown by the model in the hypothesis of van der Waals interactions. Moreover, a cluster variation analysis of the antiferromagnetic BEG model on a triangular lattice is performed and possible interpretations in terms of surface pressure–concentration phase diagrams for monolayer mixtures of enantiomers are discussed. The choice of a triangular lattice has been suggested by the triangularlike structure of condensed phases of Langmuir monolayers, shown by x-ray diffraction experiments.
Accuracy of atomization energies and reaction enthalpies in standard and extrapolated electronic wave function/basis set calculations
Authors: Bak Keld L. , Jørgensen Poul , Olsen Jeppe , Helgaker Trygve , Klopper Wim
Published: July 2002

The accuracy of standard ab initio wave-function calculations of atomization energies and reaction enthalpies has been assessed by comparing with experimental data for 16 small closed-shell molecules and 13 isogyric reactions. The investigated wave-function models are Hartree–Fock (HF), Møller–Plesset second-order perturbation theory (MP2), coupled-cluster theory with singles and doubles excitations (CCSD) and CCSD with perturbative triple-excitation corrections [CCSD(T)]; the one-electron basis sets used are the correlation-consistent cc-pVxZ and cc-pCVxZ basis sets with cardinal numbers x=D, T, Q, 5, and 6. Results close to the basis-set limit have been obtained by using two-point extrapolations. In agreement with previous studies, it is found that the intrinsic error of the CCSD(T) method is less than chemical accuracy (≈4 kJ/mol) for both atomization energies and reaction enthalpies. The mean and maximum absolute errors of the best CCSD(T) calculations are 0.8 and 2.3 kJ/mol for the atomization energies and 1.0 and 2.3 kJ/mol for the reaction enthalpies. Chemical accuracy is obtained already from the extrapolations based on the cc-pCVTZ and cc-pCVQZ basis sets—with mean and maximum absolute errors of 1.7 and 4.0 kJ/mol for atomization energies and 1.3 and 3.1 kJ/mol for reaction enthalpies. The intrinsic errors of the Hartree–Fock, MP2, and CCSD wave-function models are significantly larger than for CCSD(T). For CCSD and MP2, the mean absolute errors in the basis set limit are about 32 kJ/mol for the atomization energies and about 10 and 15 kJ/mol, respectively, for the reaction enthalpies. For the Hartree–Fock model, the mean absolute errors are 405 and 29 kJ/mol for atomization energies and reaction enthalpies, respectively. Correlation of the core electrons is important in order to obtain accurate results with CCSD(T). Without compromising the accuracy, the core contribution may be calculated with a basis set that has one cardinal number lower than that used for the valence correlation contribution. Basis-set extrapolation should be used for both the core and the valence contributions.
Analyses of the ScO− and ScO2− photoelectron spectra
Authors: Gonzales Jason M. , King Rollin A. , Schaefer Henry F.
Published: July 2002

We have optimized geometries for various electronic states of both neutral and anionic ScO and ScO2 using density functional theory (DFT) and coupled cluster theory. Adiabatic and vertical separation energies have been computed using both DFT and coupled cluster theory. For the ScO− anion the 1Σ+ state is predicted to lie lower than the 3Δ state by 1.48 eV. In fact, the anion 3Δ state is higher in energy than the 2Σ+ neutral ground state. This contradicts the assignment of the ScO− ground state made by Wu and Wang, in their recent report of photoelectron spectroscopy experiments. The CCSD(T) adiabatic electron affinity for the ground state of ScO is 1.30 eV, while the vertical detachment energy is 1.33 eV. This compares favorably with the experimental value of 1.35 eV. For ScO2 the 2B2 ground state with a CCSD(T) bond angle of 140.5° is lower in energy than the 2A1 state with a bond angle of 48.4° by 1.13 eV. The anion minima include two 1A1 states, with the CCSD(T) global minimum corresponding to 140.9° and the 2.00 eV higher energy state having a bond angle of 47.4°. For ScO2 the adiabatic electron affinity was computed with CCSD(T) to be 2.22 eV with a corresponding vertical detachment energy of 2.30 eV. This compares with an experimental vertical detachment of 2.32 eV.
Dissociation of fast N2 molecules scattered from different fcc(110) surfaces
Authors: Brüning K. , Heiland W. , Schlathölter T. , Wojciechowski I. A. , Medvedeva M. B. , Ferleger V. Kh.
Published: July 2002

