bluuebunny/crossref_metadata_2025 huggingface dataset:
Roles of nuclear attraction and electron repulsion energies in the relative stability of atomic LS terms
Authors: Koga Toshikatsu , Koshida Yoshinori
Published: July 2002

Numerical Hartree–Fock values of the electron–nucleus attraction Ven and electron–electron repulsion Vee energies are examined for 2392 spectroscopic terms of 170 electronic configurations (with two or more terms) arising in 80 different neutral atoms of the periodic table. For 161 configurations, it is confirmed that a lower energy term has smaller Ven and larger Vee than a high-energy term, as considered to be general in the literature. In particular, the ground term has the smallest Ven and the largest Vee. The differences ΔVen and ΔVee between two terms arising from a configuration are found to have a good linear correlation with the corresponding difference ΔE in the total energy. However, peculiar exceptions are observed for nine electronic configurations with two open subshells. In five configurations, the ground term has the smallest Ven but not the largest Vee. In four configurations, the ground term has neither the smallest Ven nor the largest Vee.
A comment on dielectric hole burning
Authors: Wagner A. , Kliem H.
Published: July 2002

The method of dielectric hole burning is used to distinguish a homogeneous broadened spectrum from a distribution of relaxation times in a dielectric material. After stimulation with a sinusoidal high electric field a time-dependent shift of the response function Φ(t) is observed. This shift is considered to be induced by a frequency selective absorption of energy and an increase of a local fictive temperature. A computer simulation, which is based upon the model of asymmetric double-well potentials for dipole orientations, also shows a time-dependent shift of the response function after applying and removing a sinusoidal high electric field. This behavior is explained considering the time-dependent polarization only. It is shown in this article that it is not necessary to assume an increase of a local fictive temperature caused by a frequency selective absorption of energy.
Generation and observation of GHz ultrasonic waves on liquid surfaces and a liquid/liquid interface by transient reflecting grating method
Authors: Ikeda Sachiyo , Katayama Kenji , Tanaka Takayuki , Sawada Tsuguo , Tsuyumoto Isao , Harata Akira
Published: July 2002

We optically generated and observed GHz ultrasonic waves on liquid surfaces and a liquid/liquid interface for the first time using the transient reflecting grating (TRG) method. Four kinds of samples were used for measurement of the surfaces; two types of black ink, an aqueous solution of crystal violet (CV aq solution) and ethanol aqueous solutions of CV. A cyclohexane/CV aq solution interface was used for measurement of the liquid/liquid interface. The 0.7 GHz and 0.6 GHz ultrasonic waves were generated on the liquid surfaces and the liquid/liquid interface, respectively. These ultrasonic waves resemble longitudinal acoustic waves partly localized at the surface, and they cause surface displacement. The amplitudes of TRG signals from surfaces of the CV mixed solvent solutions were found to be greatly affected by both the viscosity and surface tension. This result indicated the viscosity and interface tension must be considered as perturbations in the elastic theory. The strong dependence on interface tension showed the high selectivity of the TRG signals for the interface.
Valence one-electron and shake-up ionization bands of carbon clusters. I. The Cn (n=3,5,7,9) chains
Authors: Deleuze M. S. , Giuffreda M. G. , François J.-P. , Cederbaum L. S.
Published: July 2002

The 1h (one-hole) and 2h-1p (two-hole; one-particle) shake-up bands in the valence ionization spectrum of small carbon chains (C3,C5,C7,C9) are investigated up to 40 eV, using the one-particle Green’s function approach. Calculations have been performed at the second- and third-orders of an algebraic diagrammatic construction (ADC) scheme based on partial renormalization series, which incorporate static and dynamic electronic correlation consistently through those orders. The results obtained indicate a major or complete breakdown of the orbital picture of ionization extending down into the outer-valence energies for the largest chains (12.4 eV for C9). Cumulenic carbon chains represent the only case reported so far where outer-valence ionization lines of π character can be affected by severe fragmentation in shake-up sets. The one-hole states associated with the terminal carbon lone pairs are also very strongly affected by electronic relaxation.
Accurate nonadiabatic couplings for H3: Application to predissociation
Authors: Schneider I. F. , Orel A. E.
Published: July 2002

We report the results of an ab initio calculation, using analytic techniques, of nonadiabatic couplings for H3 between the degenerate 2E′ ground state and the 2s(2A1′), 3s(2A1′) and 3p(2E′) Rydberg states. The calculations employed extensive correlated wave functions that accurately reproduced the energy levels of these states. We have used these couplings as input to a two-dimensional wave packet calculation of dissociation dynamics in order to predict the predissociation lifetimes and final state vibrational distributions produced by the predissociation. A significant isotope effect is found in the final vibrational distributions produced from H3 and D3 predissociation.
Microscopic formulation of solute and solvent reactive coordinates for solution reaction and examination of contact-ion-pair formation oft-BuCl in four waters
Authors: Okuno Yoshishige
Published: July 2002

The microscopic formulation of the solute and solvent reactive coordinates is reported. This formulation enables us to reduce the solution reaction to a simple barrier-crossing reaction on a potential-energy contour surface in the two-dimensional configuration space determined by these coordinates. We applied this formalism to the examination of the title reaction.
Variational nonequilibrium thermodynamics of reaction-diffusion systems. II. Path integrals, large fluctuations, and rate constants
Authors: Gaveau Bernard , Moreau Michel , Toth Janos
Published: July 2002

