bluuebunny/crossref_metadata_2025 huggingface dataset:
Preferential deuterium bonding at the ice surface: A probe of surface water molecule mobility
Authors: Devlin J. Paul
Published: July 2002

Infrared spectra have been used to determine the temperature dependence of the preferential D-bonding of HDO at the single-donor (dangling O–H) sites on the ice surface. Data for ice nanocrystals containing H2O, D2O, and HDO were in the form of the relative peak intensities of the O–D stretch mode bands of three-coordinated single-donor surface molecules of HDO and D2O. The magnitude of the enhanced stability of the D-bonded HDO molecules at these surface sites is estimated as 52±8 cm−1. This value matches, within experimental error, the literature value for the D-bonded dimer of HDO [Engdahl and Nelander, J. Chem. Phys. 86, 1819 (1987)]. The thermal equilibrium between the H-bonded and D-bonded configurations of HDO at these sites is lost upon cooling below 60 K. This identifies the temperature of onset of molecular rotation of the single-donor surface molecules as 60 K, on a time scale of 105 s. The possibility exists for determination of the onset temperatures of more complex molecular motions on the surface of ice from related data. In that respect, the constant intensity of the O–D stretch mode band of single-donor D2O molecules suggests that more complex surface motions, necessary for interchange with neighboring H-bonded HDO/H2O molecules, are frozen at temperatures below 130 K.
Deuteron and carbon magnetic resonance studies of supercooled liquid and glassy salol
Authors: Döß Axel , Hinze Gerald , Böhmer Roland , Sillescu Hans , Kolshorn Heinz , Vogel Michael , Zimmermann Herbert
Published: July 2002

The glass-former salol was studied using carbon and deuteron NMR. For the 13C measurements protonated samples were used. For the deuteron experiments salol was selectively deuterated at the phenyl ring. The measurement of the spin-lattice relaxation times provides clear evidence for an anisotropic reorientation of the molecules in the supercooled liquid. Close to the glass transition a bimodal longitudinal magnetization recovery is observed which indicates the presence of relatively slow intramolecular degrees of freedom. From deuteron solid echo spectra this process is identified as a uniaxial large amplitude motion of the phenyl group which exhibits a broad distribution of correlation times.
The detection of the free radical FO (X 2Π3/2) by submillimeter-wave spectroscopy
Authors: Tamassia Filippo , Brown John M. , Saito Shuji
Published: July 2002

Pure rotational transitions of the free radical FO in its X 2Π3/2 ground electronic state have been detected by millimeter-wave spectroscopy. Four transitions, which are all magnetic dipole in character, were measured in the frequency region from 219 to 408 GHz. The radical was produced by a well-known efficient reaction between ozone and fluorine atoms. The high sensitivity available in the submillimeter-wave region and a very efficient production method were essential for the detection of rotational transitions in this radical, which many other people have attempted in the past. No electric dipole transitions have been detected in this experiment. The precision of parameters associated with the rotational motion of FO has been improved considerably by fitting these lines together with previous data. Moreover, the parity-dependent nuclear spin rotation term CI′ has been determined for the first time. The r0 and re structures of FO have been revised accordingly.
Time-resolved k(E*) measurements for dissociation of allyl iodide vibrationally excited via C–H overtones (v=6)
Authors: Baklanov Alexey V. , Aldener Mattias , Lindgren Bosse , Sassenberg Ulf
Published: July 2002

The direct time-resolved measurements of the energy dependent rate constant k(E*) have been carried out for dissociation of allyl iodide (AI) vibrationally excited via C–H overtones (v=6). Resonant two-photon ionization (R2PI) technique has been used for the detection of atomic iodine I(2P3/2) arising from the dissociation of photoexcited AI molecules. For R2PI detection a method with narrow-band vacuum ultraviolet radiation (VUV) was used. VUV radiation was generated by means of nonresonant frequency tripling of visible dye-laser radiation in gaseous xenon. Measured k(E*) values were found to be in excellent agreement with those calculated within the microcanonical version of the statistical Rice–Ramsperger–Kassel–Marcus theory in its “phase space” or “loose” transition state limit. The canonical version of the same model is also in good agreement with experimental data from the literature on the dissociation of allyl iodide under thermal heating conditions where collisional excitation takes place.
Sequential addition of particles: Integral equations
Authors: Wang Q. , Danwanichakul P. , Glandt E. D.
Published: July 2002

We present an integral-equation solution of the structure of systems built through the sequential quenching of particles. The theory is based on the Replica Ornstein–Zernike equations that describe the structure of equilibrium fluids within random porous matrices. The quenched particles are treated as a polydisperse system, each of them labeled by the total density at the time of its arrival. The diagrammatic expansions of the correlation functions lead to the development of the liquid-theory closures appropriate for the present case. Numerical solutions for the deposition of hard disks show excellent agreement with simulation. We also discuss a binary-mixture treatment, which is shown to provide a very good approximation to the polydisperse approach.
Rotational and translational energy distributions of CN(v=0,J) from the hot atom reactions: H+XCN→HX+CN(v=0,J), where X=Br, Cl, and CN
Authors: He G. , Tokue I. , Macdonald R. Glen
Published: July 2002