The dissociation of fast nitrogen molecules with kinetic energies ranging from 200 to 2000 eV/atom was studied for grazing collisions with various fcc surfaces. At these energies, the dissociation is caused by vibrational and rotational excitation, the latter being favored for scattering along the surface semichannels. N2 is chemically inert and interacts mainly elastically with the surfaces. A controversial question is the role of the dynamic screening of the molecular constituents by the bulk electron gas during the dissociation process. Another interesting issue is the dependence of the dissociation probability on the azimuthal scattering angle—the fragmentation is highest for the low indexed direction. We treat both problems, by comparing results obtained from the different surfaces Pd(110), Ag(110), and Pt(110). The experimental data are compared to molecular dynamics simulations based on realistic interaction potentials as obtained from density functional theory calculations. The potentials are improved by adding an explicit dependence of the intramolecular bond strength on the molecule surface distance z, which leads to excellent agreement of experiment and simulations.
Shear thinning of suspensions of sterically stabilized spheres studied by Stokesian dynamics simulations
Authors: Schaink H. M. , Nommensen P. A. , Jongschaap R. J. J. , Mellema J.
Published: July 2002

Stokesian dynamics simulations are presented of suspensions of sterically stabilized spheres in a viscous medium, subjected to simple shear. The steric repulsion between the grafted polymer layers of different particles is modeled using an interaction potential that is calculated using a self-consistent field lattice theory. The shear rate dependence and the volume fraction dependence of the suspension viscosity are calculated and compared to experimental data [Nommensen et al. Phys. Rev. E 59, 3147 (1999)]. It is found that shear thinning is mainly caused by the interaction contribution to the viscosity. The present paper, combined with a recent paper of Nommensen et al. [Langmuir 16, 1902 (2000)], shows that computer simulations, theoretical analysis, and experimental work give a consistent physical picture of the rheology of these suspensions when the proper interaction potential is used.
Exact solutions of the wave equation with complex source locations
Authors: Ziolkowski Richard W.
Published: July 2002

New exact solutions of the homogeneous, free-space wave equation are obtained. They originate from complex source points moving at a constant rate parallel to the real axis of propagation and, therefore, they maintain a Gaussian profile as they propagate. Finite energy pulses can be constructed from these Gaussian pulses by superposition.
Three-dimensional gauge theory in Dirac formalism
Authors: Kamimura Kiyoshi
Published: July 2002

The Hagen model [C. R. Hagen, Ann. Phys. (NY) 157, 342 (1984); Phys. Rev. D 31, 331 (1985)] is studied using the method of constrained Hamiltonian formalism developed by Dirac [P. A. M. Dirac, Can. J. Math. 2, 129 (1950); Lectures on Quantum Mechanics (Yeshiva U. P., New York, 1964)]. The results recently obtained by Burnel and Van Der Rest-Jaspers [A. Burnel and M. Van Der Rest-Jaspers, J. Math. Phys. 26, 3155 (1985)] are reexamined and modified. There appear two second-class constraints and their choice is not crucial. The equivalence of different gauges is proved without referring to the current conservation law.
Killing spinors on spheres and hyperbolic manifolds
Authors: Fujii Yasunori , Yamagishi Kengo
Published: July 2002

Properties of Killing spinors on spheres and hyperbolic manifolds are investigated with an emphasis on the relations to Killing vectors, conformal Killing vectors, and solutions of Maxwell’s equations.
Dynamics of para-Bose coherent states
Authors: Saxena G. M. , Mehta C. L.
Published: July 2002

The most general form of the Hamiltonian is obtained under the restriction that initially coherent states of a multimode para-Bose system remain coherent at all times. The equation of motion for the square of the annihilation operator for the multimode system using this Hamiltonian is solved.
Propagation of electromagnetic plane waves in random media
Authors: Hillion P. , Quinnez S.
Published: July 2002