We consider reaction-diffusion systems that can be out of equilibrium. In the preceding article a path integral formation of the Hamilton–Jacobi approximation of the Master equation of such systems. Using this path integral formulation, it is possible to calculate rate constants for the transition from one well to another well of the information potential and to give estimates of mean exit times.
Electronic structure and magnetic properties of high-spin octahedral Co(II) complexes: Co(II)(acac)2(H2O)2
Authors: Lohr Lawrence L. , Miller Jeremy C. , Sharp Robert R.
Published: July 2002

An analysis of the electronic structure of the high-spin 3d7 Co(II) ion in the approximately octahedral Co(II)(acac)2(H2O)2 complex is presented in terms of crystal fields of descending symmetry from octahedral to orthorhombic. The energies and wave functions resulting from the interplay of these fields with the spin–orbit coupling are used to obtain zero-field splittings, magnetic moments, magnetic susceptibilities, and g values for the complex. The calculated temperature dependence of the susceptibility is compared to the reported dependence for Co(II)(acac)2(H2O)2, yielding bounds on the strength of the tetragonal component of the crystal field. The calculated anisotropy in the susceptibility is used in an analysis of our observed pseudocontact NMR shifts for methyl and methine protons in the complex. A procedure is outlined for using a crystal field analysis to compute pseudocontact contributions to proton chemical shifts starting from g values extracted from ESR spectra. The relationship between molecular structure and crystal-field splittings is also explored via a series of ab initio electronic structure calculations for the M(II)(acac)2(H2O)2 complexes with M=Mn, Co, Ni, and Zn.
Magnetic field effects on the dynamics of a Rydberg electron: The residence time near the core
Authors: Kono Hirohiko , Tazaki Takayuki , Kawata Isao , Fujimura Yuichi
Published: July 2002

Using symplectic integrator schemes, we calculate the classical trajectory of a Rydberg electron in external electric and magnetic fields. We also solve the equation of motion obtained by taking the mean values over one revolution of the electron in the undisturbed motion. The resulting secular motion is periodic. When only an electric field F is applied, as long as the modulation period in the orbital angular momentum l is longer than the revolution period, the motion agrees with the secular one and the duration for which l is much larger than its low initial value is stretched. The residence time (RT), namely, the probability of finding the electron at the distance r, is hence smaller than that at F=0. In crossed electric and magnetic fields, the secular motion predicts that an additional time stretching due to a magnetic field occurs up to the critical value of magnetic field strength, Bc=33nF (n is the principal action). In the actual simulations, the RT near the core is smaller than that at B=0 even beyond Bc, regardless of the magnitude of the non-Coulombic interaction C2/r2. Slow modulations in l are generated by transitions to secular motions that maintain high l, in addition to the fast modulation originating from the secular motion. When the magnetic field is so strong as to induce chaotic motion (∼4000 G for the energy of −5 cm−1), the RT is one order of magnitude as large as those in weak field cases around 40 G. In the intermediate region (> a few hundred Gauss), without a non-Coulombic interaction, the RT monotonically increases as B increases. In the presence of C2/r2, transitions from low l states to high l states occur: the RT decreases. The motions in high l states can be explained by the well-known model in which an electron bound to the core by a harmonic force moves in a magnetic field.
How do hydrogen atoms on surfaces affect the trajectories of heavier scattered atoms?
Authors: Lui K. M. , Bolotin I. , Kutana A. , Bykov V. , Lau W. M. , Rabalais J. W.
Published: July 2002

The recently developed technique of scattering and recoiling imaging spectrometry (SARIS) is used to probe the effect of hydrogen atoms on the trajectories of 5 keV Ne+ scattering from a Pt(111) surface. Classical kinematic calculations and ion trajectory simulations, using the scattering and recoiling imaging code (SARIC), are carried out in order to probe the details of the interaction and the nature of the perturbation. It is demonstrated that adsorbed hydrogen atoms are capable of deflecting these low kilo-electron-volt Ne trajectories scattering from a Pt surface. These perturbations result in spatial shifts and broadenings of the anisotropic features of the SARIS images that are readily detectable. The scattered Ne atoms lose 0–18% of their initial kinetic energy as a result of the perturbation by the H atoms. The physics of the perturbation on the trajectories can be understood from straightforward classical kinematic calculations and SARIC ion trajectory simulations.
Bound and quasibound states of the Na⋯FH van der Waals molecule
Authors: Špirko V. , Piecuch P. , Bludský O.
Published: July 2002

