bluuebunny/crossref_metadata_2025 huggingface dataset:
A new hybrid approach for modeling reactions in molecular clusters: Application for the hydrogen bonded systems
Authors: Nemukhin Alexander V. , Grigorenko Bella L. , Skasyrskaya Ekaterina Ya. , Topol Igor A. , Burt Stanley K.
Published: July 2002

A hybrid quantum mechanical diatomics-in-molecules (QM/DIM) method is formulated that aims to describe chemical reactions in an environment within the framework of a discrete (or cluster) approach. Starting from the conventional DIM formalism, first-order intermolecular perturbation theory is applied to calculate interactions between reacting particles and environmental molecules, and to introduce ab initio QM energies for the central system. In this approach no boundary problems appear when combining two parts of the entire system. The pairwise contributions to the interaction energy come from the true potential curves of the fragments. A proper treatment of excited electronic states is also provided in this approach. As a first application, we compute potential curves for the dissociation reaction of a single hydrogen fluoride molecule surrounded by a selected number of solvent HF molecules.
Pattern formation in a thin random copolymer film: Evolution of an intermediate morphology
Authors: Masson J.-L. , Green P. F.
Published: July 2002

Previous studies of structural instabilities in thin, nonwetting, liquid homopolymer films on substrates have focused on systems that dewet, forming patterns that reflect fluctuations in the local film thickness. These patterns range from discrete cylindrical holes throughout the surface of the film to bicontinuous “spinodallike” patterns. In this paper we show that a thin liquid film, a random copolymer, styrene-ran-acrylonitrile (SAN) comprised of 75% styrene and 25% acrylonitrile, of thickness h=12 nm becomes unstable and dewets silicon substrates, forming what we describe here as an intermediate morphology. During the early stage of dewetting, discrete noncylindrical, irregular, shaped holes appear spontaneously in the film. The number of holes, N, initially increase with time and the morphology of the late stage of growth, after 18 days, is characterized by a bicontinuous pattern, distinct from conventional spinodal dewetting patterns. The dynamics of pattern evolution of this intermediate morphology are discussed.
Spin relaxation by dipolar coupling: From motional narrowing to the rigid limit
Authors: Nevzorov Alexander A. , Freed Jack H.
Published: July 2002

A coupled system of two molecules bearing spins of 1/2, which are allowed to diffuse relative to each other, is considered. By using a symmetry-adapted basis operator set, the overall density matrix equation is decoupled into two equations for the time-resolved isochromat components, the sum of which yields the observed signal. The appropriate stochastic Liouville equation is solved by a combination of eigenfunction expansion and finite-differences for the angular and radial relative motions, respectively. A full range of spectra from classic Pake patterns in the rigid limit to motionally narrowed Lorentzians is recovered. As an extension of the above approach, the solid-echo experiment is described in terms of the ensemble-averaged isochromats. Homogeneous transverse relaxation times (T2) as a function of the translational diffusion coefficient (DT) are obtained from simulating SECSY (spin-echo correlation spectroscopy) signals, which show distinct T2 minima vs DT. The present method of separating the quantum and stochastic classical variables constitutes a useful approach for treating multiquantum statistical systems, and it can be generalized to an arbitrary number of spins as shown in a companion paper. In the present study we obtained the usual linear dependence of T2 on DT in the motional narrowing (or Redfield) limit, whereas in the slow motional regime a DT−1/2 dependence is observed, consistent with studies of rotational diffusion. Varying the distance of maximum separation between the two spins (rmax) has virtually no effect on the location of the T2 minimum with respect to DT, implying that the onset of slow motion is essentially independent of rmax.
Core-induced photofragmentation of acetonitrile adsorbed on Au(111) and Pt(111)
Authors: Parent Ph. , Laffon C. , Bournel F.
Published: July 2002

Photodissociation of acetonitrile (CH3CN) condensed, physisorbed on Au(111), and chemisorbed on Pt(111), has been studied at the C(1s) and N(1s) edges in H+ yield and/or in total positive ion yield. The H+ yield C(1s) absorption experiment on the condensed acetonitrile shows a selective fragmentation of the C–H bond at the C 1s→π*CH3 excitation, that is still observed when acetonitrile is physisorbed on Au(111) and chemisorbed on Pt(111). Transitions to the π*C≡N state give rise to unselective fragmentations, which are strongly quenched by charge transfer from the substrate when acetonitrile is chemisorbed on Pt(111). The π⊥*C≡N level that plunges into the Pt(111) is the most affected and vanishes in the total ion yield measurement. The quenching is weaker on the π∥*C≡N which is parallel to the surface, and thus is less hybridized with the metal than the π⊥*C≡N. For acetonitrile physisorbed on Au(111), the influence of the surface is limited to the quenching of the desorption of the heaviest outgoing fragments.
Figures of merit of push–pull molecules in photorefractive polymers
Authors: Barzoukas M. , Blanchard-Desce M.
Published: July 2002