In the frame of the spinor formalism of the electromagnetic field, the propagation of a plane wave in a random medium with a view to obtaining the moments of the energy density is considered. Using two different approximations to the solution of the spinor wave equation, it is shown that the energy conservation requires, on the statistics of the refractive index, some extra conditions difficult (eventually impossible) to satisfy. For the variance of the light intensity, a result valid for weakly scattering media is given. It is concluded that ‘‘dishonest’’ methods (in Keller’s terminology) have to be used.
The Fermi surface for point interactions
Authors: Ho/egh-Krohn Raphael , Holden Helge , Johannesen Steinar , Wentzel-Larsen Tore
Published: July 2002

Using a computer, the Fermi surface for the one-electron model of an infinite crystal in three dimensions with zero range interactions, i.e., with so-called point interactions, is studied. A computer program is available which has, as input, the crystal structure, the scattering length of the solid considered, and the Fermi energy, and, as output, a drawing of the corresponding Fermi surface inside its Brillouin zone.
On the stability of dense point spectrum for self-adjoint operators
Authors: Thomas Lawrence E. , Wayne C. Eugene
Published: July 2002

Let A be a (random) self-adjoint operator with fixed orthonormal eigenvectors, but with independently distributed random eigenvalues. [Typically, for the eigenvalue distributions, A is considered to have a dense point spectrum almost surely (a.s.).] A class of perturbations {B} is exhibited such that A+B has only point spectrum a.s. Examples are also constructed, including a rank-one perturbation B, such that A+μB has no eigenvalues (for μ≠0) a.s., despite A having dense point spectrum a.s.
Factorization of systems of differential equations
Authors: Humi Mayer
Published: July 2002

It is shown that the classical Infeld–Hull factorization method can be extended to coupled systems of second-order equations. A complete solution of the factorization equations in two dimensions is given and a partial enumeration of factorizable systems is made.
Symmetries and integrability of the cylindrical Korteweg–de Vries equation
Authors: Zhu Guo-Cheng , Chen H. H.
Published: July 2002

The direct scheme to test integrability of a given nonlinear equation proposed by Chen, Lee, and Liu is tested on the cylindrical Korteweg–de Vries equation. The explicit dependence on t of this equation does not present any real difficulties. Constants of motion and symmetries are found readily and the Lax operators for the scattering problem constructed accordingly.
Application of the Hamilton–Jacobi method to linear nonconservative vibration theory
Authors: Vujanovic B. , Strauss A. M.
Published: July 2002

In this paper it is shown how linear, strictly nonconservative, oscillatory systems with one and many degrees of freedom may be analyzed by application of the theory of Hamilton and Jacobi.
Theory for correlation functions of fermion quantum fluids
Authors: Sinha Suresh K.
Published: July 2002

A theory for the pair correlation function of a fermion fluid is developed in terms of a function S(m) defined as a certain sum over graphs. The theory is further extended to derive expressions for the radial distribution function and for the four distinct direct correlation functions. These four direct correlation functions are combined together leading to an integral equation for fermion quantum fluids, which is much simpler and is expressed in a computationally convenient form.
Helicity eigenstates of a relativistic spin-0 and spin-1/2 constituent bound by minimal electrodynamics: Zero orbital angular momentum, zero four-momentum solutions
Authors: Mainland G. Bruce
Published: July 2002

Zero four-momentum, helicity eigenstates of the Bethe–Salpeter equation are found for a composite system consisting of a charged, spin-0 constituent and a charged, spin- 1/2 constituent bound by minimal electrodynamics. The form of the Bethe–Salpeter equation used to describe the bound state includes the contributions from both single photon exchange (ladder approximation) and the ‘‘seagull’’ diagram. Attention is restricted to zero orbital angular momentum states since these appear to be the most interesting physically.
Solitonic solutions in the Kaluza–Klein–Jordan formalism as cosmological models in general relativity
Authors: Díaz Mario C. , Gleiser Reinaldo J. , Pullin Jorge A.
Published: July 2002

A new renormalization procedure for the solutions of Einstein’s field equations in d dimensions obtainable by the inverse scattering method (ISM) of Belinskii and Zakharov [Sov. Phys. JETP 48, 985 (1978)] is presented. It allows one to obtain families of diagonal metrics which, in addition to the solitonic parameters that characterize the ISM, depend on 2(d-3) extra arbitrary parameters. An example of cosmological relevance where the source is a massless scalar field in five dimensions is presented. It represents a general family of two-parameter four-dimensional metrics that for great times go into the perfect fluid Friedman–Robertson-Walker regime.
Analytic solutions of the SU(3) Yang–Mills field equations with external sources
Authors: Oh C. H. , Parwani Rajesh R.
Published: July 2002