A recently developed diabatic representation for the two lowest A'2 electronic states of the NaFH system [M.S. Topaler, D.G. Truhlar, X.Y. Chang, P. Piecuch, and J.C. Polanyi, J. Chem. Phys. 108, 5349 (1998)], augmented with highly accurate multireference configuration interaction data, is used to construct a new potential energy function for the ground electronic state of NaFH. The refined potential is used to calculate the bound and quasibound rovibrational states of the Na⋯FH molecule. The focus is on the quasibound states corresponding to excitation of the H–F mode in the complex, although states in which the H–F mode is not excited are also studied. All rovibrational calculations are performed within the framework of the Sutcliffe–Tennyson Hamiltonian for triatomic molecules. The energy positions and lifetimes of quasibound states are obtained using the stabilization method. Three methods are employed to solve the rovibrational problem: (i) the variational approach, in which the Hamiltonian matrix, as defined by a discrete basis set, is diagonalized, (ii) the coupled-channel method, in which the van der Waals stretching coordinate is handled by direct numerical propagation on a grid, and (iii) two perturbative approaches based on the adiabatic separation of vibrational motions. The effect of rotational excitation on the lifetimes of calculated resonances is studied. The main results of this study are the strong evidence for the existence of many long-lived rovibrational resonances corresponding to excitation of the H–F mode in the complex and the rationalization of this finding in terms of effective potentials defining adiabatic separations. Possible impact of the results obtained in this study on new experimental ways of probing potential energy surfaces of the NaFH system, with emphasis on the dynamics of photo-induced charge transfer in Na⋯FH, is discussed.
Instantaneous normal mode theory of more complicated correlation functions: Third- and fifth-order optical response
Authors: Keyes T. , Fourkas John T.
Published: July 2002

A general procedure is given for calculation of time correlations in liquids, including complex multitime functions, with instantaneous normal modes (INM). The method requires equilibrium averages only and eliminates any need to invoke a fictitious harmonic well. The third and fifth order optical response functions, and the self- and collective-density correlations, are obtained and compared with the results of other methods. INM provides several advantages for evaluating the nonlinear response function required for fifth-order scattering. The time expansions of the response functions, and the role of anharmonicity, are discussed.
Ab initio calculation of the zero-field splitting parameter D of benzene and naphthalene
Authors: Bomfleur B. , Sironi M. , Raimondi M. , Voitländer J.
Published: July 2002

The zero-field splitting (zfs) parameter D of benzene and naphthalene in their lowest excited triplet state has been calculated within the framework of spin-coupled valence bond theory. The predicted parameters of these molecules turn out to be 0.168 cm−1 and 0.124 cm−1, respectively, in reasonably good agreement with the observed values of 0.159 cm−1 and 0.101 cm−1.
Structure and energetics of SinNm clusters: Growth pathways in a heterogenous cluster system
Authors: Jungnickel Gerd , Frauenheim Thomas , Jackson Koblar Alan
Published: July 2002

We present a detailed study of the structures and energetics of SinNm clusters with n+m⩽6. We have determined the lowest-energy isomers of these clusters as a function of total cluster size and cluster stoichiometry. The properties of the low-energy isomers were calculated using an accurate, all-electron full-potential density-functional method at both the local density approximation (LDA) and the generalized gradient approximation (GGA) levels of theory. We found the most stable clusters by conducting an extensive phase space exploration for all the clusters containing up to 6 atoms, checking all bonding topologies and all possible atom type decorations. The search was done using a fast, but accurate, density-functional based tight-binding method. The calculations reveal several trends in the silicon–nitrogen binary cluster system. For N-rich clusters, linear or quasi-linear structures predominate, with strong multiple-bond character. Si-rich clusters favor planar or three-dimensional structures. Near the n=m stoichiometry the lowest energy isomers feature a strong alternation of Si and N atoms. Pairing of nitrogen atoms is unfavourable as is strong isolation of nitrogens. We use the results of the calculations to discuss possible growth pathways for the clusters.
Calculation of the vibrational linewidth and line shape of Raman spectra using the relaxation function. II. Application to the mixture neon–nitrogen with inhomogeneous broadening due to concentration fluctuations
Authors: Kooi M. Eline , Michels Jan P. J. , Schouten Jan A.
Published: July 2002

The Raman spectra of nitrogen in the mixture neon–nitrogen have been measured for neon mole fractions, xM, of 0.10, 0.65, and 0.95 at 296 K and 408 K up to the solidification pressure. It was found that the frequency increases as a function of xM. The linewidth is strongly composition dependent, with a very large value for xM=0.65. Further, it is shown that the width decreases as a function of temperature. Molecular dynamics simulations have been performed in order to calculate the linewidth and shape, using the relaxation function. The simulations are in good agreement with experiment. It is shown that the increase in linewidth in the intermediate concentration range is due to an increase of the correlation time, rather than an increase of the amplitude of modulation. In this range inhomogeneous broadening due to concentration fluctuations occur: the vibrational line shape starts to deviate from a Lorentzian curve, and gets a Gaussian component. The simulations also provide insight into the relatively large decrease of the width as a function of temperature in the intermediate concentration range. When the temperature is increased from 296 to 408 K, the amplitude of modulation increases, but the correlation time decreases more.
Valence one-electron and shake-up ionization bands of carbon clusters. II. The Cn (n=4,6,8,10) rings
Authors: Deleuze M. S. , Giuffreda M. G. , François J.-P. , Cederbaum L. S.
Published: July 2002