Push–pull molecules are the most widely used nonlinear optical chromophores incorporated in polymers to generate photorefractivity. They are at the origin of the Pockels and the Kerr electrooptic effects in high-Tg photorefractive polymers and give also rise to the optical birefringence in low-Tg photorefractive polymers. High-Tg and low-Tg figures of merit characterize the efficiency of push–pull molecules to generate phototrefractivity. We present, here, the two-level figures of merit of various push–pull molecules determined by using electrooptical absorption measurements in solution. Analysis of the results within the framework of the two-form two-state model provides useful guidelines for the design of push–pull molecules for photorefractive applications. This model enables us to evaluate the optimum structures as well as the corresponding maximum optical birefringence, Pockels and Kerr electrooptic responses. It also shows how these maxima are related. Tuning a molecular structure to reach an optimum one will not automatically lead to a very large figure of merit. An essential parameter that is usually overlooked is the magnitudes of these maxima. We show that the maxima are affected both by the conjugation length and by the choice of the donor/acceptor substituents. Some of the longest compounds investigated here exhibit very large high-Tg and low-Tg figures of merit.
High pressure Raman scattering studies on adamantane
Authors: Rao Rekha , Sakuntala T. , Deb S. K. , Roy A. P. , Vijaykumar V. , Godwal B. K. , Sikka S. K.
Published: July 2002

High pressure behavior of adamantane is investigated up to pressures of 26 GPa at ambient temperature using Raman spectroscopy. A detailed study of changes in the Raman spectrum of the C–H stretching modes across the disorder–order transition around 0.5 GPa is reported. Pressure dependence of the internal mode frequencies suggest two more subtle transitions around 2.8 GPa and 8.5 GPa, respectively, which are reversible. Evolution of spectra at higher pressures show evidence for another structural transition above 24 GPa.
Equilibrium and nonequilibrium effects of a single polymer chain during cyclic deformation: A Monte Carlo study
Authors: Kreitmeier Stefan
Published: July 2002

Using the bond-fluctuation model, the conformational, energetic, and entropic changes of a single polymer chain caused by cyclic deformation is studied. The drawing velocity is varied by means of different relaxation times between deformation steps. The simulated temperatures reach from far above the Θ temperature to well below. Above the Θ temperature, the deformation is homogeneous and controlled by the entropy. No differences between loading and unloading can be seen. All simulations appear to be in equilibrium conditions. Below the Θ temperature, the deformation behavior for fixed drawing velocity is found to be completely different. Nonequilibrium effects show up. In the cyclic deformation, a hysteresis in the total force as well as in its energetic and entropic parts occur. A quasi reversible behavior of the globule-strand system in further cycles is described.
Collision-induced dissociation and density functional study of the structures and energies of cyclic C2nN5− clusters
Authors: Tang Zichao , BelBruno Joseph J. , Huang Rongbin , Zheng Lansun
Published: July 2002

In this paper, we report mass spectrometry studies on C2nN5− cluster ions by collision-induced dissociation (CID). The mass-selected cluster ions were dissociated by collision with a crossed nitrogen beam and the fragment ions were mass analyzed in a secondary mass spectrometer. Characterization of the species as cyano-substituted, planar five-membered rings is supported by density functional theory (DFT) calculations. Based on the analysis of the experimental and computational results, cluster structures, energies, and stabilities are discussed.
Simulation of heteropolymer collapse with an explicit solvent in two dimensions
Authors: Polson James M. , Zuckermann Martin J.
Published: July 2002

Molecular dynamics simulations are used to study the equilibrium properties and collapse dynamics of a heteropolymer in the presence of an explicit solvent in two dimensions. The system consists of a single copolymer chain composed of hydrophobic (H) and hydrophilic (P) monomers, immersed in a Lennard-Jones solvent. We consider HP chains of varying hydrophobic number fraction nH, defined as the ratio of the number of H monomers to the total number of monomers. We also consider homopolymer chains with a uniform variable degree of hydrophobicity λ, which describes the hydrophobic-solvent interaction, and which ranges from hydrophilic (λ=0) to hydrophobic (λ=1). We investigate the effects of varying nH and λ, the HP sequencing, and the solvent density on the equilibrium and collapse properties of the chain. For sufficiently high nH, we observe a collapse transition for random copolymers from a stretched coil to a liquidlike globule upon a decrease in temperature; the transition temperature decreases with increasing nH. The transition can also be induced at a fixed (and sufficiently low) temperature by varying nH for random copolymers or λ for homopolymers. We find that polymer size varies inversely with solvent density. The rate of polymer collapse is found to strongly vary inversely with increasing nH and λ for copolymers and homopolymers, respectively. Further, the collapse rates for these two cases are very close for nH=λ, except at lower values (nH=λ≈0.5), where the homopolymers collapse more rapidly. At moderate densities (ρ=0.5–0.7, in LJ reduced units), we find that random copolymers collapse more rapidly at low density and that this difference tends to increase with decreasing nH. At fixed solvent density and nH we find the collapse rate differs little for random copolymers, and multi-block copolymers with equal nH. Finally, the simulations suggest that copolymers tend to collapse by a uniform thickening rather than by first forming locally collapsed clusters which aggregate at longer time. The exception to this appears to be block-copolymers comprised of sufficiently long alternating H and P blocks.
Nuclear magnetic resonance study of xenon-131 interacting with surfaces: Effective Liouvillian and spectral analysis
Authors: Deschamps Michaël , Burghardt Irene , Derouet Christiane , Bodenhausen Geoffrey , Belkić Dževad
Published: July 2002