For external sources specified in the radial gauge frame, it is demonstrated how the SU(3) Yang–Mills field configuration can be constructed from the SU(2) solutions. This is explicitly illustrated for the type-II solutions that exhibit the bifurcation phenomenon.
Irreducible tensor description. III. Thermodynamics of a low-temperature phonon gas
Authors: Banach Zbigniew , Piekarski Slawomir
Published: July 2002

Let one assume that the interacting phonon gas, whose behavior is governed by the Boltzmann–Peierls equation, inhabits an insulating crystal at sufficiently low temperature. Then, within the framework of a single acoustic phonon branch and of an isotropic long-wavelength approximation to the dispersion relation, the simplest acceptable version of extended irreversible thermodynamics, based upon the nine-moment system of differential equations for the slow and fast gas-state variables, is carefully investigated. It is clearly demonstrated that, in virtue of the structure simplifications just mentioned, the conceptually different (macroscopic, kinetic, and variational) procedures, which are discussed in this paper, appear complementary to each other. Finally, with the help of a suitable contraction of the nine-moment system of field equations, for Callaway’s relaxation model a slightly generalized nonlinear variant of ordinary low-temperature phonon hydrodynamics is explicitly derived.
On the approach to statistical equilibrium in an infinite-particle lattice dynamic model
Authors: Courbage M.
Published: July 2002

A deterministic reversible model dynamic system of infinite interacting particles on a lattice is studied. The model is a modification by de Haan of the Kac ring model. The time evolution of the statistical states can be described by a hierarchy for the reduced distribution functions. It is shown that the system is isomorphic to a Bernoulli shift. The isomorphism is given in terms of the infinite process of observation of the states of one particle in a fixed site. The approach to equilibrium is studied and time-asymmetric initial states that approach equilibrium are constructed. It is shown that these states contain nonvanishing correlations between infinitely distant particles. The Bernoulli property allows the construction of a Markovian irreversible description of the model, realized by a nonunitary transformation. The action of this transformation on the statistical states, the correlations, and the rate of the approach to equilibrium is studied.
New higher-dimensional instanton and monopole solutions
Authors: Jian-jun Xu , Xin-zhou Li
Published: July 2002

Two classes of spherically symmetric solutions to the empty space Einstein equations in even dimensions are presented. The solutions are constructed as radial extensions of circle bundles over a compact homogeneous Kähler manifold M. Type B solutions can be turned into higher-dimensional Kaluza–Klein monopoles. Both the Gross–Perry–Sorkin solution and the Bais–Batenburg solutions are contained as special cases of the general solutions.
Irreducible tensor description. II. A quasiparticle gas
Authors: Banach Zbigniew , Piekarski Slawomir
Published: July 2002

Let E be a three-dimensional Euclidean vector space and assume that ℏΩ(k) is a quasiparticle energy in the mode k∈E; thus k is a wave vector. Within the framework of the Boltzmann-Peierls equation and a broad class of isotropic dispersion relations [Ω(k)⇒Ω(𝓀), 𝓀: =‖k‖], the exact system of irreducible equations of transfer for the symmetric traceless moments of the distribution function f is derived and the range of validity of Grad’s moment procedure is extended to the case of quasiparticle gases. Thus not without reason, an expansion with respect to k of the one-particle density f around the local Bose–Einstein occupation probability f0 in terms of the appropriately chosen Tchebychef functions Aβ(z;Θ) and Ikenberry’s harmonics Yα(g) is carefully recognized. Also, the importance of the Tchebychef basis {Aβ; β=0,1,...}, both in any serious analysis of equilibrium fluctuations and in exploiting the Chapman–Enskog procedure, is clearly established.
Simple calculation of Löwdin’s alpha function. III. Procedure for calculating h
n,2n−i(L
M‖ℓ )/(2n−i )! successively
Authors: Suzuki Noboru
Published: July 2002