The 1h (one-hole) and 2h-1p (two-hole; one-particle) shake-up bands in the valence ionization spectrum of small carbon rings (C4, C6, C8, C10) are investigated up to 40 eV, using the one-particle Green’s Function approach. Calculations have been performed using both the third-order algebraic diagrammatic construction [ADC(3)] scheme and the outer-valence Green’s function (OVGF) approximation. The obtained ADC(3) results indicate a major fragmentation of lines into complex sets of 2h-1p satellites, even for outer-levels of Π-character. The simulated ionization spectra provide striking structural signatures for the carbon rings vs. the carbon chains, that could be usefully exploited to discriminate these two types of clusters in plasma conditions. In general and in spite of the extent of the shake-up spreading, one can rather easily trace from our convolutions the energy degeneracies, and in the outer-valence region, the Σ–Π near-energy degeneracies which characterize the electronic structure of these doubly conjugated rings. In relationship to its doubly antiaromatic (i.e., polyynic) nature and lower symmetry, C8 is subject to stronger many-body effects than the other rings. ADC(3) calculations on first-order saddle point forms of C6 and C10 indicate that thermal averaging of conformations could have a substantial effect on the spectral bands, in particular the shake-up ones.
Monte Carlo simulation of homopolymer melts in plane Poiseuille flow
Authors: Gleiman Seth S. , Dorgan John R.
Published: July 2002

A special biased Monte Carlo algorithm is used to study flow of homopolymer melts between neutral, hard walls on a fcc lattice at full occupancy (φ=1). A random number biasing technique is developed to mimic slot flow of a melt; the biasing method preferentially moves the chains in the direction of flow. System properties including velocity profiles, chain-end density distributions, average radii of gyration, and end-to-end vector order parameters are investigated as functions of chain length and biasing parameter. Chain connectivity leads to non-Newtonian flow behavior evidenced as velocity profile blunting. Observation suggests a relationship between the logarithm of the biasing parameter and the pressure drop. Based on the prescribed biasing profile, it is shown that flow causes greater chain deformation for longer chains (N=64,256) than for smaller chains (N=16). Findings also include the ordering of chains with end-to-end vectors aligned with respect to the flow direction.
The formation of subsurface oxygen on Pt{110} (1×2) from molecular-beam-generated O2 Δg1
Authors: Walker A. V. , Klötzer B. , King D. A.
Published: July 2002

An unusually high-peak-temperature desorption state of O2 from Pt{110} (1×2) has been characterized in temperature programmed desorption spectra after O2 adsorption from a supersonic beam at a translational energy of 190 meV and at nozzle temperatures, Tn, greater than 870 K. It shows the characteristics of a subsurface atomic state of oxygen. From the nozzle temperature dependence of the rate of population of this state we conclude that it is formed exclusively from electronically excited O2 Δg1 generated in the molecular beam source.
Deuteron spectroscopy and deuteron field-cycling nuclear magnetic resonance relaxometry of the hydration water of lipid bilayers: The corrugated-sheet model for interface molecular dynamics in the ripple phase
Authors: Seitter R.-O. , Link (Zavada) T. , Kimmich R. , Kobelkov A. , Wolfangel P. , Müller K.
Published: July 2002

Lipid bilayers are known to form the so-called ripple phase in a certain temperature interval between the gel and the liquid crystalline phase transitions. The dynamics of heavy water at the corrugated water/lipid interface was studied with the aid of field-cycling nuclear magnetic resonance (NMR) relaxometry and NMR spectroscopy of the water deuterons. Based on the “reorientation mediated by translational displacement” relaxation mechanism, model calculations were carried out. It is shown that the features of the spin-lattice relaxation dispersion and the coalescence of the deuteron quadrupole splitting in the ripple phase commonly are a consequence of the geometrical surface topology. The deuteron splitting and T1 dispersion data for the ripple phase can be explained in complete accordance with the results of freeze etching electron microscopy and tunneling microscopy. That is, the structural surface features are mirrored in the reorientational dynamics of hydration water.
Line strengths, self-broadening, and line mixing in the 200←0110 (Σ←Π)Q branch of carbon dioxide
Authors: Predoi-Cross Adriana , Luo Caiyan , Berman R. , Drummond J. R. , May A. D.
Published: July 2002

Using a difference frequency spectrometer we have measured the Q(2) to Q(38) 2000←0110,Σ←Π transitions of carbon dioxide at 296 K and pressures up to 15 kPa. These low pressure spectra were analyzed using both the Voigt model, and an empirical line shape that blends together a hard collision model and a speed dependent Lorentzian profile. The broadening coefficients were obtained with an accuracy of 1% or better. The low density or first order low pressure line mixing parameters were also determined. We have compared both our measured low pressure line-mixing parameters and the complete band spectrum at high pressures with those predicted by a relaxation matrix calculated from an EPG fitting law. Spectra at the highest pressures were recorded using both the difference frequency spectrometer and an FTIR spectrometer, the temperature for the latter experiments being 303 K. The vibrational band intensity and linear pressure shift of the branch as a whole were also measured.
The capacitance of the solvent primitive model double layer at low effective temperatures
Authors: Boda Dezsö , Henderson Douglas
Published: July 2002

The effect of the solvent, modeled as a hard sphere fluid, on the behavior of the double layer at low temperatures is studied by means of Monte Carlo simulations. We find that the density profiles are strongly affected by the addition of solvent molecules. The profiles pass from near monotonic functions that exhibit partial drying to oscillatory functions that exhibit partial wetting as the bulk density of the solvent is increased in the system. However, the capacitance, as in the case of the primitive model, increases at low effective temperatures, while after a maximum it decreases at higher effective temperatures as the temperature increases. We find that the adsorption of the ions decreases and changes sign from positive to negative with the decreasing temperature at low electrode charges. Some of these features can be explained by means of a contact value theorem.
Structure of a model lubricant in a mica slit pore
Authors: Curry Joan E.
Published: July 2002

