bluuebunny/crossref_metadata_2025 huggingface dataset:
The spin signature of charged photoexcitations in carbazolyl substituted polydiacetylene
Authors: Brabec C. J. , Johansson H. , Cravino A. , Sariciftci N. S. , Comoretto D. , Dellepiane G. , Moggio I.
Published: July 2002

In this article, photoinduced infrared absorption (PIA-FTIR) and light induced electron spin resonance (LESR) measurements on an asymmetric carbazolyl substituted polydiacetylene (PDA), the poly{1-(N-carbazolyl) penta-1,3-diyn-5-ol} (polyCPDO) are presented. Results from both experimental techniques imply that contrary to other well-known polydiacetylene derivatives, in polyCPDO there exist only long-living, highly localized charged photoexcitations with spin 1/2 (g value∼2.0026), indicative for polaronic excitations. PolyCPDO also shows a strong dark ESR signal with the same g value as the LESR signal and with a Curie susceptibility of approximately 10−3 spins per CPDO monomer unit. This unusually high number of defects may come from intermediates of the polymerization. Furthermore, the photoexcited states of composites from polyCPDO mixed with a special solubilized methano-fullerene [6,6]-Phenyl C61–butyric acid methyl ester (PCBM) with excellent acceptor properties are investigated and compared with those of the pristine polymer. No enhancement of PIA-FTIR and LESR signals is found for these composites. It is therefore concluded, that even polyCPDO, which shows charged spin 1/2 photoexcitations, does not exhibit a photoexcited charge transfer to fullerenes as observed in other nondegenerate ground state conjugated polymer fullerene composites.
Diffusion-stress relations in polymer mixtures
Authors: Curtiss C. F. , Bird R. Byron
Published: July 2002

A new derivation of the mass-flux equations for multicomponent diffusion in polymeric liquids is given. A precursor of the Fokker–Planck equation for a single polymer molecule is used as the starting point for the development. From this equation we derive the equation of motion for one polymer species. Then it is shown what assumptions may be made for the self-correlation tensors in order to obtain relations of the form of the Maxwell–Stefan equations for multicomponent diffusion. These results, valid for any bead-spring model, interrelate the mass-flux vectors and the stress tensor. Finally, the results are compared with the Chapman–Enskog solution of the Boltzmann equation for the limiting case of an ideal gas mixture of rigid spheres (for which no assumptions need to be made for the self-correlation tensors).
Fermi resonance coupling in a surface adsorbate: The C–H stretch in methoxy adsorbed on Cu(100) calculations and experiments
Authors: Ásmundsson R. , Uvdal P.
Published: July 2002

The C–H stretch spectrum of methoxy adsorbed on Cu(100) has been measured using Fourier transform infrared spectroscopy. Fermi resonance coupling constants in methoxy are calculated using a normal mode model where the unperturbed modes were either experimentally determined or inferred from ab initio calculations performed for a methoxy-Mo model complex. The measured frequency shifts and intensity redistribution observed in the C–H stretch region are qualitatively reproduced by the calculations.
Transition in three-dimensional micellar systems
Authors: Girardi M. , Figueiredo W.
Published: July 2002

We have studied the thermal behavior of aggregates of amphiphilic molecules in water for a three-dimensional lattice model. We have employed extensive Monte Carlo simulations to find the distribution curve for aggregate size as a function of temperature. Our model consists of amphiphile molecules with a single polar head and three monomers in its hydrophobic tail. In this lattice model each amphiphile occupies four sites of the lattice, and the water molecules occupy only one site. We determine the free amphiphile concentration and the aggregate-size distribution P(n) as functions of total surfactant concentration for different temperatures. As for the two-dimensional case, the degree of micellar organization is characterized by Δ≡P(nmax)−P(nmin), where nmin and nmax>nmin are the aggregate sizes at which P exhibits its local minimum and maximum. For this three-dimensional model we also show that Δ vanishes continuously as we increase the temperature. However, the exponent associated with the micellar to nonmicellar transition is twice that found in the two-dimensional simulations.
An exchange functional for accurate virtual orbital energies
Authors: Manby F. R. , Knowles P. J.
Published: July 2002

We show that a simple Gaussian model for exchange yields Kohn–Sham virtual orbital energies that are in significantly better agreement with Hartree–Fock theory than those arising from functionals based on the uniform electron gas. Also we show that normalization of the Gaussian model significantly improves the accuracy of total exchange energies, and that reparametrizing a Becke-type asymptotic correction leads to total exchange energies which are only slightly less accurate than B88. Errors in HOMO–LUMO gaps for this new functional are typically less than a third of the corresponding B88 errors. Many-body perturbation theory using B88 exchange in the zeroth-order Kohn–Sham problem is shown to be divergent or very slowly convergent for some typically well-behaved closed shell systems; using the functional presented here, though, convergence is in each case at a rate comparable with normal Møller–Plesset perturbation theory.
The ab initio calculated dipole moment surface and overtone relative intensities of CH chromophore in CHCl3
Authors: Lin Hai , Yuan Lan-feng , He Sheng-gui , Wang Xiao-gang , Zhu Qing-Shi
Published: July 2002