When r/a≊0, Löwdin’s α function (1/r)αℓ(fLM‖a,r) is expressed as (1/r)αℓ ( fLM‖a,r) =2γ(LM‖ℓ )aL−1∑∞n=ℓ [∑imaxi=ℓ+M[hn,2n−i (LM‖ℓ )/(2n−i)!]a2n−ig(2n−i) (a)](r/a)2n−ℓ, where a is a separation between a new center placed on the origin and the old center located at a given point on the z axis that is the origin of the coordinate system defining a function f (R)YML(Θ,Φ) to be expanded around the new center [ f(R) is an arbitrary radial function, and YML(Θ,Φ), a complex spherical harmonics], and r is a distance from the new center. Here, imax=min{2n,2(L+ℓ )}, and the function g(j)(a) is expressed as g(j)(a)=[(d/dR)j ( f(iR)/RL−1)]R=a.

The closed form of the coefficients hn,2n−i(LM‖ℓ ) is given by Eq. (27) in J. Math. Phys. 26, 3193 (1985) (referred to as Part II). Since they are expressed in terms of the different coefficients bKk(LM‖ℓ ) independent of the form of f(R), hn,2n−i(LM‖ℓ ) constitute a set of universal constants as do bKk(LM‖ℓ ). The explicit expression for the factor γ(LM‖ℓ ) in front of the summation symbol is given by Eq. (2.9) in J. Math. Phys. 25, 1133 (1984). Hereafter the coefficients expressed by hn,2n−i(LM‖ℓ )/(2n−i)! are symbolized by In,2n−i(LM‖ℓ ). Although they are expressed in a complex form with a triple sum, that expression can be reduced to two considerably simple forms by changing the summation indices to others by using the addition theorem for binomial coefficients and the condition for the sum in this theorem to vanish. Moreover, in the two special cases that i=ℓ+M and i=2(L+ℓ ) or 2(L+ℓ )−1, those two expressions are reduced to two single-term forms, respectively.

Introducing into the expression for In,2n−i(LM‖ℓ ) in terms of bKk(LM‖ℓ ) the recursion formula for bKk(LM‖ℓ ) in only M given by Eq. (24) in Part II, leads to the recursion formula for In,2n−i(LM‖ℓ ) with respect to M. On the other side, the recursion formulas for In,2n−i(LM‖ℓ ) with M=L and ℓ as to i are obtained through a skillful manipulation. By connecting those recursion formulas for In,2n−i(LM‖ℓ ) to each other, we can obtain a procedure for calculating In,2n−i(LM‖ℓ ) successively. As the result of actual performance of the procedure, all the formulas expressing In,2n−i(LM‖ℓ ) with restriction 0≤M≤min{L,ℓ }≤max{L,ℓ }≤2 are presented as functions of the parameter n in a table.
Basic equations of three-dimensional radiative transfer
Authors: Wang Alan P.
Published: July 2002

Chandrasekhar developed one-dimensional mathematical models of radiative transfer in 1949 [Radiative Transfer (Oxford U.P., New York, 1950)]. This paper is a systematic extension of Chandrasekhar’s work to three dimensions, including discussions of specular and diffused parts, reciprocity, solutions, and approximation.
Stochastic field theory, holomorphic quantum mechanics, and supersymmetry
Authors: Bandyopadhyay Pratul , Hajra Kohinur , Ghosh Pradip
Published: July 2002

Holomorphic quantum mechanics are studied from the point of view of stochastic quantization in Minkowski space which involves the introduction of two stochastic fields, one in the external space and the other in the internal space. The equilibrium condition is given by Z2 symmetry between the external and internal fields. In the nonequilibrium case, N=2 Wess–Zumino quantum fields are arrived at giving rise to supersymmetry. This helps to define the supercharge operator Q when the Hamiltonian is given by H=Q2 and an index theorem is derived for an interacting case when the superpotential is given by V(φ)=λφn, φ being complex with n>2. It is found that the vacuum is degenerate and is in conformity with the result obtained by Jaffe, Lesniewski, and Lewenstein [Ann. Phys. 178, 313 (1987)] in the two-dimensional N=2 Wess–Zumino quantum field model.
Quantization of bi-Hamiltonian systems
Authors: Kaup D. J. , Olver Peter J.
Published: July 2002