Coherent and dissipative phenomena induced by transient adsorption of xenon-131 on a glass surface are studied by nuclear magnetic resonance spectroscopy. We report the results of multiple-quantum filtered experiments over a range of temperatures, covering different relaxation regimes. An analysis in terms of an effective Liouvillian is proposed, the complex eigenvalues of which may be directly extracted from the experimental spectra. For this purpose, we apply recently developed techniques for spectral analysis, in particular decimated signal diagonalization. The results are compared with a conventional fit of the multiple-quantum build-up behavior.
Numerical integration in many dimensions. II
Authors: Schwartz Charles
Published: July 2002

Two new techniques are presented that appear to be useful in obtaining accurate numerical values for the numerical integration of fairly smooth functions in many dimensions. Both methods start with the idea of a mesh containing n points laid out in each of the d dimensions, then seek strategies that use far less than all nd points in some systematically improved sequence of approximations.
Elementary properties of a new kind of path integral
Authors: Hajicek P.
Published: July 2002

A new kind of path integral is introduced. In ordinary quantum mechanics, it gives the projectors on the eigenspaces of the Hamiltonian. For parametrized systems, it represents a direct path integral version of the Dirac canonical quantization method by giving the projector on the physical space. Its properties on the most simple examples are studied. Applying it to quantum cosmology, the Hartle–Hawking wave function of the universe is recalculated.
Statistical mechanics approach in minimizing a multivariable function
Authors: Khachaturyan Armen
Published: July 2002

The method of minimization of a multivariable function based on the statistical mechanics analogy with a fictitious physical system of many particles is proposed. The function is assumed to be the Hamiltonian of the fictitious physical system to fit the global minimum of the function and the ground state ‘‘energy’’ of the fictitious system. In this model the global minimum search can be imitated by various relaxation processes in the fictitious system described by statistical mechanics. These relaxation processes lead to the equilibrium state, which is the ground state at the zero temperature limit. The imitation of a relaxation process confers to the minimization procedure the advantage of a relaxation process in a real physical system: because of thermal fluctuations a real system cannot be trapped by metastable states related to local minima. It always reaches the equilibrium state. The simulations of the relaxation processes based on the macroscopic kinetic equations and on the Monte Carlo algorithms are discussed. The new Monte Carlo algorithm based on the simulation of random walks of the representative point of the system in multidimensional phase space of the variables of the function under investigation is proposed. Unlike the conventional Metropolis–Rosenbluths–Tellers Monte Carlo method, each elementary transition in the proposed algorithm results in simultaneous movement of all atoms of the system, i.e., it generates a fluctuation involving any number of atoms.
Two-loop counterterms for the Wess–Zumino model on anti-de Sitter space
Authors: Jack I.
Published: July 2002

The two-loop counterterms for the Wess–Zumino model on a four-dimensional anti-de Sitter space background are computed. It is shown that, as at the one-loop level, the counterterms preserve supersymmetry but the nonrenormalization theorem is violated by the addition of a divergent linear term to the superpotential.
Simulation of classical particle trajectories in a complex two-dimensional space
Authors: Derrick G. H.
Published: July 2002

Classical particles of arbitrary rest mass and spin are modeled in a two-dimensional space C2 (which has two complex coordinates ξA, A=1, 2) in the following way. It is first shown that a preferred set of trajectories ξA=ζA(s), designated geodesics, can be introduced from a variation principle that makes stationary the real variable s. The latter plays the role of proper time and serves to parametrize the trajectories. The geodesics so defined are then shown to be associated with a nonlinear representation of the Poincaré group. A set of Poincaré vectors and tensors are constructed from ζA and its proper time derivatives and these simulate the properties of the position, momentum, angular momentum, and internal angular momentum variables of a classical massive particle of arbitrary spin.
Electromagnetic binding of a minimally interacting, relativistic spin-0 and spin- 1/2 constituent: Zero four-momentum solutions
Authors: Mainland G. Bruce
Published: July 2002

Bound states of a composite system consisting of a charged spin-0 and a charged spin- 1/2 constituent interacting via minimal electrodynamics are investigated using the Bethe–Salpeter equation in the ladder approximation (single photon exchange). Although the interaction involves derivative couplings, in the limit that the four-momentum is zero, it is possible to solve the integral equation by performing a Wick rotation and employing a method due to Fock. The eigenvalue spectrum of the coupling constant is found to be discrete.
On the phase transition of the three-dimensional Percus–Yevick equation for an arbitrary potential of finite range
Authors: Chen M.
Published: July 2002

A qualitative study of the three-dimensional Percus–Yevick (PY) equation by means of Baxter’s relations is considered for an arbitrary potential of finite range l by a perturbation method. It is shown that the PY equation has a unique solution Y(r,η,β§) and a unique solution Q(r,η,β§) if the following conditions are satisfied: (i) 0<η<0.175, (ii) 0<β§<(β§)0, (iii) Supr∈[0,l]‖Qn‖0‖Yn(r)‖<n!, where both Q and Y are continuous functions of the reduced density η, and can expressed as absolutely and uniformly convergent series Y=∑∞n=0(1/n!)(β§)nYn(r,η), Q=∑∞n=0(1/n!)(β§)nQn(r,η) within the radius of convergence of the inverse reduced temperature (β§)0. As functions of r, Q∈C(0)[0,l] with Q(l)=0, whereas Y is continuous for r≥0 except for a possible finite discontinuity at r=1, and Y−r→0 exponentially as r→∞. Based on the solution of Y and Q, the isothermal compressibility KT =KT(∂ρ/∂P)T is a continuous and bounded function of η. As η→ηc =0.175, KT becomes divergent. The critical density ηc (or ρc) is independent of the range of the attractive potential l. On the other hand, the critical temperature (β§)c is determined by the positive root of F(β§)=12η∫l0Q(r)dr =1, which depends explicitly on the value of l.
Shear-free perfect fluids in general relativity. I. Petrov type N Weyl tensor
Authors: Carminati J.
Published: July 2002