Relative absorption intensities of the Fermi resonance polyads of isolated CH chromophore for the CHCl3 molecule were calculated with one-dimensional and two-dimensional dipole moment surfaces, which are obtained by the ab initio density functional method. The calculation showed an unusual strong absorption at the second Fermi resonance polyad, which agrees well with the experimental data. Such an intensities anomaly can be attributed to the nonlinearity of the dipole moment surface in the vicinity of the equilibrium configuration. By taking advantage of the two-dimensional dipole moment surface where both CH stretching and bending vibrations are taken into consideration, the ν1 and 2ν4 bands which constitute the first Fermi resonance polyad and have little wave function mixture, are found to be of almost equal intensity. Such a calculation agrees with observations.
Isotope effect on bifurcating reaction path: Valley–ridge inflection point in totally symmetric coordinate
Authors: Kumeda Yuko , Taketsugu Tetsuya
Published: July 2002

The isotope effects on bifurcating reaction paths have been studied for two reactions, H3CO→H2COH and HF+C2H4→C2H5F, both of which have a valley–ridge inflection (VRI) point related to nontotally symmetric directions on the symmetry-conserved intrinsic reaction coordinate (IRC). As the result of the VRI occurrence, the IRC connects a reactant minimum, the transition state, and another first-order saddle point. The deuterium substitution of one or two hydrogen atoms in molecular systems reduces the symmetry of the IRC, resulting in the direct linkage of the transition state and a product minimum through the IRC. In the above two reactions with deuterium substitution, it is found that the VRI occurs relative to the totally symmetric directions. Analyses of the steepest descent paths that start from a zero-point energy region around the VRI point demonstrate that those paths bifurcate toward two different product minima.
Predissociation in the E 1Π, v=1 state of the six natural isotopomers of CO
Authors: Ubachs W. , Velchev I. , Cacciani P.
Published: July 2002

The E 1Π, v=1 state of carbon monoxide is studied in high resolution using a tunable and narrowband laser source in the vacuum ultraviolet near 105 nm. Calibration with respect to a reference standard consisting of iodine lines in the visible range, measured by saturated absorption spectroscopy, yields an absolute accuracy of 0.003 cm−1 for the CO resonances. Transition frequencies of the E–X(1,0) band were determined for all six natural isotopomers (12C16O, C1712O, C1812O, C1613O, C1713O, and C1813O) and improved molecular constants derived. Natural lifetime broadening, caused by predissociation was investigated quantitatively for single rotational and (e)–(f ) parity levels. The accidental predissociation phenomena, giving rise to line shifts and broadening, could be explained up to the experimental accuracy in a model based on spin–orbit-coupling between E 1Π, v=1 and k 3Π, v=6 states, with a coupling constant of HE,k=1.88±0.01 cm−1 for all six isotopomers. The overall line broadening parameter ΓE for the E state, ascribed to interaction with a repulsive Π1 state, and Γk for the k state, were determined as well; the predissociation rates were found to decrease with increasing reduced mass of the isotopomers for both E 1Π, v=1 and k 3Π, v=6 states.
Rotationally inelastic collisions of OH(X 2Π)+Ar. I. State-to-state cross sections
Authors: van Beek M. C. , ter Meulen J. J. , Alexander M. H.
Published: July 2002

Inelastic collisions of OH(X 2Π)+Ar at an energy of 746 cm−1 have been studied in a crossed molecular beam experiment. The OH(X 2Π) radicals were prepared in the v=0, Ω=32, J=32, f state by hexapole state selection. Parity-resolved integral state-to-state cross sections for rotational excitation have been determined up to the Ω=32, J=92 and Ω=12, J=52 states. A strong preference is found for spin–orbit manifold conserving transitions to final states of e symmetry. The experimental results are compared to quantum scattering calculations on ab initio potential energy surfaces developed by Degli-Esposti and Werner [J. Chem. Phys. 93, 3351 (1990)] and by Klos et al. [J. Chem. Phys. 112, 4952 (2000)]. The overall agreement between experiment and theory is very good; however, the calculated cross sections for spin–orbit changing transitions are a bit larger than the experimental values. The results are also compared to previous experiments at a collision energy of 451 cm−1.
Classical characters of highly excited bend dynamics of acetylene in two coupled SU(2) coset spaces
Authors: Yu Jin , Wu Guozhen
Published: July 2002

The classical characters of the highly excited bend dynamics of acetylene are analyzed in terms of two coupled SU(2)/U(1) coset spaces corresponding to the right and left circular motion of the two C–H bends. The vibrational modes show a wide variety of behaviors that are not observed in the simple SU(2)/U(1) coset case which deals with, e.g., two coupled stretches, in which case the vibrational modes can be characterized as (low-lying) local and (high-lying) normal modes with a so-called local-normal transition in between. For the two coupled SU(2)/U(1) cosets of acetylene, the general trend is that most modes are perturbed local or normal modes, with distinct characters that are not found in the SU(2) dynamics. Details of their classical characters and the dynamical action flow between the two C–H bends were deduced. When the total action number Nb is small (less than 14), normal mode motions dominate, i.e., trans bend modes at the bottom of each polyad and cis bend at the top. At higher Nb, the vibrational modes are more or less of local character though they, individually, do possess very unique characters. Specifically, as Nb ranges from 12 to 22, the characters of the low-lying levels change from the trans character with action asymmetrically distributed in the two C–H bonds to one hydrogen bending, while those of the high-lying levels change from well concerted cis to local counter rotation. These results are consistent with recent quantal and semiclassical results. [M. P. Jacobson, R. J. Silbey, and R. W. Field, J. Chem. Phys. 110, 845 (1999); M. P. Jacobson, C. Jung, H. S. Taylor, and R. W. Field, ibid. 111, 600 (1999)].
The D 1Σ+ state of LiH7
Authors: Huang Yen-Ling , Luh Wei-Tzou , Jeung Gwang-Hi , Gadéa F. Xavier
Published: July 2002