The dynamics of the reactions of translationally energetic H atoms with BrCN, ClCN, and (CN)2 was studied by determining both the rotational state distribution and the translational energy disposition of the CN product ground vibrational level. The reaction was carried out using H atoms with a most probable translational energy of 92 kJ mol−1. The CN radical was monitored by time- and frequency-resolved absorption spectroscopy using the CN red system (A 2Π←X 2Σ) (2,0) band near 790 nm. Sub-Doppler resolution spectroscopy was used to determine the initial translational temperature of the CN(0,J) product. The fraction of the available reaction exothermicity that appeared as CN(0) rotational energy, fR, for H+XCN→HX+CN was 0.034±0.006, 0.061±0.02, and 0.13±0.007, for X=Br, Cl, and CN, respectively. Likewise, the fraction of the available reaction exothermicity that appeared as relative product translational energy, fT, was 0.52±0.25, 0.52±0.20, and 0.59±0.05, for X=Br, Cl, and CN, respectively. The absolute reaction cross sections for the H+XCN→HX+CN reactions were also measured to be 0.03, 0.02, and 0.3×10−16 cm2 for X=Br, Cl, and CN, respectively.
An initial value representation for semiclassical time-correlation functions
Authors: McWhirter J. Liam
Published: July 2002

We derive a new initial value representation for semiclassical time-correlation functions. This derivation combines the initial value formalism developed by Miller with the stationary phase analysis of integrals over endpoint velocities developed by Xiao and Coker [J. Chem. Phys. 102, 496 (1995)] and more recently extended by Bonella, Ciccotti, and Coker [Molec. Phys. 62, 1203 (1996)]. As a result, the determination of the classical paths within the correlation function does not require “root” searches; furthermore, the thermal density matrix within this function weights the initial and not the final positions of these paths. To prevent the correlation function from being not a smooth function of time, a semiclassical phase index similar to the Maslov index is introduced. A simple numerical example is provided and possible criticisms of our approach are discussed.
Density functional study of adsorption of molecular hydrogen on graphene layers
Authors: Arellano J. S. , Molina L. M. , Rubio A. , Alonso J. A.
Published: July 2002

Density functional theory has been used to study the adsorption of molecular H2 on a graphene layer. Different adsorption sites on top of atoms, bonds and the center of carbon hexagons have been considered and compared. We conclude that the most stable configuration of H2 is physisorbed above the center of a hexagon. Barriers for classical diffusion are, however, very small.
Photoinduced nucleation: A novel tool for detecting molecules in air at ultra-low concentrations
Authors: Katz Joseph L. , Lihavainen Heikki , Rudek Markus M. , Salter Brian C.
Published: July 2002

This paper describes the development of a novel detection method and the demonstration of its capability to detect substances at concentrations as small as a few parts per trillion. It is shown that photoinduced nucleation is not in itself a nucleation process; rather, supersaturated vapor condenses onto long-lasting clusters formed by chemical reaction of photo-excited molecules. The role of the supersaturated vapor is to increase the size of these photoproducts by condensation to a size readily detectable by light scattering. Furthermore, the measured nucleation rate variation with illumination wavelength exactly matches the substance’s vapor-phase UV light absorption wavelength dependence, thus providing species identification. The ability to detect and identify molecules of substances at extremely low concentrations from ambient air is useful for detecting and monitoring pollutants, and for detecting explosives such as TNT.
Low-lying excited states of HOOOCl and HOOOBr
Authors: Peterson Kirk A. , Francisco Joseph S.
Published: July 2002

A theoretical investigation of the low-lying singlet and triplet electronic states of HOOOCl and HOOOBr is presented. Calculations of excitation energies and oscillator strengths using CASSCF, first-order CI, MRCI and the equation of motion coupled-cluster singles and doubles methods are presented. The calculations predict that for HOOOCl and HOOOBr there are two singlet states that are accessible by wavelengths longer than 235 nm. These transitions, however, are predicted to be relatively weak. Spin–orbit calculations yield oscillator strengths for the lowest two triplet states of HOOOBr that are only one order of magnitude smaller than those of its low-lying singlet states.
The electronic structures and properties of Alq3 and NPB molecules in organic light emitting devices: Decompositions of density of states
Authors: Zhang R. Q. , Lee C. S. , Lee S. T.
Published: July 2002

A decomposition treatment of density of states in combination with PM3 molecular orbital calculations was used to reveal the fingerprints of electronic structures of two prototypical electroluminescent molecules, tris(8-hydroxy-quinoline)aluminum (Alq3) and N,N′-bis(1-naphthyl)-N,N′-diphenyl-1,1′-biphenyl-4,4′-diamine (NPB). High convenience and accuracy of such a treatment were found for these large organic molecules in the determinations of (1) the distribution of important molecular orbitals such as the highest occupied orbital and the lowest unoccupied orbital; (2) the contribution to valence and conduction bands as well as gap states from constituent atoms, and thus the attribution of ultraviolet photoemission spectrum; (3) the sites and properties of reaction and excitation of a molecule; and (4) the localization property of electronic states. In particular, this study indicates that Alq3 is most possibly attacked by other atoms at the oxygen atoms while the reaction site for NPB is at the nitrogen atom.
Efficient real-space solution of the Kohn–Sham equations with multiscale techniques
Authors: Wang Jian , Beck Thomas L.
Published: July 2002