One of the distinguishing features of soliton equations is the fact that they can be written in Hamiltonian form in more than one way. Here we compare the different quantized versions of the soliton equations arising in the AKNS inverse scattering scheme. It is found that, when expressed in terms of the scattering data, both quantized versions are essentially identical.
Matching p
p waves to the Kerr metric
Authors: Hoenselaers C. , Ernst F. J.
Published: July 2002

Alternative pairs of impulsive pp waves (accompanied by shocks) that interact to produce a Kerr geometry are compared. In one case, discovered by Chandrasekhar and Xanthopoulos [Proc. R. Soc. London Ser. A 408, 175 (1986)], analytic extension across the horizon revealed a timelike singularity analogous to the ring singularity of the Kerr metric. In another, presented here for the first time, analytic extension across the horizon reveals instead an asymptotically flat exterior Kerr geometry. The pp wave pulse shapes that result in the formation of these two different Kerr interaction regions are displayed graphically.
Properties of cyclic permutation matrices on Potts spin spaces and associated arithmetical polynomials
Authors: Audit Philippe
Published: July 2002

Exploring cyclic permutation matrices on a space of N q-state spins, novel arithmetical polynomials in q of degree N are introduced, which satisfy interesting relations (especially congruence relations zero to modulus N. i.e., generalization to an arbitrary integer of Fermat’s little theorem) and provide a natural representation of spectral properties with much physical significance.
Self-dual Yang–Mills hierarchy: A nonlinear integrable dynamical system in higher dimensions
Authors: Nakamura Yoshimasa
Published: July 2002

A self-dual Yang–Mills (SDYM) hierarchy is presented that has some properties similar to those of the celebrated Kadomtsev–Petviashvili (KP) hierarchy having one spacial variable. The SDYM hierarchy is an infinite system of GL(∞)-invariant compatible SDYM equations depending on an infinite number of spacial variables, on which an exponential operator acts as a time evolution operator. A nontrivial GL(∞) symmetry of the SDYM hierarchy called the Bruhat transformation is found. The existence of the GL(∞) SDYM hierarchy supports the complete integrability of the single GL(∞)SDYM equation with a reduction condition, however, our observation suggests that the SDYM equation without the condition may not be completely integrable in sharp contrast with the KP equation.
Structure of the Lie algebra of polynomial vector fields on the Riemann sphere with three punctures
Authors: Bremner Murray R.
Published: July 2002

The Lie algebra of polynomial vector fields on the sphere with two punctures (also known as the Witt algebra or the centerless Virasoro algebra) can be generalized in different ways. In this paper the Lie algebra obtained by allowing poles at three points rather than only two is considered. Using some elementary representation theory of the symmetric group on three letters, a convenient basis for this Lie algebra is determined, such that the commutator of two basis elements is a linear combination of at most three other basis elements. The expressions for the basis elements show that this Lie algebra is related to modular forms for a level-2 congruence subgroup of SL2(Z). A conclusion is given with some suggestions for further investigation.
Multibody operator matrix elements and subduction coefficients in U(n)
Authors: Kent R. D. , Schlesinger M.
Published: July 2002

An approach to decomposing the specialized types of U(n) 3ν−j coefficients which arise in operator matrix element calculations in the Gel’fand basis is presented. Previous work on matrix elements of U(n) generator products will be extended to cases involving three generators and beyond. In addition, the methods of evaluation of SU(m)⊗SU(n)↓SU(m+n) subduction coefficients will be applied. The techniques are easily formulated in terms of Yutsis graphs. Explicit phase relations are incorporated throughout the treatment.
Representations of the quantum algebra suq(2) on a real two-dimensional sphere
Authors: Rideau G. , Winternitz P.
Published: July 2002

Representations of the quantum algebra suq(2) are constructed in terms of q-special functions, defined on real O(3) spheres and real planes. They include q-Vilenkin functions, related to little q-Jacobi functions, q-spherical functions, and q-Legendre polynomials.
Quadratic Poisson algebras and their infinite-dimensional extensions
Authors: Fokas A. S. , Gel’fand I. M.
Published: July 2002

A certain generalization of the classical modified Yang–Baxter equation is presented. Also certain Poisson algebras arising in the calculus of variations are investigated.
On acoustic Helmholtz resonator and on its electromagnetic analog
Authors: Gadyl’shin Rustem R.
Published: July 2002