Petrov type N, shear-free, perfect fluid solutions of the Einstein field equations are investigated. It is shown that if the fluid pressure p and energy density w are related by a barotropic equation of state p=p(w) satisfying w+p≢0, and if the Weyl tensor is of Petrov type N then the fluid’s volume expansion is zero but the vorticity is necessarily nonzero. The differential equation determining p as a function of w is given. For this class of solutions the fluid’s vorticity vector is orthogonal to the acceleration.
Long-range dynamics and broken symmetries in gauge models. The Schwinger model
Authors: Morchio G. , Strocchi F.
Published: July 2002

The occurrence of variables at infinity in the dynamics of gauge models (in positive gauges) as a result of the Coulomb-type interaction is rigorously shown in two-dimensional quantum electrodynamics, in the Coulomb gauge. The general structures associated to the algebraic dynamics of systems with long-range interactions, like the removal of the infrared cutoff, the effective dynamics, the classical motion of the variables at infinity, and their relevance for the generalization of the Goldstone theorem and the spectrum of the generalized Goldstone bosons, are explicitly shown in this model; in particular, the chiral symmetry breaking and the associated mass generation is discussed in detail. The analogous results for the chiral Schwinger model are briefly summarized.
Explicit solutions of Grassmannian σ models
Authors: Piette B.
Published: July 2002

Classical solutions of the two-dimensional Grassmannian σ models of, respectively, Euclidean and Minkowskian type are compared with each other. Some explicit solutions of both types are constructed and some of their graphs are presented.
Matrix methods for the numerical solution of relativistic wave equations
Authors: Durand Loyal , Gara Alan
Published: July 2002

An efficient new method is presented for the solution of eigenvalue problems that involve nonlocal operators of the type that appear in the solution of relativistic wave equations. The method, which has wider utility, allows very accurate results to be obtained with small matrix approximations to the eigenvalue equation. The method is illustrated for the equation [2(−∇2+m2)1/2+V(r)−M]ψ=0.
Collision theory for massless particles in the framework of a Wightman field theory
Authors: Strube Dieter
Published: July 2002

A collision theory of massless Fermions and Bosons is constructed within the framework of a Wightman field theory. To this end, using essentially the temperedness of the Wightman distributions, the main ideas of the collision theory of Buchholz formulated in a field theory of bounded operators are carried over.
BRS cohomology in string theory: Geometry of Abelization and the quartet mechanism
Authors: Aratyn Henrik
Published: July 2002

The Abelian representation of the string Becchi–Rouet–Stora (BRS) cohomology in terms of basic operators naturally forming two dual Kugo–Ojima quartets is found. Furthermore, using a gauge-fixing scheme, a contracting homotopy operator associated with the string BRS operator is constructed. This formalism gives the explicit realizations of the physical and unphysical subspaces. The passage between Abelian and non-Abelian quantities is realized geometrically through the use of the moments of the vertex operator, which act as vielbeins between infinite-dimensional algebras. The connection between the Virasoro and spectrum-generating algebras is clarified and the algebraic duality relation between them is uncovered.
Angular distributions, rotational summations, and integrations in the quadrupole and two-photon photodissociation of molecules
Authors: Lai Shan-Tao , Chiu Ying-Nan
Published: July 2002

In this work, the closed forms of the angular distributions in quadrupole and two-photon photodissociation of molecules are obtained. These are applicable to the angular factors of other second-order, nonlinear, or quadratic processes.
Propagators for relativistic systems with non-Abelian interactions
Authors: Corns R. A. , Osborn T. A.
Published: July 2002

The relativistic evolution of a system of particles in the proper-time Schwinger–DeWitt formalism is investigated. For a class of interactions that can be represented as Fourier transforms of bounded complex matrix-valued measures, a Dyson series representation of the propagator is obtained. This class of interactions is non-Abelian and includes both external electromagnetic and Yang–Mills fields. The study of the relativistic problem is facilitated by embedding the original quantum evolution into a larger class of evolution problems that result if one makes an analytic continuation of the metric tensor gμν. This continuation is chosen so that the extended propagator shares (for all signatures of gμν ) the Gaussian decay properties typical of heat kernels. Estimates of the nth-order Dyson iterate kernels are found that ensure the absolute convergence of the perturbation series. In this fashion a number of analytic and smoothness properties of the propagator are determined. In particular, it is demonstrated that the convergent Dyson series representation constructs a fundamental solution of the equations of motion.
A class of exact solutions of Yang’s K gauge equation for SU(2) gauge fields
Authors: Matsuno Y.
Published: July 2002