We present a multigrid algorithm for a self-consistent solution of the Kohn–Sham equations in real space. The entire problem is discretized on a real-space mesh with a high-order finite difference representation. The resulting self-consistent equations are solved on a hierarchy of grids of increasing resolution with a nonlinear full approximation scheme, full multigrid algorithm. The self-consistency is effected by updates of the Poisson equation and the exchange-correlation potential at the end of each eigenfunction correction cycle. The algorithm leads to highly efficient solution of the equations, whereby the ground-state electron distribution is obtained in only two or three self-consistency iterations on the finest scale.
Determination of conformational energy differences of propynlidyne isomers using the effective valence shell Hamiltonian method
Authors: Chaudhuri Rajat K. , Majumder Sonjoy , Freed Karl F.
Published: July 2002

We have applied the highly correlated ab initio effective valence shell Hamiltonian (Hv) method to determine the energy difference between the cyclic and linear isomers of propynlidyne (C3H). Calculations are also described for the vertical excitation energies, ionization potentials, electron affinities, dipole moments, oscillator strengths, and some harmonic vibrational frequencies, which are all determined using the third order Hv method. Computations at both the experimental and theoretically optimized geometries are used to illustrate the geometrical dependence of the computed properties. The Hv optimized geometry is obtained using a two-configurational reference function describing the two dominant resonance structures. Our third-order vertical excitation energy to the lowest excited state in the cyclic isomer, dipole moments, and ground state isomer conformational energy difference are all in good agreement with experiment and with other highly correlated many-body calculations. The computations for higher excited states and for ionization potentials, electron affinities, and oscillator strengths represent the first reports of these quantities. An explanation is provided for persistent theoretical difficulties in computing b1 bending vibrational frequencies of the cyclic isomer.
Heterogeneous nucleation or homogeneous nucleation?
Authors: Liu X. Y.
Published: July 2002

The generic heterogeneous effect of foreign particles on three dimensional nucleation was examined both theoretically and experimentally. It shows that the nucleation observed under normal conditions includes a sequence of progressive heterogeneous processes, characterized by different interfacial correlation function f(m,x)s. At low supersaturations, nucleation will be controlled by the process with a small interfacial correlation function f(m,x), which results from a strong interaction and good structural match between the foreign bodies and the crystallizing phase. At high supersaturations, nucleation on foreign particles having a weak interaction and poor structural match with the crystallizing phase (f(m,x)→1) will govern the kinetics. This frequently leads to the false identification of homogeneous nucleation. Genuine homogeneous nucleation, which is the up-limit of heterogeneous nucleation, may not be easily achievable under gravity. In order to check these results, the prediction is confronted with nucleation experiments of some organic and inorganic crystals. The results are in excellent agreement with the theory.
Semiclassical description of nonadiabatic quantum dynamics: Application to the S1–S2 conical intersection in pyrazine
Authors: Thoss Michael , Miller William H. , Stock Gerhard
Published: July 2002

A recently proposed semiclassical approach to the description of nonadiabatic quantum dynamics [G. Stock and M. Thoss, Phys. Rev. Lett. 78, 578 (1997), X. Sun and W. H. Miller, J. Chem. Phys. 106, 916 (1997)] is applied to the S1–S2 conical intersection in pyrazine. This semiclassical method is based on a transformation of discrete quantum variables to continuous variables, thereby bypassing the problem of a classical treatment of discrete quantum degrees of freedom such as electronic states. Extending previous work on small systems, we investigate the applicability of the semiclassical method to larger systems with strong vibronic coupling. To this end, we present results for several pyrazine models of increasing dimensionality and complexity. In particular, we discuss the quality and performance of the semiclassical approach when the number of nuclear degrees of freedom is increased. Comparison with quantum-mechanical calculations and experimental results shows that the semiclassical method is able to describe the ultrafast dynamics in this system.
Laser fluorescence excitation spectroscopy of the CAr van der Waals complex
Authors: Lei Jie , Dagdigian Paul J.
Published: July 2002

Laser fluorescence excitation spectra of the CAr van der Waals complex, in the vicinity of the carbon 2s22p3s 3P°←2s22p2 3P and 2s2p3 3D°←2s22p2 3P atomic resonance transitions at 165.7 and 156.1 nm, respectively, are reported. A single, weak band was observed ∼100 cm−1 to the blue of the 2s22p3s 3P°←2s22p2 3P atomic transition. An excited-state (v′,0) progression correlating with the carbon atomic 2s2p3 3D°←2s22p2 3P transition was recorded near the 156.1 nm atomic transition and was assigned to the CAr F 3Π←X 3Σ− transition. The upper-state vibrational constants, ωe′=31.82±0.34 cm−1, ωexe′=3.58±0.11 cm−1, were determined. The excited F 3Π state was found to be less strongly bound than the ground state: D0′=54.8±1 and D0″=120.4±1 cm−1. Differences in the rotational contours of bands of the 12CAr to 13CAr isotopomers were ascribed to differences in the fine-structure splittings of the excited F 3Π state. The rotational constant Be′=0.112±0.005 cm−1 was estimated for the 12CAr isotopomer. A Morse function was constructed to describe the potential energy curve of the F 3Π state. The CAr binding energy is compared with that of other diatomic complexes, and the role of predissociation in the decay of excited CAr states is discussed.
Hybrid quantum/classical study of ICN in an Ar matrix: Photofragmentation and cage exit
Authors: Fernandez Alberti S. , Echave J. , Engel V. , Halberstadt N. , Beswick J. A.
Published: July 2002