The LiH7 D 1Σ+ excited electronic state has been observed for the first time by a pulsed optical–optical double resonance fluorescence depletion spectroscopic technique. Several rovibrational levels of the A 1Σ+ and B 1Π electronic states have been used as the intermediate states. Among 22 vibrational levels, 128 rovibrational levels have been observed. The spectral assignment is identified by the observed rotational structures and term values and by a comparison between the derived vibrational and rotational constants with the theoretical values. An ab initio adiabatic potential energy curve for the D 1Σ+ state and relevant D 1Σ+–A 1Σ+ and D 1Σ+–B 1Π transition moment functions are presented. An overall measure of three different aspects, the energetics, the spectral line shape, and the transition probability, strongly favors the argument that the vibronic approach is a better approach for characterizing the excited D 1Σ+ electronic state.
Coupled-cluster electronic spectra for the Ca+–acetylene π complex and comparisons to its alkaline earth analogs
Authors: Wesolowski Steven S. , King Rollin A. , Schaefer Henry F. , Duncan Michael A.
Published: July 2002

Equation of motion coupled-cluster (EOM-CCSD) predictions of structures and electronic excitation energies for the recently detected Ca+–acetylene π-complex confirm three experimental state assignments, but suggest reinterpretation of the signals associated with the (2) B12 and (2) B22 states that correlate to the P2←2S Ca+ atomic transition. The originally assigned 000 band for the (2) B12 state corresponds to the computed excitation energy to the (2) B22 state and simple reassignment is proposed. The true (2) B12 state was not assigned in the original spectrum. However, the computed oscillator strength is large and its optimized geometry is similar to that of the ground state. Furthermore, the experimental band tentatively attributed to the onset of the symmetric C–H stretching progression of the assigned state has a relative energy conspicuously close to the computed electronic energy for the unassigned (2) B12 state. Based on the computed energy separations of the optimized EOM-CCSD structures, reassignment of this vibronic band to the 000 line of the (2) B12 state is proposed. The newly assigned bands are also compared to the analogous transitions in the beryllium–and magnesium–acetylene π complexes.
Electron and hole trapping in WS2 nanoclusters
Authors: Huang J. M. , Kelley D. F.
Published: July 2002

Time resolved emission polarization spectroscopy has been used to study the electron and hole trapping dynamics in room temperature WS2 nanoclusters. The results indicate that radiative recombination of conduction band electrons and valence band holes results in polarized emission. Hole trapping partially depolarizes the emission, and emission from trapped electrons and holes is unpolarized. The kinetics of electron versus hole trapping can be separated by comparison of the depolarization kinetics in the presence and absence of 2,2′-bipyridine. Bipyridine acts as an acceptor for electrons in the conduction band, but not in traps. The decay of the polarized emission and the rise of the unpolarized emission indicate that electron and hole trapping take place on the 300–500 ps and 30 ps time scales, respectively. Time resolved spectral reconstruction results indicate that hole traps are about 3000 cm−1 deep while electron traps are about 270 cm−1 deep.
Thermally induced surface relief gratings in azobenzene polymers
Authors: Leopold A. , Wolff J. , Baldus O. , Huber M. R. , Bieringer T. , Zilker S. J.
Published: July 2002

Recently, Ramanujam and co-workers described for the first time that surface relief gratings can be inscribed into azobenzene copolymers with a single pair of nanosecond laser pulses. We performed a detailed investigation of the involved processes. Two contributions to the diffraction efficiency are observed, one arising from a surface relief and one from a transient cis–trans grating which decays on millisecond time scales. The stable surface relief, in contrast, is caused by a thermal effect which sets in at a well-defined threshold value of the pulse energy. © 2000 American Institute of Physics.
The trapping of methane on ordered structures of CO on Pt(111)
Authors: Carlsson A. F. , Madix R. J.
Published: July 2002

The dynamics of methane trapping on CO-covered Pt(111) in low coverage, c(√3×5)rect, and c(4×2) structures was investigated using supersonic molecular beam techniques at a surface temperature of 50 K; at this temperature methane was stably adsorbed on the clean (A. F. Carlsson and R. J. Madix, to be published) surface, but not in multilayers (A. F. Carlsson and R. J. Madix, to be published), and thus trapped amidst adsorbed CO molecules. Molecular trapping was enhanced to greater degrees with increasing CO coverage, and the methane uptake decreased with increasing CO coverage, as would be expected. The trapping probability further increased as methane covered the Pt(111)–CO surface; the modified Kisliuk model [J. Chem. Phys. 92, 1397 (1990); J. Phys. Chem. 95, 2461 (1991)] describes the coverage-dependent trapping probability. Methane adsorption may occur directly on the surface, or via two entrance channels into an extrinsic precursor, where the trapping probability is higher. The angular dependence of methane trapping on the CO-covered surface suggests an increasing corrugation in the gas–surface potential as the CO coverage increases; the corrugation may also contribute to the enhancement of the overall trapping probability by facilitating interconversion of perpendicular to parallel momentum during the gas–surface collision.
Multiplicity-free, unitary and nonunitary irreducible representations of SL(3,R)
Authors: Güler Y.
Published: July 2002