Using a simple ansatz, Yang’s K gauge equation for SU(2) gauge fields is reduced to a system of nonlinear ordinary differential equations. Exact solutions for the equations are obtained together with corresponding gauge potentials.
Generating functions, bi-Hamiltonian systems, and the quadratic-Hamiltonian theorem
Authors: Cariñena José F. , Rañada Manuel F.
Published: July 2002

The concept of bi-Hamiltonian systems and its connection with the theory of canonoid transformations is shown from a geometrical viewpoint. The relations between symplectic and canonoid diffeomorphisms are studied using an approach based on the theory of generating functions. These results are used for obtaining a new theorem which will represent an intrinsic and coordinate-free generalization of the ‘‘quadratic Hamiltonian theorem.’’
The Overhauser model: Equilibrium fluctuation dynamics
Authors: Broidioi Marino , Nachtergaele Bruno , Verbeure André
Published: July 2002

A Goldstone-type theorem is derived to reveal the nature of the spontaneous symmetry breaking occurring in the Overhauser model. Explicit expressions for the equilibrium states of the model are calculated. The fluctuations of the fields satisfy a central limit theorem. The limit is a new set of Fermionic fields that inherit their dynamics from the original model. In the low-temperature phase, where the order parameter does not vanish, this dynamics is nontrivial and basically shows oscillations with a frequency related to the order parameter.
Perturbation theory of C*-systems without norm-continuity properties
Authors: Amann Anton
Published: July 2002

Dynamical C*-systems without norm-continuity properties (e.g., the dynamics of a boson-type system) are studied. The respective dynamics cannot be perturbed by (bounded, self-adjoint) elements of the underlying abstract C*-algebra. Hence, it is necessary to define notions like ‘‘invariant state,’’ ‘‘ground state,’’ ‘‘KMS-state,’’ etc. with respect to the perturbed dynamics in suitable Hilbert space representations. Here, the original dynamical system is supplemented by an auxiliary pointwise norm-continuous dynamical system in such a way that invariant states of the original system correspond to certain invariant states of the auxiliary system. This bijective correspondence is sequentially continuous and preserves the KMS- (ground state) characterizing conditions. As a typical application it is verified that Spohn’s ground states of the spin-boson model (arising as a temperature to zero limit of thermic equilibrium states) are ground states in the algebraic sense, i.e., are eigenstates of the respective (Gel’fand–Naimark–Segal) Hamiltonian with an eigenvalue at the lower end of the Hamiltonian’s spectrum.
Surface quadrupling and regularized off-shell amplitudes for unoriented, open, bosonic strings
Authors: Collins Graham P. , Weisberger William I.
Published: July 2002

Off-shell, unoriented, open bosonic string amplitudes correspond to Klein surfaces with mixed (Neumann and Dirichlet) boundary conditions and corners. The standard surface-doubling procedures (Schottky, orienting, and complex) are generalized to yield new doubles of use for mixed boundary conditions. Multiple doubling yields various quadruple and octuple surfaces. In particular, a Klein surface with mixed conditions and corners has a compact oriented quadruple which is a Riemann surface with certain symmetries. Determinants of Laplacians on the Klein surface are related to determinants on this quadruple, and to determinants on a compact, oriented (but singular) double surface. Unlike the case for uniform boundary conditions, which uses one double surface, it does not seem possible to obtain the amplitude on the Klein surface as an elegant ‘‘fourth root’’ of an amplitude on the quadruple alone. When regularized, the relation between the amplitudes acquires correction terms, involving the integrated geodesic curvature of the boundary. A Weyl anomaly from the corners of the original surface is hidden in a determinant on the singular double.
Deconfinement phase transition within the MIT bag model
Authors: Savatier F.
Published: July 2002

On the basis of statistical mechanics of a gas of hadronic MIT bags, a thermodynamic study of the deconfinement phase transition is realized. A comparison between the static model and a model with bag surface fluctuations is realized. The temperature dependences of the main physical quantities are plotted. Finally, the critical behavior of baryonic matter is investigated.
Asymptotic behavior of Jost functions near resonance points for Wigner–von Neumann type potentials
Authors: Klaus Martin
Published: July 2002

In this work are considered radial Schrödinger operators −ψ″+V(r)ψ=Eψ, where V(r)=a sin br/r+W(r) with W(r) bounded, W(r)=O(r−2) at infinity (a,b real). The asymptotic behavior of the Jost function and the scattering matrix near the resonance point E0=b2/4 are studied. If ‖a‖>‖b‖, then this point may be an eigenvalue embedded in the continuous spectrum. The leading behavior of the Jost function for all values of a and b were determined. Somewhat surprisingly, situations were found where the Jost function becomes singular as E→E0 even if E0 is an embedded eigenvalue. Moreover, it was found that the scattering matrix is always discontinuous at E0 except in a few special cases. It is also shown that the asymptotics for the Jost function and the scattering matrix hold under weaker assumptions on W(r), in particular an angular momentum term l(l+1)r−2 may be incorporated into W(r). The results were also applied to a whole line problem with a potential V(x) such that V(x)=0 for x<0 and V(x) of Wigner–von Neumann type for x>0, and the behavior of the transmission and reflection coefficients as E→E0 was also studied.
Finite-size scaling for the correlation function of the spherical model with long-range interactions
Authors: Brankov J. G. , Danchev D. M.
Published: July 2002