The Ã continuum photoexcitation of ICN in an Ar matrix is studied using an implementation of the molecular dynamics with quantum transitions method of Tully. Five excited electronic potential energy surfaces of the ICN molecule, Π0+3, Π11(A′,A″), Π13(A′,A″), as well as its ground state, are included in these calculations. The couplings between electronic states at large I–CN internuclear distances are modeled using a diatomic in molecules treatment of the mixing of the different spin-orbit states of iodine induced by the Ar atoms. The electronic motion, as well as the I–CN distance and the corresponding bending angle, are treated quantum mechanically using wave-packet techniques. The rotation and translation of the ICN molecule in the Ar cage are treated classically, as well as the motion of the Ar atoms. In contrast with previous calculations, in which all nuclear degrees of freedom were treated classically, we found a 2% of CN cage exit during the first 0.5 ps of the dynamics.
Resonant enhancement of pulsed-field ionization zero-kinetic-energy photoelectron spectra using microwave fields
Authors: Murgu Elena , Martin J. D. D. , Gallagher T. F.
Published: July 2002

In pulsed-field ionization zero-kinetic-energy spectroscopy (PFI-ZEKE), Rydberg states are typically field-ionized approximately 1 μs after photoexcitation. During this waiting period optically accessible Rydberg states in zero field would decay due to autoionization or predissociation, however their lifetimes are lengthened by the electric fields due to ions or macroscopically applied fields. In this work, we experimentally demonstrate that the introduction of an appropriate microwave field can appreciably lengthen the lifetimes of Rydberg states of the NO molecule, which would otherwise decay by predissociation. The microwave field mixes optically accessible states with longer-lived noncore penetrating states. The resulting enhancement in field-ionization signal is seen at energies where the n, n+1 spacing matches the microwave frequency. This method of suppressing predissociation introduces sharp, symmetric, resonances in the PFI-ZEKE spectra, at specific energies below the ionization thresholds, thus providing a new technique for the accurate determination of molecular ionization thresholds.
Gauge fields in algebraically special space-times
Authors: Torres del Castillo G. F.
Published: July 2002

It is shown that in an algebraically special space-time which admits a congruence of null strings, a source-free gauge field aligned with the congruence is determined by a matrix potential which has to satisfy a second-order differential equation with quadratic nonlinearities. The Einstein–Yang–Mills equations are then reduced to a scalar and two matrix equations. In the case of self-dual gauge fields in a self-dual space-time, the existence of an infinite set of conservation laws, of an associated linear system, and of infinitesimal Bäcklund transformations is demonstrated. All the results apply for an arbitrary gauge group.
Exact Bogoliubov limits for the Bassichis–Foldy model and continued fractions
Authors: Masson D.
Published: July 2002

The critical values of coupling for the Bassichis–Foldy model are explained. For a finite number of bosons N they are associated with changes in the bounded above and below properties of the Hamiltonian. Exact N → ∞ spectral properties are obtained using continued fractions and a duality in terms of competing Bogoliubov-type limits is exhibited. The critical coupling limits are then associated with transitions from either a discrete to a continuous spectrum or from one Bogoliubov-type limit to another.
Algebra representations on eigenfunctions of the Rosen–Morse potential
Authors: Englefield M. J.
Published: July 2002

The bound state eigenfunctions of the Rosen–Morse [N. Rosen and P. M. Morse, Phys. Rev. 42, 210 (1932)] potential are investigated using ladder operators that give a representation of the algebra A1. The representations are generally infinite-dimensional and indecomposable, the representation space containing unbounded functions as well as the normalizable eigenfunctions. Operators giving eigenfunctions of a potential with different strength are also found, giving a representation of D2. The A1 (or su2) representations are identified in terms of a classification proposed by Sannikov (S. S. Sannikov, Yad. Fiz. 6, 1294 (1967) [Sov. J. Nucl. Phys. 6, 939 (1968)]), and the connection with representations obtained by Gruber and Klimyk [B. Gruber and A. U. Klimyk, J. Math Phys. 19, 2009 (1978); 25, 755 (1984)] is given. The evaluation of matrix elements is considered.
Weak rigidity in the PPN formalism
Authors: del Olmo V. , Olivert J.
Published: July 2002

The influence of the concept of weakly rigid almost-thermodynamic material schemes on the classical deformations is analyzed. The methods of the PPN approximation are considered. In this formalism, the equations that characterize the weak rigidity are expressed. As a consequence of that, an increase of two orders of magnitude in the strain rate tensor is obtained.
Perfect fluids satisfying a less than extremely relativistic equation of state
Authors: Xanthopoulos Basilis C.
Published: July 2002