Multiplicity-free, irreducible representations of the group ∼(SL(3,R)) are obtained from SU(2) subgroup representations by a constructive method. It is observed that there exist two series of unitary representations with k contents {k0,k0+1,k0+2,...}k0≥3, {k0,k0+2,k0+4,...} k0=0, 1,  1/2 and finite-dimensional representations with k content {k0+1,k0+3,...,k0+2n+1} k0=1,  1/2  {2,4,6,...,2n}, n=1,2,...,k0=0.
A Fock–Krein realization of the Landau gauge
Authors: Pierotti Dario
Published: July 2002

An explicit Fock realization of the Landau gauge of the free electromagnetic field with a Hilbert space structure which is simply the same as in the Gupta–Bleuler gauges is given.
A note on the meaning of covariant derivatives in supersymmetry
Authors: Aldaya Víctor , de Azcárraga José A.
Published: July 2002

We analyze in this paper the group theoretical meaning of the covariant derivatives, and show that they are horizontal left-invariant vector fields on superspace obtained from a (super)Lie group which at the same time exhibits the structure of a principal bundle with a canonical connection. The geometrical construction is general and not restricted to the super-Poincaré group.
On the wave operator in few-body quantum scattering with Coulomb-like interactions
Authors: Kröger Helmut
Published: July 2002

Functional analytical methods like strong approximation of operator-valued functions and Dunfords’ calculus are applied to yield a contour integral representation with a finite contour of wave operators for nonrelativistic potential scattering with Coulomb and short-range interactions, which avoids high singularities of Coulomb-like Green’s functions of stationary scattering theory. The Green’s function is the unique solution of the resolvent equation, which has an A-proper kernel allowing projector methods for its solution.
Feynman rules in the Anderson model: Generalization to the (2J+1)-component case
Authors: Matsumoto H. , Umezawa H. , Whitehead J. P.
Published: July 2002

The Feynman rules for the Anderson model with a (2J+1)-component localized spin are formulated by means of a generalized Wick’s expansion together with the reduction formulas in the thermo-field-dynamics. In the U→∞ limit, Feynman rules for arbitrary J correspond closely to those for the case J= 1/2 and may be obtained from them by a simple replacement rule.
Smoothness of the action of the gauge transformation group on connections
Authors: Abbati M. C. , Cirelli R. , Manià A. , Michor P.
Published: July 2002

The NLF–Lie group structure of the group 𝒢 of the gauge transformations, defined as the group of sections of the bundle P[G] associated to the principal bundle P(M,G), is discussed. Other current definitions of the group of gauge transformations are shown to admit a nontrivial smooth structure only in the case of compact G. The space 𝒞 of principal connections, as well, is given the structure of local affine NLF-manifold, after identifications of connections with sections of a convenient vector bundle on M. Finally, the smoothness of the action of 𝒢 on 𝒞 is proved in general. In the case of compact M, the group 𝒢 becomes a tame Fréchet–Lie group and the action a tame smooth action.
Periodic fixed points of Bäcklund transformations
Authors: Weiss John
Published: July 2002

The discussion of the periodic fixed points of Bäcklund transformations for the Korteweg–de Vries equation is completed. It will be shown that the systems of equations defined by the KdV periodic fixed points are equivalent to the periodic Kac–Van Moerbeke systems. As a consequence, for even order fixed points, the KdV systems are equivalent to the periodic Toda lattice. The periodic fixed points of the Bäcklund transformation for the Boussinesq equation are found to have a Hamiltonian structure. The integrals of these systems are found.
Graded spinors as an underlying geometry for extended supersymmetries
Authors: Luehr C. P. , Rosenbaum M.
Published: July 2002

Spinors associated with an eight-dimensional Euclidean space are used for constructing a graded vector representation space for OSp(4/N,R). The underlying geometry fixes both the nature and highest dimensionality of the family of internal symmetry groups of the bosonic subspace, as well as those of the fermionic subspace through an appropriately defined inner product. The basic ingredients of the theory are fermionic variables while the bosonic fields occur as composite quantities made up from an even number of products of the fermionic entities.
Solutions of Einstein’s equations for the interior of a stationary axisymmetric perfect fluid
Authors: Kyriakopoulos E.
Published: July 2002

The problem of finding a class of solutions of Einstein’s field equations for the interior of a uniformly rotating, axisymmetric perfect fluid is reduced to the integration of a known function. A number of solutions of the class is given explicitly. The equipressure surfaces of all solutions of the class are planes. The class contains solutions with the equation of state p=γμ, γ>0, 0>γ≥−1+2/(5)1/2, and γ≤−1−2/(5)1/2, which are given explicitly.
Quantum kinematics of strings: Quantization on C∞(M3,  R2 )/C∞(M3,GL(2, R ))
Authors: Szabó László
Published: July 2002

Global quantum kinematics is discussed on the configuration manifold C∞(M3, R2 )/C2mi(M3,GL(2, R )) with respect to the possible relevance to the string theory.
Phenomenological electrodynamics in curvilinear space, with application to Rindler space
Authors: Brevik I.
Published: July 2002