Finite-size scaling for the effective correlation length and the pair correlation function of the mean spherical model is studied in the case of general geometry Ld−d′×∞d′, periodic boundary conditions, and long-range interactions decaying like R−d−σ at large distances R, with arbitrary real parameters 0<σ≤2, σ≤d≤2σ, d′≥0. The analytical technique used is based on integral transformations with kernels of Mittag–Leffler type. It makes it possible to easily generalize a number of results available only for short-range interactions or in special cases of the Ld−d′×∞d′ geometry. The effective correlation length is identified at arbitrary temperatures from the finite-size large-distance asymptotic behavior of the pair correlation function. It is explicitly shown that the finite-size scaling functions are not singular in the ε-expansion when ε→0+ neither at d=σ+ε, nor at d=2σ−ε. Moreover, the applicability of the ε-expansion is tested in the specific finite-size case of d′=σ±ε. The definition of the scaled field variable and the finite-size scaling in the regime of the first-order phase transition are also considered.
On the invariance properties and conservation laws for Landau–Lifshitz equation in three dimensions with Tijon–Wright ansatz
Authors: Sen Shibani , Chowdhury A. Roy
Published: July 2002

Invariance properties of three-dimensional Landau–Lifshitz equation with the Tijon–Wright ansatz are discussed. These transformations are similar to the hidden symmetries of the nonlinear sigma model. The main difference is in the structure of the gauge function which in our case depends also on the field variables. Lastly, the composition rule of two such transformations will be discussed which is seen to generate an infinite-dimensional Lie algebra, and the structure of local and nonlocal conservation laws is found.
Solutions to the quantum Yang–Baxter equation for the exceptional Lie algebras with a spectral parameter
Authors: Chung H. J. , Koh I. G.
Published: July 2002

The trigonometric solutions to the quantum Yang–Baxter equation with a spectral parameter for the fundamental representations of the exceptional Lie algebras, E6, E7, and E8 will be explicity presented. Moreover, reduction and inversion-like formulas are obtained in the presence of the spectral parameter.
Spherically symmetric scalar fields
Authors: Papacostas Taxiarchis
Published: July 2002

The Einstein equations coupled with a spherically symmetric time-dependant scalar field are solved. The problem of two distinct cases is reduced and the first of them is successfully solved completely, the resulting solutions being cosmological models. For the second one which is static, only a partial solution is found.
Octonionic representations of SO(8) and its subgroups and cosets
Authors: Dündarer A. Reşit , Gürsey Feza
Published: July 2002

The generators of the subgroups SO(7)L,R and the cosets S7L,R=SO(8)/SO(7)L,R and Σ7L,R=SO(7)L,R/G2 of SO(8) are constructed out of the generators of SO(8) using octonionic structure tensors, and the representations of these generators are given as products of octonions.
Invariant states of C*-systems without norm-continuity properties
Authors: Amann Anton
Published: July 2002

Dynamical C*-systems without norm-continuity properties (e.g., the dynamics of a boson system) are studied. For each such C*-system, an auxiliary pointwise norm-continuous C*-system is constructed such that ‘‘continuously’’ invariant states of the original system correspond to invariant states of the auxiliary system. ‘‘Continuous invariance’’ is to mean that the unitary time-evolution group in the Gel’fand–Naimark Segal representation (GNS-representation) is strongly continuous. The above correspondence is bijective and respects sequential limits. The GNS-representations of corresponding states can be identified on the W*-level. Hence, KMS-states (ground states, etc.) of the two systems correspond. This helps to carry over mathematical proofs that rely on the generator of a dynamical group (which exists only for pointwise norm-continuous C*-systems). As a typical example one might consider the verification that the temperature to zero limit of thermic equilibrium states is a ground state in the algebraic sense, i.e., is an eigenstate of the respective GNS-Hamiltonian with an eigenvalue at the lower end of the Hamiltonian’s spectrum.
Quantum algebras on phase space
Authors: Lu Zhicheng
Published: July 2002

Quantum algebras are represented by functions on phase space in terms of *-product, and explicit examples for Uη(sl(n+↑ 1), R) with n≥1 are given.
Matrix representations of SOn+2 in an SOn×SO2 basis and some isoscalar factors for SOn+2⊇SOn×SO2
Authors: Pan Feng , Cao Yu-Fang
Published: July 2002

Vector coherent state (VCS) theory is applied to the group chain SOn+2⊇SOn×SO2. Matrix elements of SOn+2 generators in the SOn+2⊇SOn×SO2 basis are derived. A new formula for the evaluation of some isoscalar factors for SOn+2⊇SOn×SO2 with branching multiplicity is derived in the VCS framework. As a simple example, a new expression of some isoscalar factors for SO5⊇SO3×SO2, which involves only 6j coefficients and K-normalization factors, are obtained by using this formula.
Analytic solutions for Wheeler–Feynman interaction: Two bodies in straight-line motion
Authors: Stephas Paul
Published: July 2002