The Einstein perfect-fluid equations for a fluid with ‘‘energy density ε=pressure p+constant’’ equation of state are considered ab initio for space-times with two hypersurface orthogonal, spacelike, commuting Killing fields. Gauge conditions compatible with the field equations are imposed while the fluid is described by means of a stream potential. Contrary to the vacuum Einstein equations, the gauge functions cannot be specified in early stages of the analysis. Instead, the problem is described by a system of five (coupled) partial differential equations for the two gauge functions, the conformal factor of the two-dimensional geometry orthogonal to the two Killing fields, a scalar determining the norms of the Killing fields, and the stream potential of the fluid. It is remarkable that the last two scalars satisfy conjugate equations in the sense that each of them is a potential for the other. By using this conjugation, a subcase of the problem is eventually reduced to a system of two highly nonlinear equations for the two gauge functions. This system is explicitly solved, leading to three distinct families of solutions. To complete the solution for each family one has to solve a second-order, linear, hyperbolic equation and perform certain quadratures.
On gauge fields with sources
Authors: Torres del Castillo G. F.
Published: July 2002

It is shown that in an algebraically special space-time that admits a congruence of null strings, the Yang–Mills equations with sources reduce to a pair of nonlinear first-order differential equations for two matrices, provided that the gauge field is aligned with the congruence. In the case where the current is tangent to the null strings, the gauge field is determined by a matrix potential that has to satisfy a second-order differential equation with quadratic nonlinearities. As an example of this case, the Yang–Mills–Weyl equations are reduced, assuming that the multiplet of Weyl neutrino fields are also aligned with the congruence, and a reduced form of the Einstein–Yang–Mills–Weyl equations is also given.
Dirac spinor orbits
Authors: Hall Richard L.
Published: July 2002

It is supposed that a single fermion with Hamiltonian H=α⋅p+βμ(r)+φ(r), where μ(r) and φ(r) are central potentials, obeys the Dirac equation. If ψ1(r) and ψ2(r) are the radial factors in the Dirac spinor, then the graph {ψ1(r), ψ2(r)} for r∈(0,∞) is called a spinor orbit. In cases where discrete eigenvalues exist, the corresponding spinor orbit eventually returns to the origin. However, if there is a constant a≥0 such that, for r>a, the three functions φ(r), φ(r)/μ(r), and rμ(r) increase monotonically without bound, then it is proved that the spinor orbit must eventually be confined to an annular region excluding the origin. Consequently, the spinor orbit approaches a ‘‘spinor circle,’’ the spinor is not L2, and there are no eigenvalues. This happens, for example, if μ is constant and φ(r) is any monotone increasing and unbounded potential. In such cases the radius of the spinor circle is sensitive to the energy, and instead of eigenvalues one finds a sequence of resonant energies for which the radii of the spinor circles are local minima.
Branching rules for unitary representations of Virasoro and super-Virasoro algebras at c=1
Authors: Baake Michael
Published: July 2002

The branching rules for unitary highest weight representations of Virasoro and super-Virasoro algebras that contain a subalgebra with central charge c=1 are presented. These rules are useful for identifying points of higher symmetry in two-dimensional critical systems with c=1 and for the analysis of a defected Ising chain.
A theorem on the rate of regeneration in decay processes
Authors: Nishioka Michio
Published: July 2002

There is given a generalization of the theorem of Misra and Sinha [Helv. Phys. Acta 50, 99 (1977)], which shows that in the decay process the regeneration of the undecayed unstable states from the decay products cannot proceed too slowly at arbitrarily short time and, correspondingly, the deviation from exponential decay at arbitrarily short time cannot be too small either. The generalization presented here is shown to be valid in the region where the theorem of Misra and Sinha cannot be applied.
Partial *-algebras of matrices and operators
Authors: Epifanio Giuseppina , Trapani Camillo
Published: July 2002

The set ℳ∞ of infinite matrices and the set Q∞ of squarable matrices are considered as partial *-algebras. The connection between Q∞ and two partial *-algebras of closed operators is studied. Conditions for a matrix representation in ‘‘von Neumann’s sense’’ of a family of closed operators are given.
The trace identity, a powerful tool for constructing the Hamiltonian structure of integrable systems
Authors: Tu Gui-zhang
Published: July 2002

A new approach to Hamiltonian structures of integrable systems is proposed by making use of a trace identity. For a variety of isospectral problems that can be unified to one model ψx=Uψ, it is shown that both the related hierarchy of evolution equations and the Hamiltonian structure can be obtained from the same solution of the equation Vx=[U,V].
Localizability and covariance in analytical mechanics
Authors: Grigore D. R.
Published: July 2002

Two familiar concepts in quantum mechanics, namely localizability and covariance, are investigated in the framework of classical mechanics. The analysis of such well-known problems in quantum mechanics as localizability of elementary relativistic particles gives the same result in classical mechanics as well.
Linear realizations of the superrotation and super-Lorentz symmetries. I
Authors: Kouadik Smain , Minnaert Pierre
Published: July 2002

This paper is the first of a series in which various aspects of the superrotation and super-Lorentz symmetries will be studied. In this paper the superrotation algebra and the super-Lorentz algebra are defined. Their linear, finite-dimensional representations are classified. A realization of the low-dimensional representations is provided under the form of irreducible tensor operator multiplets.
Positive discrete series representations of the noncompact superalgebra Osp(4/2,R)
Authors: Schmitt H. A. , Halse P. , Barrett B. R. , Balantekin A. B.
Published: July 2002

Some physically realizable positive discrete series representations of the noncompact orthosymplectic superalgebra Osp(4/2,R) are considered. The decomposition of these Osp(4/2,R) representations on reduction to Sp(2,R)×SO(4) is studied in detail, and the corresponding state vectors are explicitly constructed by acting with the generators on a general lowest weight state. Some examples are given to illustrate these results for particular single-particle spaces.
Scattering of charged particles
Authors: Barrachina R. O. , Macek J. H.
Published: July 2002