Grand canonical ensemble Monte Carlo computer simulations are used to study a monolayer octamethylcyclotetrasiloxane (OMCTS) film confined between micalike surfaces to better understand the relationship between fluid properties and the atomic structure of the surfaces. OMCTS packs as a well ordered hexagonally close-packed film for all relative alignments of the surfaces. The orientation of the fluid lattice is guided by the mica surfaces. The angle between the symmetry planes of the fluid and the hexagonal oxygen rings on the mica surfaces is approximately 30°. The coupling between OMCTS and the confining mica surfaces is shown to be intermediate in that (1) the film sustains a shear stress and (2) the hexagonal symmetry of the film becomes distorted when the surfaces are out of registry but the film does not melt. Incrementally shifting one of the surfaces laterally leads to periodic distortions in the fluid lattice that are caused by the fluid being stretched to accommodate variations in the pore space potential energy.
Stochastic averaging by functional differentiation
Authors: Becker W. , Zubairy M. S.
Published: July 2002

The stochastic average of exponential expressions that depend at most quadratically upon a Gaussian random function is evaluated using a functional method. The average can be obtained formally for arbitrary forms of the correlation function. The result, however, depends upon a functional determinant and the inverse of a linear operator. Cases are discussed, in particular the Ornstein–Uhlenbeck process, where the latter quantities can be evaluated explicitly.
Massless fields in curved space-time: The conformal formalism
Authors: Castagnino Mario A. , Sztrajman Jorge B.
Published: July 2002

A conformally invariant theory for massless quantum fields in curved space-time is formulated. We analyze the cases of spin-0, - 1/2 , and -1. The theory is developed in the important case of an ‘‘expanding universe,’’ generalizing the particle model of ‘‘conformal transplantation’’ known for spin-0 to spins- 1/2 and -1. For the spin-1 case two methods introducing new conformally invariant gauge conditions are stated, and a problem of inconsistency that was stated for spin-1 is overcome.
A Kerr object embedded in a gravitational field
Authors: Krori K. D. , Bhattacharjee R.
Published: July 2002

The exact expression for the Ernst potential for a Kerr object embedded in a gravitational field is derived using a formalism developed by Kramer and Neugebauer.
Global techniques, dual mass, and causality violation
Authors: Magnon Anne
Published: July 2002

A mathematical framework is presented for the description of (magnetic) monopoles or their gravitational analogs. Using Penrose’s global techniques, a proof of a theorem to the effect that, for vacuum space-times with wormhole and an everywhere timelike and complete Killing vector field, the topology must be that of a principal S1 fiber bundle over S2×R (topology of the manifold of orbits of the stationary Killing vector field) if the dual mass (the gravitational analog of the magnetic monopole) does not vanish, is presented. Hence the presence of this magnetic charge induces a causality violation: it is shown that it measures the number of windings of the space-time bundle around its fiber, or the periodicity of the timelike closed loops. If, in addition, the manifold of orbits of the stationary Killing field is asymptotically flat, or if a rotational Killing field is present, the resulting expressions of the dual mass reinsure the fact that it should be viewed as a monopole source of angular momentum. The NUT solution is presented as an example of space-time exhibiting the above features. The role of dual mass solutions in quantum gravity is considered.
On the microscopic derivation of the finite-temperature Josephson relation in operator form
Authors: Rieckers A. , Ullrich M.
Published: July 2002

As a microscopic description of the Josephson junction, two BCS models, are studied in the strict pair formulation with quite an arbitrary weak coupling potential. The modular formalism, the separate gauge transformations, and the limiting dynamics are analyzed for the interacting system in terms of the GNS representation of the uncoupled limiting Gibbs state. By means of the Connes theory the condensed Cooper pair and the quasiparticle spectrum is shown to be stable against weak perturbations. The modular formalism is used to construct a local approximation to the renormalized particle number operator and, by this, its time dependence, in spite of this observable not being affiliated with the von Neumann algebra of the temperature representation. The time derivation from this unbounded operator-valued function coincides with the limit of the local currents and splits under a natural assumption into a sum of the Josephson and the quasiparticle current operator extending the two-fluid picture also to the coupled model.
A class of sums of Gegenbauer functions: Twenty-four sums in closed form
Authors: van Haeringen H.
Published: July 2002

Series of the type ∑∞n=0 (n+λ) [Cλn (1)]2−k−l−m∏kh=1 Cλn (xh) ⋅ ∏li=1 Dλn (zi) ⋅ ∏m j=1 𝔇λn (u j) are studied. Here Cλn is Gegenbauer’s polynomial, also called the ‘‘ultraspherical polynomial,’’ and Dλn and 𝔇λn are Gegenbauer functions of the second kind. Interrelationships and analytic properties are discussed, and closed forms for 24 of these sums are given, more than half of which are new.
Symmetry reduction and simple supersymmetric models
Authors: Légaré Martin
Published: July 2002

The reduction by the subgroups of the conformal group space-time of the Wess–Zumino model and the four-dimensional simple (N=1) supersymmetric Yang–Mills theories is considered. It is shown for both models that the translations are the only subgroups of the Poincaré group that leave a supersymmetric residual system on the reduced space if we require compatibility of the reduction with all Poincaré supersymmetry transformations.
On the color factor of n-gluon decay from quarkonium
Authors: Biyajima Minoru , Kawabe Tetsuji , Suzuki Naomichi
Published: July 2002