A study of the acoustic Helmholtz resonator and of its electromagnetic analog (a cylinder with a narrow slit) is performed. For the associated Green functions, power series asymptotics with respect to a small parameter ε (‘‘radius’’ of the resonator hole or the width of the slit), and ln ε of poles τε with small imaginary parts are obtained by using the method of matching asymptotic expansions. The principal terms of solution asymptotics for corresponding boundary value problems are given.
Affine projection tensor geometry: Decomposing the curvature tensor when the connection is arbitrary and the projection is tilted
Authors: Gowdy Robert H.
Published: July 2002

This paper constructs the geometrically natural objects which are associated with any projection tensor field on a manifold with any affine connection. The approaches to projection tensor fields which have been used in general relativity and related theories assume normal projection tensors of codimension one and connections which are metric compatible and torsion-free. These assumptions fail for projections onto lightlike curves or surfaces and other situations where degenerate metrics occur as well as projections onto two-surfaces and projections onto space–time in the higher dimensional manifolds of unified field theories. This paper removes these restrictive assumptions. One key idea is to define two different ‘‘extrinsic curvature tensors’’ which become equal for normal projections. In addition, a new family of geometrical tensors is introduced: the cross-projected curvature tensors. In terms of these objects, projection decompositions of covariant derivatives, the full Riemann curvature tensor and the Bianchi identities are obtained and applied to perfect fluids, timelike curve congruences, string congruences, and the familiar 3+1 analysis of the spacelike initial value problem of general relativity.
Deformations of Gabor frames
Authors: Kaiser Gerald
Published: July 2002

The quantum mechanical Harmonic oscillator Hamiltonian H=(t2−∂2t)/2 generates a one-parameter unitary group W(θ)=eiθH in L2(R) which rotates the time–frequency plane. In particular, W(π/2) is the Fourier transform. When W(θ) is applied to any frame of Gabor wavelets, the result is another such frame with identical frame bounds. Thus each Gabor frame gives rise to a one-parameter family of frames, which we call a deformation of the original. For example, beginning with the usual tight frame ℱ of Gabor wavelets generated by a compactly supported window g(t) and parameterized by a regular lattice in the time–frequency plane, one obtains a family {ℱθ: 0≤θ<2π} of frames generated by the noncompactly supported windows gθ=W(θ)g, parameterized by rotated versions of the original lattice. This gives a method for constructing tight frames of Gabor wavelets for which neither the window nor its Fourier transform have compact support. When θ=π/2, ℱθ is the well-known Gabor frame generated by a window with compactly supported Fourier transform. The family {ℱθ} therefore interpolates these two familiar examples.
Path integral for the damped harmonic oscillator coupled to its dual
Authors: Chetouani L. , Guechi L. , Hammann T. F. , Letlout M.
Published: July 2002

The time independent Bateman model which describes the damped harmonic oscillator coupled to its dual is studied using the path integral approach. The related propagator is calculated by means of the matrix representation.
Variational principles for complex conductivity, viscoelasticity, and similar problems in media with complex moduli
Authors: Cherkaev A. V. , Gibiansky L. V.
Published: July 2002

Linear processes in media with dissipation arising in conductivity, optics, viscoelasticity, etc. are considered. Time-periodic fields in such media are described by linear differential equations for complex-valued potentials. The properties of the media are characterized by complex valued tensors, for example, by complex conductivity or complex elasticity tensors. Variational formulations are suggested for such problems: The functionals whose Euler equations coincide with the original ones are constructed. Four equivalent variational principles are obtained: two minimax and two minimal ones. The functionals of the obtained minimal variational principles are proportional to the energy dissipation averaged over the period of oscillation. The last principles can be used in the homogenization theory to obtain the bounds on the effective properties of composite materials with complex valued properties tensors.
Monte Carlo simulations of 4d simplicial quantum gravity
Authors: Brügmann Bernd , Marinari Enzo
Published: July 2002

Dynamical triangulations of four-dimensional Euclidean quantum gravity give rise to an interesting, numerically accessible model of quantum gravity. We give a simple introduction to the model and discuss two particularly important issues. One is that contrary to recent claims there is strong analytical and numerical evidence for the existence of an exponential bound that makes the partition function well defined. The other is that there may be an ambiguity in the choice of the measure of the discrete model which could even lead to the existence of different universality classes.