Analytic solutions are obtained for two point particles with any total energy that have charges of like sign and whose motions are confined to one dimension. These solutions are obtained by explicitly deriving the conserved quantities associated with Wheeler–Feynman interactions into forms that do not contain integrals but, rather, contain ‘‘partial contributions’’ to the momenta and potentials of particle two. The resulting conserved energy, momentum, and Lorentz momentum equations are separated in time to yield one set of equations with variables t1 and t2− (retarded) and another set with variables t1 and t1+ (advanced). These are solved to obtain auxiliary solutions x1r(t1) and x1a(t1), which are then combined for the case m1 = m2 to give the actual world lines x1(t1) and x2(t2). Comparison is made with a previous computer-generated exact solution for the same interaction and energy; good qualitative agreement is found, although some quantitative differences persist.
Inverse scattering theory at fixed energy and the design of circular optical waveguides
Authors: Hooshyar M. A. , Tamil Lakshman S.
Published: July 2002

Application of inverse scattering theory at fixed angular momentum for designing circular optical waveguides possessing prescribed propagation constants β for a fixed azimuthal mode number is well known. However, waveguides designed using such a method, in general, will not be able to transmit other azimuthal modes without being dephased. In order to overcome this problem, the inverse scattering procedure at fixed energy is modified and applied to this design problem. It is shown that when gradient of the refractive index is negligible the method can be used to design waveguides with the same propagation constant for different azimuthal modes. This allows the modes to propagate through the waveguide without dephasing.
On a different class of solutions for Minkowskian σ model on Grassmanian manifold
Authors: Dhara H. C. , Chowdhury A. Roy
Published: July 2002

A general class of exact solutions for the Minkowskian σ model of the hyperbolic Grassmanian manifold, which was considered earlier by Lambert and Piette, are constructed. The energy momentum tensor associated with these solutions can be made finite with a suitable choice of the arbitrary functions involved in their construction.
Grassmann coordinates and Lie algebras for unified models
Authors: Delbourgo R. , Jarvis P. D. , Warner Roland C.
Published: July 2002

A variety of Lie algebras and certain classes of representations can be constructed using Grassmann variables regarded as Lorentz scalar coordinates belonging to an internal space. The generators are realized as combinations of multilinear products of the coordinates and derivative operators, while the representations emerge as antisymmetric polynomials in the variables and are thus severely restricted. The nature of these realizations and the interconnections between various subalgebras, for N independent complex anticommuting coordinates, is explored. The addition of such Grassmann coordinates to the usual spacetime manifold provides a natural superfield setting for a unified theory of symmetries of elementary particles. The particle content can be further restricted by imposing discrete symmetries (Lie algebra automorphisms). For the case N=5 some anomaly free choices of multiplets are derived through the imposition of specific superfield duality conditions.
On the quantization of reducible gauge systems
Authors: Ferraro Rafael , Henneaux Marc , Puchin Marcel
Published: July 2002

Reducible gauge theories with constraints linear in the momenta are quantized. The equivalence of the reduced phase space quantization, Dirac quantization, and BRST quantization is established, provided one transforms appropriately the Dirac wave functions under changes of representation of the constraint surface and of the reducibility functions. The ghosts of ghosts are found to play a crucial role in the equivalence proof.
Feynman path integral for Dirac system with analytic potential
Authors: Ktitarev D. V. , Yegikian R. S.
Published: July 2002

The Cauchy problem for the Dirac equation for a particle in the presence of an external electromagnetic field in 3+1 space-time dimensions is considered. The potential of the external field is supposed to be an analytic function of the first order of growth. The local solution in the generalized sense is constructed in the form of rigorously defined Feynman path integral in phase space.
A second look at the Rarita–Schwinger theory
Authors: Saar R. , Kõiv M. , Ots I. , Loide R. K.
Published: July 2002

This is an alternative version of the Rarita–Schwinger theory and a demonstration of some possibilities of generalizing the usual spin-3/2 description. The main result of this article follows from the redefinition of the Hermiticity condition and the space inversion symmetry. The version has been motivated by the understanding that a spin-3/2 particle is a phenomenon of nature by itself and therefore cannot be looked upon as composed by spin-1/2 and spin-1 particles. Hence, the spin-3/2 particle will not be subjected to the symmetry properties of spin-1/2 particle. If the standpoint mentioned above was admitted, then the Rarita–Schwinger spin-3/2 equation would be equivalent to the whole class of the Bhabha-type equations.
N=2 superconformal killing equations and the harmonic differentials
Authors: Kachkachi M. , Lhallabi T.
Published: July 2002

Superconformal transformations in N=2 harmonic superspace are described by means of killing equations and the N=2 supercurrent is presented. The Becchi–Rouet–Stora–Tyutin formalism is used in order to establish the N=2 supercurrent anomaly.
Dynamical algebra of the q-deformed three-dimensional oscillator
Authors: Van der Jeugt J.
Published: July 2002

The q-deformed three-dimensional harmonic oscillator is defined in terms of the q-bosons corresponding to the spherical components of a nondeformed three-dimensional oscillator. It is shown that the dynamical algebra is spq(6,R). Two important subalgebra chains are identified: spq(6,R)⊇suq(3)⊇soq(3) and spq(6,R) ⊇ spq2(2,R) ⊕ soq(3). The basis states of the q-deformed oscillator are classified according to these subalgebras. Finally, the Hamiltonian eigenvalues are discussed.
A cylindrically symmetric solution of Einstein’s equations describing gravitational collapse of stiff fluid
Authors: Davidson W.
Published: July 2002