A method for evaluating the weight of the color factor necessary for gluon decay in the context of quantum chromodynamics (QCD) is presented. As concrete examples, the method is applied to the three- and four-gluon decays from heavy quarkonium.
Indecomposable representations of the conformal group: A nonsingular photon-Weyl graviton system
Authors: Furlan P. , Petkova V. B. , Sotkov G. M.
Published: July 2002

A large class of nonelementary indecomposable representations of G=SU(2,2) is constructed and the invariant integral operators are found. An example describing a photon and a linear Weyl graviton field along with some auxiliary fields is studied. A nonsingular Lagrangian for the system is given. The pure, linear Weyl gravity with a conformal invariant gauge fixing condition arises as a particular case.
On the integrability of multidimensional nonlinear evolution equations
Authors: Chen H. H. , Lin J. E.
Published: July 2002

The integrability-test scheme of Chen, Lee, and Liu [H. H. Chen, Y. C. Lee, and C. S. Liu, Phys. Scr. 20, 490 (1979)] from one-space dimension to multispace dimensions is generalized. The temporal equation of the Lax pair is still the linearized perturbed equation that defines the symmetries. But the spectral operator in the Lax pair is no longer the linear recursion operator for symmetries. The absence of the linear recursion operator for symmetries in higher spatial dimensions therefore presents no direct obstacle to the Chen–Lee–Liu test scheme. The Kadomtsev–Petviashvili equation is shown as an example.
Krein structures for Wightman and Schwinger functions
Authors: Jakobczyk L. , Strocchi F.
Published: July 2002

For quantum field theories that do not satisfy the Wightman positivity condition, a Hilbert space structure condition is proposed, which guarantees a Krein structure for the space of states associated to the Wightman functions. The analogous problem for the Schwinger function is also discussed, as well as the conditions that ensure the analytic continuation of a Krein structure in the Euclidean case and vice versa. The Gupta–Bleuler formulation of free quantum electrodynamics is discussed as an example.
The structure and Gel’fand patterns inherent in the Heisenberg supergenerator algebra of dual Liouville-space ‖k
q{K̃.}(k1−k
n):[λ̃],𝒮n〉〉 tensors and the Cayley algebra of scalar invariants over a (k1−k
n) field
Authors: Temme F. P.
Published: July 2002

For many-body spin cluster problems, dual-symmetry recoupled tensors over Liouville space provide suitable bases for a generalized torque formalism using the 𝒮n-adapted density operator in which to discuss NMR and related techniques. The explicit structure of such tensors is considered in the context of the Cayley algebra of scalar invariants over a field, specified by the inner ki rank labels of the Tkq(kl−kn)s. The pertinence of both lexical combinatorial architectures over inner rank sets and SU2 propagative topologies in specifying the structure of dual recoupling tensors is considered in the context of the 𝒮n partitional aspects of spin clusters. The form of Heisenberg superoperator generators whose algebra underlies the Gel’fand pattern algebra of SU(2) and SU(2)×𝒮n tensor bases over Liouville space is presented together with both the related 𝓈-boson algebras and a description of the associated {‖2k 0〉〉} pattern sets of CF29H carrier space under the appropriate symmetry. These concepts are correlated with recent work on SU(2)×𝒮n induced symmetry hierarchies over Liouville spin space. The pertinence of this theoretical work to an understanding of multiquantum NMR in Liouville space formalisms is stressed in a discussion of the nature of pathways for intracluster J coupling, which also gives a valuable physical insight into the nature of coherence transfer in more general spin-1/2 systems.
Integrability of Chern–Simons–Higgs and Abelian Higgs vortex equations in a background metric
Authors: Schiff Jeremy
Published: July 2002

The equations for Chern–Simons–Higgs and Abelian Higgs vortices are reformulated in a certain form of background metric. Painlevé analysis is applied to determine integrability of the equations, and explicit solutions for cylindrically symmetric Chern–Simons–Higgs vortices are found for a specific choice of the metric.
Quantum dynamics on (super)groups: Constraints and the ‘‘BRST’’ supergroup
Authors: Aldaya V. , Loll R. , Navarro-Salas J.
Published: July 2002

The smallest supergroup 𝔅̃ (K) containing among its generators those of a constraint group K, the BRST charge, and the corresponding ghost and antighost operators is constructed. The supergroup 𝔅̃ (K) can be enlarged to include the ordinary dynamical variables of the unconstrained physical system. In a group approach to quantization 𝔅̃ (K) generalizes the ordinary U(1) phase invariance of wave functions. In particular this mechanism reproduces the essential features of the BRST quantization. When K is diff S1 the critical values of string theory are those for which the space of polarized functions on the enlarged BRST supergroup is not irreducible.
Constants of the motion and diagonalization of the Hamiltonian for some scattering processes
Authors: Colegrave R. K. , Croxson P.
Published: July 2002