Different methods of avoiding the known difficulties of the Coulomb potential scattering theory are reviewed. Mulherin and Zinnes’ [J. Math. Phys. 11, 1402 (1976)] ‘‘distorted’’ free waves and van Haeringen’s [J. Math. Phys. 17, 995 (1976)] Coulomb asymptotic states are considered. The equivalence of both approaches on the energy shell is shown. Actually the possibility of deriving the first method within van Haeringen’s formalism by means of a distorted wave procedure is demonstrated.
The gravitational field of plane symmetric thick domain walls
Authors: Goetz Guenter
Published: July 2002

Exact solutions of Einstein’s equations for a scalar field with a potential V(Φ) =V0 cos2(1−n) (Φ/f(n)) (0<n<1) are presented describing the gravitational field of thick, plane symmetric domain walls. The scalar field has a time-independent kinklike distribution, whereas the metric depends on a time coordinate. The metric is conformally flat and the hypersurfaces parallel to the wall (z=const) are three-dimensional de-Sitter spaces. A particle horizon exists on which the metric becomes Minkowski space. It is shown that the gravitational field experienced by a test particle is repulsive.
p-adic path integrals
Authors: Zelenov E. I.
Published: July 2002

The definition of a path integral is proposed. The method suggested is analogous to Lagrange’s formulation of a path integral used in ordinary quantum mechanics. The notation of linear order on the set of p-adic number, p-adic segment, p-adic Lagrangian, integral of p-adic function of one variable and classical action are introduced. It is proven that if the action is stationary at some trajectory then the Euler–Lagrange equations are satisfied on this trajectory. A finite approximation of a path integral is constructed and the kernel of the operator of evolution is calculated for the case of p-adic harmonic oscillator.
Extensions of some infinite algebras in space-time
Authors: Jiang Wenxin , Gürsey Feza
Published: July 2002

In this paper the operator extensions for infinite algebras of residual gauge transformations and space-time transformations in physical space-time are discussed on general grounds. Possible general forms of the extensions are presented and their realizations in quantum field theories are discussed. The meaning of nontriviality for the extensions will also be discussed. In particular, cohomology methods are used to calculate the extension of spatial diffeomorphism algebra when chiral fermions are coupled to both an external U(1) gauge field and gravity.
Properties of maximum entropy approximate solutions to Fredholm integral equations
Authors: Kopeć S.
Published: July 2002

The properties of the maximum entropy approximate solutions to Fredholm integral equations of the second kind are discussed. It is proved that the approximate solutions exist and converge to the exact one for a wider class of problems than previously determined. The correspondence between the maximum entropy technique and the Galerkin method is established and on its basis an upper a posterior  bound for a solution is found.
On the possibility of confinement caused by nonlinear electromagnetic interaction
Authors: Tamura Hiroshi
Published: July 2002

The theory of Euclidean generalized random fields with nonlinear electromagnetic interaction is examined. A certain class of models described by the theory is given where ultraviolet divergences are mild and the field confines charges. In fact, for each model of the class, the Wilson loop can be defined without any renormalization of infinities and the static potential which is defined through the expectation value of the Wilson loop tends to infinity as the intercharge distance tends to infinity.
Mathieu integral transforms
Authors: Inayat-Hussain A. A.
Published: July 2002

Orthogonality and completeness relations are presented for the quasiorthogonal (i.e., orthogonal with respect to a discontinuous weight function) eigenfunctions of a singular (in the sense of Sturm–Liouville theory) boundary-value problem involving the two-dimensional Helmholtz equation in elliptic–cylinder coordinates. These relations yield as special cases integral transforms whose kernels are products of periodic Mathieu functions and modified Mathieu functions of integral order. The new transforms are analogs of the Weber–Orr transform and of a recently published [J. Math. Phys. 30, 41 (1989)] generalized Hankel transform, and would be applicable to boundary-value problems with elliptical geometries. The proof of the orthogonality and completeness relations is surprisingly simple and is based on a novel application of the Sokhotski–Plemelj equations of distribution theory.
Upper and lower bounds of the ground state energy of anharmonic oscillators using renormalized inner projection
Authors: Vinette F. , Čížek J.
Published: July 2002

Renormalization is a method often used to approximate the eigenvalues of a Hamiltonian that cannot be solved exactly. It consists of splitting the Hamiltonian into a solvable part and a remainder which is then minimized. The inner projection technique, first introduced by Löwdin in the sixties, was developed to bracket the eigenvalues between lower and upper bounds. Combining renormalization and Löwdin’s inner projection yielded the so-called ‘‘renormalized inner projection technique.’’ In this study, this method will be applied to the quartic, sextic, and octic anharmonic oscillators. Lower and upper energy bounds are obtained for finite values of the coupling constant as well as for the infinite case. The relation between the renormalized inner projection and perturbation theory will also be discussed. Another feature of this study is the importance of symbolic computation in allowing us to manipulate expressions with unevaluated parameters and to perform calculations in rational arithmetics or high decimal precision. Thus Löwdin’s rational approximants can be expressed explicitly as rational fractions in terms of the coupling constant and values for the limit constant can be obtained with amazing high accuracy, namely, 62, 33, and 21 decimal places for the quartic, sextic, and octic oscillator, respectively.
Superconformal geometry in three dimensions
Authors: Merkulov S. A.
Published: July 2002