The phenomenological Maxwell equations and the constitutive relations are derived in curvilinear coordinates endowed with a time-independent, time-orthogonal metric, when there is a uniform, isotropic, and homogeneous medium present. The way of formulating the electromagnetic theory chosen here is basically in agreement with the formulations given by von Laue and Arzeliès. The theory is thereafter applied to the case when the medium is at rest in Rindler space. The fundamental electromagnetic modes (the TE, TM, and TEM modes) are worked out in terms of modified Bessel functions, and the electromagnetic energy-momentum tensor is worked out in the Minkowski picture and shown to possess an interesting analogy with the case when an inhomogeneous medium is at rest in an inertial frame.
Classification and interpretation of the supertableaux of the orthosymplectic groups OSP(m‖4)
Authors: Gourdin Michel
Published: July 2002

The supertableaux of the orthosymplectic group OSP (m‖4) are analyzed and interpreted as representations of the corresponding superalgebras. An extension of the results to the general case OSP (m‖2p) is proposed.
Enlargeable graded Lie algebras of supersymmetry
Authors: Teofilatto Paolo
Published: July 2002

A criterion to enlarge infinite-dimensional Lie algebras to analytic Lie groups is used here for the extension of graded Lie algebras of physical interest to super-Lie groups.
Discrete supergroups and super Riemann surfaces
Authors: Teofilatto Paolo
Published: July 2002

The properties of discrete supergroups that represent the homotopy groups of super Riemann surfaces are emphasized. After the study of the superforms invariant with respect to these supergroups, the set of superconformal differentials are defined and an example is given of those by defining Poincaré’s super theta functions. Some remarks on a possible definition of the Jacobi variety of a super Riemann surface are given.
Existence of infinitely many zero-energy states in a model of supersymmetric quantum mechanics
Authors: Arai Asao
Published: July 2002

The general framework of the N=2 Wess–Zumino holomorphic supersymmetric quantum mechanics with polynomial superpotentials is extended to the case of nonpolynomial superpotentials V(z) (z∈C) in a mathematically rigorous way. It is also proved that there exist no fermionic zero-energy states. Under some conditions for V, the operator domain of the supercharges and the supersymmetric Hamiltonian are identified. As an example, the model with V(z)=λeαz (λ∈C■{0}, α>0) is analyzed in view of index theory. The following remarkable result is proved: There exist infinitely many bosonic zero-energy states which are localized in the momentum space dual to the Im z direction. The results are applied to two models in atomic and nuclear physics.
On the degeneracy in the ground state of the N=2 Wess–Zumino supersymmetric quantum mechanics
Authors: Arai Asao
Published: July 2002

It is known that the N=2 Wess–Zumino supersymmetric quantum mechanical model has p−1 degenerate zero-energy ground states consisting of only bosonic states, where p≥3 is the degree of the polynomial superpotential V(z)(z∈C) of the model [Jaffe et al. Ann. Phys. (NY) 178, 313 (1987)]. In this paper, the mathematical structure of the degenerate ground states is analyzed in the special case V(z)=λzp (λ>0). The following facts are discovered: (i) there exists a strongly continuous one parameter unitary group acting as a symmetry group in the quantum system under consideration; (ii) the generator of the symmetry group has infinitely many eigenspaces ℋm, m∈Z, and the bosonic part H+ of the Hamiltonian of the model is reduced by each of them; and (iii) there exist exactly p−1 ℋm’s in each of which the reduced part of H+ has a unique zero-energy ground state. It is noted also that H+ has infinitely many generalized eigenfunctions with eigenvalue zero. Moreover, a family of operators interrelating the zero-energy ground states is constructed. The coupling constant dependence of the nonzero eigenvalues of H+ is exactly found.
Superconformal algebra of meromorphic vector fields with multipoles on a super Riemann sphere
Authors: Wang Shikun , Xu Kaiwen
Published: July 2002

The superconformal algebras of meromorphic vector fields with multipoles and the relevant Abelian differential of the third kind on a super Riemann sphere were constructed. The algebra includes two Ramond sectors as subalgebras.
The complete root systems of the affine Kac–Moody superalgebras
Authors: Tsohantjis I. , Cornwell J. F.
Published: July 2002

By using certain special automorphisms, the complete root structures of all the affine Kac–Moody superalgebras, both twisted and untwisted, are derived in detail.
Representations of affine Kac–Moody algebras and the affine scalar product
Authors: Capps Richard H.
Published: July 2002

Simple procedures are given for finding all the dominant weights in a highest weight representation of an affine algebra, for finding the Weyl orbit of an arbitrary weight, and for determining whether or not any given weight is in any given representation. A simple definition of congruency is given that applies to all affine algebras. The standard indefinite scalar product is generalized; the generalization is used in the procedures.
A nonconfocal generator of involutive systems and three associated soliton hierarchies
Authors: Cao Cewen , Geng Xianguo
Published: July 2002

Quite a few new finite-dimensional integrable systems have been obtained by the nonlinearization procedure of eigenvalue problems suggested by the author. Almost all of their associated involutive systems are generated from a confocal generator: Γ̂k =∑Nj=1′(λk−λj)−1 B2kj, Bkj =pkqj −pjqk. In the present paper, a nonconfocal generator Γk =∑Nj=1′(λ2k−λ2j)−1 [(λk−λj)2A2kj+ε(λk+λj)2 B2kj], Akj =pkpj +εqkqj is found, from which some new integrable systems and soliton hierarchies are obtained.
Gauge theories on loop groups
Authors: Bandelloni Giuseppe
Published: July 2002

A Becchi–Rouet–Stora (BRS) operator is built whose nilpotency is fixed not only by the group algebra relations, but also by the algebra extensions consistency conditions. It is applied on the renormalization of a simple Kac–Moody inspired gauge model.
Scattering and inverse scattering in one-dimensional nonhomogeneous media
Authors: Aktosun Tuncay , Klaus Martin , van der Mee Cornelis
Published: July 2002