Complex invariants (for SHO modes) or pairs of real invariants (for RHO modes) are obtained for the frequency converter, the parametric amplifier, and for a three-mode system that describes Raman or Brillouin scattering. All possible constants of the motion and the diagonalization of the Hamiltonian follow as a consequence. Under the assumption made in this paper, the Hamiltonian has also been considered by Moshinsky and Winternitz, who have established the existence of its reduction to diagonal form. However, it is not easy to select the correct transformation (from the totality comprising the symplectic group) to reduce a given H. This has been done explicitly showing, among other results, that the constants of the motion are similar (often identical) in the stable (frequency converter) domain and in the unstable (amplifier) domain.
Path integrals and supercoherent states
Authors: Chaichian M. , Ellinas D. , Prešnajder P.
Published: July 2002

For the real supergroup Osp(1‖2;R), with both its compact and noncompact versions, supercoherent states are introduced with a method close to the one by Perelomov for the even subgroups SU(2) or SU(1,1). These states labeled by a complex c number and Grassmann variable minimize the uncertainty of the quadratic Casimir operator of the group. A path integral formalism is developed for the transition amplitude between supercoherent states for a Hamiltonian linear in the generators of the superalgebra, which leads to a super-Riccati equation. Finally, in the classical limit the canonical equations of motion are derived which involve a generalized super Poisson bracket.
A note on the universal behavior of Schwinger terms in higher dimensional conformal field theories
Authors: Jiang Wenxin
Published: July 2002

It is shown that the structures of the c-number parts of the Schwinger terms for the current algebra and stress tensor algebra are universal for conformal field theories in higher than two dimensions. New results on the structure of these Schwinger terms are presented. Some related general conclusions will be obtained from these results.
Nonzero scalar curvature generalizations of the ALE hyperkähler metrics
Authors: Galicki Krzysztof , Nitta Takashi
Published: July 2002

A quaternionic quotient construction of families of self-dual Einstein metrics with positive scalar curvature on compact Riemannian orbifolds (V-manifolds) is described. The metrics are the positive scalar curvature quaternionic analogs of the asymptotically locally Euclidean (ALE) gravitational instantons constructed by Kronheimer.
Cosmological Yang–Mills hydrodynamics
Authors: Choquet-Bruhat Yvonne
Published: July 2002

The partial differential equations that govern the evolution of a self-gravitating fluid endowed with a density of charge taking its values in a Lie algebra, generating a Yang–Mills current, and hence a Yang–Mills field are written and studied. The local properties of the solutions are analogous to those of gravitating plasmas, but may be quite different globally.
On a phenomenological generalized Boltzmann equation
Authors: Wiesen Bernd
Published: July 2002

In this paper the existence and uniqueness of the solution for a generalized Boltzmann equation is proved and the positivity of this solution is discussed. Two series representations of the solution of the equation will be given.
A note on the construction of the C*-algebra of bosonic strings
Authors: Wiesbrock Hans-Werner
Published: July 2002

This work continues investigations on the C*-algebra of bosonic strings started in Comm. Math. Phys. 136, 369 (1991). There a canonical section of a bundle was used implicitly in order to pass to an algebra of functions. In this article an algebra of sections is worked with directly. This clarifies the discussion on associativity of the algebra.
Graded algebras and geometry based on Yang–Baxter operators
Authors: Marcinek W.
Published: July 2002

The Γ-graded algebras such as the ε-symmetric algebra, generalized Lie algebras and the concept of generalized Lie–Cartan pairs are given in terms of graded Yang–Baxter operators.
Super Wigner function
Authors: Abe Sumiyoshi
Published: July 2002

The phase-space representation of supersymmetric quantum mechanics is given. The super Wigner function is constructed and its transformation property is investigated. In the case of a supersymmetric oscillator, it is explicitly shown how the invariance under the supersymmetry transformation determines the form of the super Wigner function.
Continuous Hahn polynomials
Authors: Micu M.
Published: July 2002

Continuous Hahn polynomials Sn(x) appear in a formulation of quantum mechanics on a discrete time lattice, where they form a natural basis for the state vectors. In this paper we derive some of their generating functions, the expression of the raising and lowering operators and give a lower bound for the largest root of the equation Sn(x)=0.
A new quasitriangular Hopf algebra as the nontrivial quantum double of a simplest C algebra and its universal R matrix for Yang–Baxter equation
Authors: Sun Chang-Pu , Liu Xu-Feng , Ge Mo-Lin
Published: July 2002

Endowing a simple C algebra generated by two commuting elements and a unit with a noncocommutative Hopf algebra structure, a new quantum double and the corresponding universal R matrix for the Yang–Baxter equation is constructed. The finite-dimensional representations of the quantum double is also studied and a concrete R matrix is presented as an example.
Flat connections on quantum bundles and fractional statistics in geometric quantization
Authors: Yu Yue , Zhu Zhong-yuan , Lee H. C.
Published: July 2002

It is shown that in geometric quantization formulation, fractional statistics in a quantized system of N indistinguishable particles in two spatial dimensions arise from the nontrivial cohomology of the flat connection on the quantum line bundles as well as from the nontrivial homology of the configuration space. The propagator of a nonrelativistic interacting system with fractional statistics is derived.
Conservation laws of the quantized Davey–Stewartson I system in (2+1) dimensions
Authors: Pang Gen-Di , Zhao Bao-Heng
Published: July 2002

The explicit expressions of the 2N commuting conserved quantities of the N-particle Davey–Stewartson I (DSI) system are given. The conserved quantities are also expressed in terms of field operators, thus the infinitely many conservation laws are obtained.
Superconformal covariantization of superdifferential operator on (1‖1) superspace and classical N=2 W superalgebras
Authors: Huang Wen-Jui
Published: July 2002