A category of superconformal (3‖2)-dimensional supermanifolds is introduced and studied. It is shown that each superconformal structure has associated with it a distinguished vector bundle (or local supertwistor bundle) equipped with a superconnection that has to be regarded as a supersymmetric extension of three-dimensional conformal Cartan’s connection. The curvature of the superconnection provides a superconformal invariant that vanishes if and only if the (3‖2) supermanifold is locally isomorphic to isotropic super-Grassmanian GI(0‖2;C1‖4;b) with b∈0Sp(1‖4). A choice of scale of superconformal structure on a 3‖2-supermanifold ℳ determines canonically a volume form on ℳ that induces on the underlying manifold ℳrd the action of N=1, D=3 supergravity with cosmological constant. It is proved that a superconformal structure on ℳ can be encoded into the holomorphic structure of the associated with ℳ (3‖1)-dimensional complex superspace of null supergeodesics, 𝒩. A twistor correspondence between free holomorphic data on 𝒩 and solutions of various field equations (including supersymmetric Einstein equations with cosmological constant) on ℳ is established.
A multipolar stationary object embedded in a gravitational field
Authors: Krori K. D. , Goswami D.
Published: July 2002

The task of embedding a multipolar stationary object in a gravitational field is undertaken in this paper. It is believed that such an object will be astrophysically interesting.
Nondispersive solutions of the Klein–Gordon equation
Authors: Hillion Pierre
Published: July 2002

The nondispersive solutions of the Klein–Gordon equation, that is, solutions depending on an arbitrary function F(u), where u is itself a solution of the characteristic equation of the homogeneous three-dimensional scalar wave equation (∇u)2−(c−1∂tu)2=0, are discussed.
Global gravitational instantons and their degrees of symmetry
Authors: Baadhio Randy A.
Published: July 2002

It is shown that the n ten-dimensional very exotic spheres−or, equivalently, global gravitational instantons or solitons−admit only a finite number of involutions. They are realized as smooth SU(3) biaxial actions on Σ10 and are classified by the universal group manifold CP2. A formula, referred to as the degree of symmetry, which quantizes the maximal symmetry that a global gravitational instanton could possess is derived. Namely, it is established that Σ10 admits no more than 20 SU(3) involutions. These results, when combined with the ones found by the author and Lee [J. Math. Phys. 32, 2869 (1991)] yield a better appreciation of Witten’s conjecture [Commun. Math. Phys. 100, 197 (1985)].
The Hamiltonian structure of the (2+1)-dimensional Ablowitz–Kaup–Newell–Segur hierarchy
Authors: Athorne C. , Dorfman I. Ya.
Published: July 2002

By considering Hamiltonian theory over a suitable (noncommutative) ring the nonlinear evolution equations of the Ablowitz–Kaup–Newell–Segur (2+1) hierarchy are incorporated into a Hamiltonian framework and a modified Lenard scheme.
Limiting dynamics of generalized Bardeen–Cooper–Schrieffer models beyond the pair algebra
Authors: Gerisch Thomas , Honegger Reinhard , Rieckers Alfred
Published: July 2002

Bardeen–Cooper–Schrieffer (BCS)-like models for permutation invariant electronic interactions are investigated in terms of recent rigorous mean-field methods. Their limiting dynamics is constructed in the Heisenberg picture on (extensions of) the full canonical commutation relation (CAR) algebra and also restricted to (extensions of) the pair algebra. The classical part of the proper BCS dynamics on the CAR algebra is shown to exhibit 15 macroscopic collective variables, the time dependence of which is explicitly integrated and discussed.
Klein–Gordon propagation of Daubechies wavelets
Authors: Battle Guy
Published: July 2002

Scale-commensurate decay estimates inside the light cone for the solution of the Cauchy problem for the Klein–Gordon equation with a Daubechies wavelet as initial data were obtained. Similar estimates on the solution of the radiation problem with a space–time Daubechies wavelet as the source were derived.
Universal R matrix of Uqsl(n,m) quantum superalgebras
Authors: Hakobyan T. S. , Sedrakyan A. G.
Published: July 2002

In this article Rosso’s formula for the universal R matrix of Uqsl(n) algebras in case of Uqsl(n,m) quantum superalgebras is generalized.
Coherent states on the m-sheeted complex plane
Authors: Vourdas A.
Published: July 2002

Coherent states on the m-sheeted complex plane are introduced and properties like overcompleteness and resolution of the identity are studied. Operators am+, am which create and annihilate clusters of m particles are considered and it is shown that the properties of our coherent states with respect to them are analogous to the properties of the ordinary (Glauber) coherent states with respect to a+, a. An extended Bargmann representation in the m-sheeted complex plane and P and Q representations with respect to our coherent states, are studied. Applications of this formalism in the study of Hamiltonians that describe m-particle clustering are also considered.
Eigenvalues and eigenfunctions of the Dirac operator on spheres and pseudospheres
Authors: Clarkson Eric
Published: July 2002