The wave propagation in a one-dimensional nonhomogeneous medium is considered, where the wave speed and the restoring force depend on location. In the frequency domain this is equivalent to the Schrödinger equation d2ψ/dx2+k2ψ=k2P(x)ψ+Q(x)ψ with an added potential proportional to energy. The scattering and bound-state solutions of this equation are studied and the properties of the scattering matrix are obtained; the inverse scattering problem of recovering the restoring force when the wave speed and the scattering data are known are also solved.
Quantum harmonic oscillator algebra and link invariants
Authors: Gómez César , Sierra Germán
Published: July 2002

Associated with the q-deformation of the harmonic oscillator algebra we define an infinite dimensional braid group representation on the Hilbert space of the harmonic oscillator, and an extended Yang–Baxter system in the sense of Turaev. The corresponding link invariant is computed in some particular cases and coincides with the inverse of the Alexander–Conway polynomial. The R matrix of Uq(h4) can be interpreted as defining a baxterization of the intertwiners for semicyclic representations of SU(2)q at q=e2πi/N in the N→∞ limit. Finally we define new multicolored braid group representations and study their relation to the multivariable Alexander–Conway polynomial.
Boson–fermion models for osp(1,2) and U
q[osp(1,2)]
Authors: Bracken A. J. , Gould M. D. , Tsohantjis I.
Published: July 2002

A reducible representation of the simple Lie superalgebra osp(1,2) is constructed from two pairs of boson and one pair of fermion creation and annihilation operators. The representation contains in direct sum every distinct (up to equivalence), finite-dimensional, irreducible representation of osp(1,2) exactly once and so defines a model, generalizing to osp(1,2) Schwinger’s boson model of su(2). The model of osp(1,2) is further generalized to a model of the quantum superalgebra Uq[osp(1,2)] in the case that q is not a root of unity. Matrix elements of generators and basic properties of the R matrix, known from previous studies, are rederived using the boson–fermion calculus.
Application of zero-range models to the problem of diffraction by a small hole in elastic plate
Authors: Andronov Ivan V.
Published: July 2002

The theory of zero-range potentials is applied to the boundary-contact acoustics problem of diffraction by small round holes in elastic plates. First the set of all point models of small inhomogeneities, represented by zero-range potentials in L2 is constructed. Then the problem of choosing the model corresponding to the examined diffraction problem is simplified by decomposition of the model into two components. One corresponds to the case of an absolutely rigid plate, the other to the case of an isolated plate. Problems of diffraction for both components can be solved exactly by variables separation method. Comparing the far field asymptotics for these problems with that produced by point models one can find the parameters of the zero-range potential. When the potential is fixed the solution, being a number of leading terms in the asymptotical on the small radius of the hole decomposition of far field, is explicitly calculated.
Asymptotic behaviors of the heat kernel in covariant perturbation theory
Authors: Barvinsky A. O. , Gusev Yu. V. , Vilkovisky G. A. , Zhytnikov V. V.
Published: July 2002

The trace of the heat kernel is expanded in a basis of nonlocal curvature invariants of nth order. The coefficients of this expansion (the nonlocal form factors) are calculated to third order in the curvature inclusive. The early-time and late-time asymptotic behaviors of the trace of the heat kernel are presented with this accuracy. The late-time behavior gives the criterion of analyticity of the effective action in quantum field theory. The latter point is exemplified by deriving the effective action in two dimensions.
Some solutions of the wave and Maxwell’s equations
Authors: Borisov Victor V. , Utkin Andrei B.
Published: July 2002

Novel solutions of the homogeneous and inhomogeneous wave equations are obtained. Their relation to the previously published solutions is considered. On this basis, the potential possibility to launch a localized electromagnetic wave is discussed.
Affine algebras on the torus
Authors: Zakkari M.
Published: July 2002

The analysis of the Kac–Moody ‘‘like’’ algebra L̂2( ℊ) on the torus is performed. It will be seen that the root systems construction leading to a Cartan matrix is not possible. Different twists of L̂2λ( ℊ) are discussed. Connections with known results are performed.
Multiple Hamiltonian structures for Toda-type systems
Authors: Damianou Pantelis A.
Published: July 2002

Results on the finite nonperiodic Toda lattice are extended to some generalizations of the system: The relativistic Toda lattice, the generalized Toda lattice associated with simple Lie groups and the full Kostant–Toda lattice. The areas investigated include master symmetries, recursion operators, higher Poisson brackets, invariants, and group symmetries for the systems. A
On the existence of nonclassical symmetries of partial differential equations
Authors: Grundland A. M. , Tafel J.
Published: July 2002

Relations between determining equations for nonclassical symmetries of Bluman and Cole and integrability conditions of differential equations supplemented by invariance conditions are studied. It is shown that every system of equations with p independent variables admits p-dimensional groups of such symmetries. Nonclassical symmetries of the eikonal equation in a curved space are investigated. They are related to shear-free congruences of null geodesics.
Scattering by singular potentials. B. Varying the linear parameters
Authors: Dolinszky T.
Published: July 2002