A study of the superconformal covariantization of superdifferential operators defined on (1‖1) superspace is presented. It is shown that a superdifferential operator with a particular type of constraint can be covariantized only when it is of odd order. In such a case, the action of superconformal transformation on the superdifferential operator is nothing but a Hamiltonian flow defined by the corresponding supersymmetric second Gelfand–Dickey bracket. The covariant form of a superdifferential operator of odd order is given.
An algebraic interpretation of the continuous big q-Hermite polynomials
Authors: Floreanini Roberto , LeTourneux Jean , Vinet Luc
Published: July 2002

The continuous big q-Hermite polynomials are shown to realize a basis for a representation space of an extended q-oscillator algebra. An expansion formula is algebraically derived using this model.
Dynamical triangulations, a gateway to quantum gravity?
Authors: Ambjo/rn J. , Jurkiewicz J. , Watabiki Y.
Published: July 2002

We show how it is possible to formulate Euclidean two-dimensional quantum gravity as the scaling limit of an ordinary statistical system by means of dynamical triangulations, which can be viewed as a discretization in the space of equivalence classes of metrics. Scaling relations exist and the critical exponents have simple geometric interpretations. Hartle–Hawking wave functionals as well as reparametrization invariant correlation functions which depend on the geodesic distance can be calculated. The discretized approach makes sense even in higher-dimensional space–time. Although analytic solutions are still missing in the higher-dimensional case, numerical studies reveal an interesting structure and allow the identification of a fixed point where we can hope to define a genuine non-perturbative theory of four-dimensional quantum gravity.
A rigorous treatment of conformal blocks in a model of bosonic conformal field theory
Authors: Bovier Pierre-Alain
Published: July 2002

A free massless field coupled to a background charge Q is considered. The conformal blocks of the theory are adequately described by the N-point vertex VN;0 which is, up to a multiplicative constant, completely determined by the Knizhnik–Zamolodchikov equations and a set of Ward identities on the sphere. The N-point g-loop vertex VN;g for compact Riemann surfaces Σg of genus g≠0 is constructed by a sewing procedure. The main new result is a rigorous proof of the fact that VN;0 is trace class for nonoverlapping disks. This allows one to show that the set of all N-point vertices (for all N) is a modular functor.
Hidden local gauge invariance in the one-dimensional Heisenberg XXZ model with the general boundary terms
Authors: Zhou Huan-Qiang , Guan Xi-Wen
Published: July 2002

Hidden local gauge invariance in the one-dimensional Heisenberg XXZ model with the general boundary terms is studied in the framework of the quantum inverse scattering method. The Bethe ansatz equations are established for the model with the special boundary terms. Our results show that the Hamiltonian and its eigenvectors are explicitly gauge dependent whereas the energy eigenvalues and the Bethe ansatz equations are gauge invariant.
Global cocycle dynamics for infinite mean field quantum systems interacting with the boson gas
Authors: Honegger Reinhard
Published: July 2002

In the framework of operator algebraic quantum statistical mechanics, the global nonequilibrium dynamics for a general class of interactions of infinite mean field quantum lattice systems with the boson field is investigated. The associated interaction operators consist of arbitrary powers of the collective density operators of the mean field system and are linear with respect to the bosonic field operators. Instead of the usual perturbation expansions, here the interacting dynamics are studied by means of cocycle techniques. The cocycle methods are more appropriate to the considered class of interactions, and lead to explicit closed expressions for the dynamical automorphism groups. The cocycle equations connect the classical, collective dynamical behavior of the mean field system with the one-boson dynamics. In physical applications such systems are due to collectively ordered finite-level atoms or the Josephson junction in the thermodynamic limit weakly interacting with the electromagnetic field.
A new algebraic approach for calculating the heat kernel in quantum gravity
Authors: Avramidi I. G.
Published: July 2002

It is shown that the heat kernel operator for the Laplace operator on any covariantly constant curved background, i.e., in symmetric spaces, may be presented in the form of an averaging over the Lie group of isometries with some nontrivial measure. Using this representation, the heat kernel diagonal, i.e., the heat kernel in coinciding points is obtained. Related topics concerning the structure of symmetric spaces and the calculation of the effective action are discussed.
ISO
q
(3) and ISO
q(2,1)
Authors: Sachse Sebastian , Weixler Ralf
Published: July 2002

We prove the embedding of ISOq(3) → ISU√qex(2) and ISOq(2,1) → ISLqex(2,R) as *-algebras and give a Hilbert space representation of ISU√qex(2).
Quantized braided linear algebras relating to quantized braided groups
Authors: Gao Ya-Jun , Gui Yuan-Xing
Published: July 2002

An R-matrix pair (R,Z) solving a system of Yang–Baxter-type equations is needed to define a quantized braided (matrix) group [L. Hlavaty, J. Math. Phys. 35, 2560 (1994)]. It is found that a series of such kind of R-matrix pairs (R(n),Z) (n=0,±1,±2,…) can be constructed from a known pair (R,Z), and a series of realizations of the quantized braided (matrix) bialgebras A(R(n),Z) in V(R(n+1))⊗¯V*(R(n)) can be obtained. Some covariant quantized braided linear algebras and their transformation properties under the braided coactions of the quantized braided group A(R,Z) are considered. Some examples are presented.