The Dirac equation for an electron on a curved space–time may be viewed as an eigenvalue problem for the Dirac operator on the spinor fields of the space–time. A general eigenvalue problem for the Dirac operator on a metric manifold M in terms of spinor and tangent fields defined via the Clifford algebra is derived herein. Then it is shown how to solve the Dirac eigenvalue problem on an imbedded submanifold N, of codimension one in M, by solving an eigenvalue equation on M. This is applied to the case of a sphere or pseudosphere imbedded in flat space. Eigenvalues and eigenfunctions for the Dirac operator on any sphere or pseudosphere are determined. In particular, when the pseudosphere is a space–time, the Dirac equation for a free lepton in this space–time can be solved. The resulting mass spectrum is discrete and depends on the curvature of the space–time.
Analysis of the Green’s function approach to one-dimensional inverse problems. II. Simultaneous reconstruction of two parameters
Authors: He Sailing , Romanov Vladimir G. , Ström Staffan
Published: July 2002

The wave-splitting Green’s function approach to one-dimensional electromagnetic inverse problems of simultaneous reconstructions with different types of scattering data is analyzed. Theorems of existence, uniqueness, and stability are given for the following types of scattering data: reflection and transmission data for one round trip, two-sided reflection data for one round trip, reflection data for two round trips.
Quantum group covariant noncommutative geometry
Authors: Isaev A. P.
Published: July 2002

An algebraic formulation of the quantum group covariant noncommutative geometry in the framework of the R-matrix approach to the theory of quantum groups is given. Structure groups are considered taking values in the quantum groups. The notion of noncommutative connections and curvatures is introduced transforming as comodules under the ‘‘local’’ coaction of the structure group that is an exterior extension of GLq(N). These noncommutative connections and curvatures generate GLq(N)-covariant quantum algebras. For these algebras combinations of generators are found which are coinvariants under the ‘‘local’’ coaction of the exterior extension of the quantum group, and one can formally consider these coinvariants as noncommutative images of the Lagrangians for the topological Chern–Simons models, non-Abelian gauge theories, and the Einstein gravity. Also an explicit realization of such covariant quantum algebras is presented via the investigation of the coset construction GLq(N+1)/(GLq(N)⊗GLq(1)).
A nonprincipal value prescription for the temporal gauge
Authors: Lee Kuo-Cheng , Nyeo Su-Long
Published: July 2002

A nonprincipal value prescription is used to define the spurious singularities of Yang–Mills theory in the temporal gauge. Typical one-loop dimensionally regularized temporal-gauge integrals in the prescription are explicitly calculated, and a regularization for the spurious gauge divergences is introduced. The divergent part of the one-loop self-energy is shown to be local and has the same form as that in the spatial axial gauge with the principal-value prescription. The renormalization of the theory is also briefly mentioned.
Covariant algebraic calculation of the one-loop effective potential in non-Abelian gauge theory and a new approach to stability problem
Authors: Avramidi I. G.
Published: July 2002

The recently proposed algebraic approach is used for calculating the heat kernel on covariantly constant background to study the one-loop effective action in the non-Abelian gauge theory. The general case of arbitrary space-time dimension, arbitrary compact simple gauge group and arbitrary matter is considered and a covariantly constant gauge field strength of the most general form, which has many independent color and space-time invariants, and covariantly constant scalar fields as a background (Savvidy type chromomagnetic vacuum) is assumed. The explicit formulas for all the needed heat kernels and zeta-functions are obtained. A new method is proposed to study the vacuum stability and it will be shown that the background field configurations with covariantly constant chromomagnetic fields can be stable only in the case when the number of independent field invariants is greater than one and the values of these invariants differ little from each other. The role of space-time dimension is analyzed in this connection and it is shown that this is possible only in space-times of dimension greater than four.
Dielectric screening in a plasma: Some rigorous results
Authors: Shivamoggi Bhimsen K.
Published: July 2002

In this article, we give some rigorous results about the properties of the solution of Poisson’s equation describing dielectric screening by electrons trapped and/or untrapped in the Coulomb field of the test charge.
Calabi–Yau compactifications and the global structure of the standard group
Authors: McInnes Brett
Published: July 2002

The ‘‘standard group’’ of elementary particle theory is locally isomorphic to SU(3)×SU(2)×U(1). The global structure is completely fixed in unified theories, often in a subtle way; and such theories can be physically unacceptable if they predict the ‘‘wrong’’ global structure for the standard group. A particularly striking example of this is provided by Calabi–Yau compactifications of string theory with the linear (rather than the more conventional spinor) connection interpreted as an E8 connection. Remarkably, these more unconventional compactifications break E8 to a group which is locally isomorphic to the standard group (instead of E6); but they are physically unacceptable, and we argue that the basic reason for this is their failure to produce the correct global structure.
Spinor structures and nonlinear connections in vector bundles, generalized Lagrange and Finsler spaces
Authors: Vacaru Sergiu I.
Published: July 2002

It is our purpose here to show that the spinor theory admits generalization for curved spaces with local anisotropy (for example, for Finsler, Lagrange, and generalized Lagrange spaces).
Transformation bracket for 2D harmonic oscillator functions and its application to few-electron quantum dots
Authors: Ruan W. Y.
Published: July 2002

Transformation bracket relating 2D harmonic oscillator product states with different sets of Jacobian coordinates is derived for systems composed of an arbitrary number of particles with arbitrary masses. The numerical diagonalization of the Hamiltonian of a three-electron quantum dot is given as an example to illustrate its applications.