In part A a convergent WKB (Wentzel-Kramers-Brillouin) expansion has been developed for the wave function of Schrödinger scattering by highly singular potentials. In part B we look for the term-by-term dependence of this series on energy, coupling constant and orbital angular momentum. While we vary these parameters each point of fixed value of the new dimensionless radial coordinate invariably belongs either to the exponential or the trigonometric WKB region. By this technique, the series was proven to become exact even after the 2nd term both in the short wavelength, the strong coupling or the high partial wave limits.
Hypercomplex numbers and the description of spin states
Authors: Hamilton J. J.
Published: July 2002

A family of hypercomplex numbers is introduced in which multiplication is commutative and members can have up to eight components. In particular, the eight basis elements {E} contain those for ordinary complex numbers, E**=E, as well as new elements where E**=−E; the operation * being the generalization of complex conjugation. This family lends itself to the description of quantum mechanical spin states in that it offers a simple treatment of time reversal, representations with the same conjugation properties as underlying operators, and explicit continuous-angle spherical harmonic functions Zsm(θ,φ) analogous to the Ylm(θ,φ) for orbital angular momentum. The new elements are especially well suited for half-integral spin states, whereas conventional complex numbers remain useful for integral spin states.
Thermal field dynamics and bialgebras
Authors: Kopf Tomáš , Santana A. E. , Khanna F. C.
Published: July 2002

In thermal field dynamics, thermal states are obtained from restrictions of vacuum states on a doubled field algebra. It is shown that the suitably doubled Fock representations of the Heisenberg algebra do not need to be introduced by hand but can be canonically handed down from deformations of the extended Heisenberg bialgebra. No artificial redefinitions of fields are necessary to obtain the thermal representations and the case of arbitrary dimension is considered from the beginning. Our results support a possibly fundamental role of bialgebra structures in defining a general framework for thermal field dynamics.
r
D
oscillators with arbitrary D>0 and perturbation expansions with Sturmians
Authors: Znojil Miloslav
Published: July 2002

In contrast to widespread belief the current Rayleigh-Schrödinger perturbation theory may provide an easy description of double well oscillators and/or of the strongly anharmonic forces with an arbitrary power-law asymptotical growth. One has only to work in a suitable Sturmian basis. The feasibility and numerical efficiency of the construction is illustrated on a few one-dimensional one-body examples.
Casimir energy of the massless conformal scalar field on S-2 by the point-splitting method
Authors: Bayın Selçuk Ş. , Özcan Mustafa
Published: July 2002

We calculate the Casimir energy of the massless conformal scalar field on the surface (S-2) of a 3 dimensional Riemann sphere by using the point-splitting, mode sum and the ζ-function renormalization methods. We also consider the half space case with both the Dirichlet and the Neumann boundary conditions. This problem is interesting since the Casimir energy could be calculated analytically by various methods, thus allowing us to compare different regularization schemes.
Singularity-free static fluid spheres in general relativity
Authors: Orlyansky Oleg Yu.
Published: July 2002

The relations between the metric coefficients, the energy density, the pressure, and the speed of sound at the center of a perfect fluid sphere which are necessary for singularity-free static solutions are considered. In order to find exact singularity-free static solutions and to construct reasonable star models it is suggested that we modify the known methods of obtaining exact spherically symmetric solutions using these relations. A known class and the new class of such solutions are obtained and the extreme static star model is constructed. At the center of the sphere the equation of state is ultrarelativistic and the sound speed is equal to the speed of light in a vacuum.
Painlevé classification of coupled Korteweg–de Vries systems
Authors: Karasu Ayşe (Kalkanli)
Published: July 2002

In this work, we give a classification of coupled Korteweg–de Vries equations. We found new systems of equations that are completely integrable in the sense of Painlevé.
Generalization of the algebra of the matrix pseudodifferential operators
Authors: Gawrylczyk Jarosław
Published: July 2002

We introduce the new nonhomogeneous graded matrix algebra Matn(R) over the ring ℜ of the pseudodifferential operators of the arbitrary orders. This algebra forms the generalization of the algebra of the standard matrix pseudodifferential operators. We show that the Matn(R) algebra admits the nontrivial central extension. The case n=2 is considered in some detail. As the example we consider the Mat2(W1+∞), Mat2(Virasoro) and Mat2(sl(2,C)) algebras.
Quantum theory of the real and the complexified projective line
Authors: Leitenberger Frank
Published: July 2002

Quantum deformations of sets of points of the real and the complexified projective line are constructed. These deformations depend on the deformation parameter q and certain further parameters λij. The deformations for which the subspace of polynomials of degree three has a basis of ordered monomials are selected. We show that the corresponding algebras of three points have “polynomiality.” Invariant elements which turn out to be cross ratios in the classical limit are defined. For the special case |λij|=1 a quantum cross ratio with properties similar to the classical case is presented. As an application a quantum version of the real Euclidean distance is given.
Variational principles for nonlinear dynamical systems
Authors: Méndez Vicenç
Published: July 2002

A variational method for Hamiltonian systems is analyzed. Two different variational characterization for the frequency of nonlinear oscillations is also supplied for non-Hamiltonian systems.
Group analysis and renormgroup symmetries
Authors: Kovalev Vladimir F. , Pustovalov Veniamin V. , Shirkov Dmitrii V.
Published: July 2002

An original regular approach to constructing special type symmetries for boundary value problems, namely renormgroup symmetries, is presented. Different methods of calculating these symmetries based on modern group analysis are described. An application of the approach to boundary value problems is demonstrated with the help of a simple mathematical model.
Integral representations of harmonic lattice sums
Authors: Huang Jingfang
Published: July 2002