This article presents a one-parameter solution of Einstein’s equations that describes a stiff fluid in gravitational collapse with cylindrical symmetry. The boundary of the fluid, of comoving radial coordinate r=r*, is a hypersurface which is regular as long as r* is chosen ≤π/2a, a being the solution parameter. The density μ and pressure p (μ=p) are well behaved (∂μ/∂r≤0) in the interval 0≤r≤r* and if we allow r* arbitrarily close to π/2a then μ*→0 as r*→π/2a. The hypersurface r=π/2a is singular as measured by the Riemann invariant RijkmRijkm. The gravitational collapse takes place in the coordinate time interval 0≤t≤t*, t*=π/4a being the moment of total collapse when μ becomes infinite. Both the geometry and the geodesic equations indicate that for r≤r*, t≤t* there are regular trapped two surfaces in the space–time. The geometrical and kinematic properties of the solution as well as the incidence of gravitational waves are discussed. Two numerical examples of the physical parameters, corresponding to two choices of the parameter a, are given to describe (a) the collapse of a stiff fluid initially of nuclear density and of radius ∼ 20 km and (b) the contraction to a singularity of a cosmological distribution of stiff matter.
p-adic superanalysis. I. Infinitely generated Banach superalgebras and algebraic groups
Authors: Cianci Roberto , Khrennikov Andrew
Published: July 2002

A sequence of infinitely generated p-adic Banach superalgebras and their locally convex projective and inductive limits were constructed; their spectral properties are characterized herein and by studying the algebras of matrices constructed with these superalgebras an exponential map and its inverse can be defined. Some examples of superalgebra with pathological spectral properties are discussed.
Asymptotic nonstandard quantum electrodynamics
Authors: Fittler Robert
Published: July 2002

Nonstandard quantum electrodynamics (Q.E.D.) is investigated from the point of view of an asymptotical development in time, using elementary but unorthodox integration methods, which also serve to define the renormalization constants. Agreement with classical Feynman-type Q.E.D. is found to be close in practice, but less so in theory. Finally a (0-) finite perturbation order cutoff is devised, causing the (renormalized) Dyson expansion to have (0-)finite length, without necessity for further renormalizations.
Linear canonical supertransformation
Authors: Nagamachi S. , Nishimura T.
Published: July 2002

On a Fock superspace, a linear canonical supertransformation is implemented by an inner-product-preserving operator which is necessarily not continuous.
Some solutions of the Yang–Mills equations in dimension greater than four
Authors: Ivanova T. A. , Popov A. D.
Published: July 2002

The Yang–Mills equations for gauge fields of an arbitrary semisimple Lie group G in Euclidean spaces Rn with dimension n≥4 is considered. For gauge fields Aa we introduce the ansätze which reduce the Yang–Mills equations in Rn to a set of nonlinear differential matrix equations (Rouhani–Ward equations). This permits us to write out the explicit form of cosmological, plane-wave, and other types of solutions.
Liapunov exponents of simple smooth flows
Authors: Roepstorff G.
Published: July 2002

An attempt is made to introduce the notion of a ‘‘simple dynamical system’’ as one, where Liapunov exponents may be obtained by purely algebraic methods, specifically by exploiting the Lie algebra relations between vector fields. Thus, in a simple system, one need not solve the dynamical equations but is often faced with an equally difficult task of unravelling the algebraic structure. The theory is presented within the framework of differential geometry. Several examples illustrate the usefulness of the proposed concept.
Virial theorem for two-body Dirac equation
Authors: Semay Claude
Published: July 2002

The quantum-mechanical virial theorem is applied to the two-body Dirac equation. It can be used as a powerful test for solutions of this equation. A direct application of the theorem is also given.
Elliptic Baker–Akhiezer functions and an application to an integrable dynamical system
Authors: Eilbeck J. C. , Enol’skii V. Z.
Published: July 2002

An ansatz for elliptic Baker–Akhiezer functions is used to find new solutions for various spectral problems—the Sturm–Liouville problem with four and five-gap Lamé potentials and two third-order problems. One of the third-order problems is the classical Halphen equation with a spectral parameter. The eigenfunctions are used to construct elliptic solutions for integrable cases of a generalized Hènon–Heiles system.
Perturbation theory based on the Einstein–Boltzmann system. II. Illustration of the theory for an almost-Robertson–Walker geometry
Authors: Banach Zbigniew , Piekarski Sl/awomir
Published: July 2002

This is the second in a pair of articles, the overall objective of which is to describe within the framework of the Einstein–Boltzmann system a self-consistent perturbation method which leads to a tractable set of integrodifferential equations for the rate of change of the metric and the distribution function. The main purpose here is to prove that, for cases where the pressure of the gas of massive particles vanishes in the background, the treatment of the Einstein–Boltzmann system by means of a suitable perturbation method automatically produces a complete scheme of hydrodynamics, consisting of a closed set of partial differential equations for the evaluation of the mean velocity, the mass density, the temperature or the pressure, and the metric. The growing hydrodynamic modes are systematically derived for an almost-Robertson–Walker universe model, and the calculations are proposed without making any restrictions on the form of the perturbed metric. To summarize, the present article suggests a scheme of hydrodynamics for the late stages of cosmic expansion and calls attention to the support and interpretation given by the general-relativistic kinetic theory of monatomic gases to this scheme. Comparison with the predictions of the Eckart and/or Landau–Lifshitz theories of dissipative fluids is also briefly presented.