We present new integral formulas for Coulombic lattice sums that arise in solid state physics, material science, and complex analysis. Unlike Ewald summation, which can yield approximate integral representations, the formulas described here are exact. Simple quadrature rules with modest numbers of nodes yield highly accurate results.
Chaotic and turbulent behavior of unstable one-dimensional nonlinear dispersive waves
Authors: Cai David , McLaughlin David W.
Published: July 2002

In this article we use one-dimensional nonlinear Schrödinger equations (NLS) to illustrate chaotic and turbulent behavior of nonlinear dispersive waves. It begins with a brief summary of properties of NLS with focusing and defocusing nonlinearities. In this summary we stress the role of the modulational instability in the formation of solitary waves and homoclinic orbits, and in the generation of temporal chaos and of spatiotemporal chaos for the nonlinear waves. Dispersive wave turbulence for a class of one-dimensional NLS equations is then described in detail—emphasizing distinctions between focusing and defocusing cases, the role of spatially localized, coherent structures, and their interaction with resonant waves in setting up the cycles of energy transfer in dispersive wave turbulence through direct and inverse cascades. In the article we underline that these simple NLS models provide precise and demanding tests for the closure theories of dispersive wave turbulence. In the conclusion we emphasize the importance of effective stochastic representations for the prediction of transport and other macroscopic behavior in such deterministic chaotic nonlinear wave systems.
Phase diagram of Ising model (S=1) with easy-plane anisotropy in a magnetic field
Authors: Loginov A. A. , Pereverzev Yu. V.
Published: July 2002

The surfaces corresponding to the loss of stability and equilibrium of paramagnetic and antiferromagnetic states are found in the mean field approximation with temperature, field, and anisotropy as variables. The characteristic temperatures at which the topology of phase diagram sections changes are determined.
The effect of endplates on the shedding frequency of circular cylinders in the irregular range
Authors: Stäger Rainer , Eckelmann Helmut
Published: July 2002

The influence of endplates on the vortex-shedding mechanism is investigated for Reynolds numbers larger than 300 (irregular range). Near the endplate, a region with a shedding frequency f2 is found, which is lower than the Strouhal frequency f1 observed over the remaining cylinder length. The dominating parameter for this end-effect is the ratio λ/d, where λ is the distance between the leading edge of the endplate and the cylinder and d is the cylinder diameter. The end-effect fades away with increasing Reynolds number for a given λ/d. For greater values of λ/d, this fading is observed at higher Reynolds numbers.
Entrainment at thin stratified interfaces: The effects of Schmidt, Richardson, and Reynolds numbers
Authors: Breidenthal Robert E.
Published: July 2002

A new model is proposed for the entrainment at stratified interfaces. In it, the effects of Schmidt, Richardson, and Reynolds numbers are explicitly addressed. There are five regimes; entrainment is controlled by a different process in each. For example, a central assumption in region II is that eddies must make a complete rotation to be directly responsible for entrainment. Therefore, in stratified flow, the eddy scale is defined by the criterion that its Richardson number Ri is equal to unity. This contrasts with unstratified flows, where the largest eddies, unconstrained by buoyancy, engulf and entrain. These results are in accord with the observations, and suggest how laboratory experiments in water may relate to the atmosphere and to the oceans.
On the RNG theory of turbulence
Authors: Lam S. H.
Published: July 2002

The Yakhot and Orszag [J. Sci. Comput. 1, 3 (1986)] RNG theory of turbulence has generated a number of scaling law constants in reasonable quantitative agreement with experiments. The theory itself is highly mathematical, and its assumptions and approximations are not easily appreciated, particularly since several rather unconventional artifices are employed. The present paper reviews the RNG theory and recasts it in more conventional terms using a distinctly different viewpoint. A new formulation based on an alternative interpretation of the origin of the random force is presented, showing that the artificially introduced Ε in the original theory is an adjustable parameter, thus offering a plausible explanation for the remarkable record of quantitative success of the so-called Ε-expansion procedure.
Neoclassical resonant-plateau transport in the noncircular equipotential surface of a tandem mirror
Authors: Katanuma I. , Kiwamoto Y. , Ishii K. , Yatsu K. , Miyoshi S.
Published: July 2002

Neoclassical resonant-plateau transport in a minimum-B anchored tandem mirror is calculated in an experimentally observed case where a flux tube of equipotential contours is not circular at the central cell.
Fluctuation spectrum of resistive pressure-gradient-driven turbulence
Authors: Lee G. S. , Carreras B. A. , Garcia L.
Published: July 2002

The spatial structure of resistive pressure-gradient-driven turbulence is studied analytically with renormalized two-point spectrum equations and numerically by multihelicity nonlinear calculations. The wavenumber spectra for the pressure fluctuations and electrostatic potential fluctuations have been calculated with spectral analysis techniques. The least-squares fit of the numerically calculated wavenumber spectrum to a power law yields a pressure fluctuation spectrum 〈p̃2〉m∼m−(2.4±0.4) and an electrostatic potential fluctuation spectrum 〈φ̃2〉m∼m−(4.3±0.3). These results agree with the predictions of the analytic theory. The power-law decay indexes of energylike spectra show the three-dimensionality of resistive pressure-gradient-driven turbulence, even in a plasma with a strong axial magnetic field. This characteristic of resistive fluid turbulence arises from the important role of the resistivity as an integral part of plasma turbulence and differentiates the resistive plasma turbulence from the homogeneous fluid turbulence.