bluuebunny/crossref_metadata_2025 huggingface dataset:
Physical and chemical properties of high density atomic oxygen overlayers under ultrahigh vacuum conditions: (1×1)-O/Rh(111)
Authors: Gibson K. D. , Viste Mark , Sanchez Errol , Sibener S. J.
Published: July 2002

In this paper, we elaborate on our previous communication of high coverages of oxygen on Rh(111) [J. Chem. Phys. 110, 2757 (1999)]. When dosing with O2, half of a monolayer of O is adsorbed. Higher coverages can be achieved when exposing the surface to O atoms. As the quantity of adsorbed O increases from a half to a full monolayer, the overlayer structure undergoes several distinct phase changes. At a full monolayer, the (1×1)-O structure is stable at surface temperatures less than ∼400 K. Continued dosing with O atoms results in the rapid migration of O into the bulk. We also report on the chemical reactivity of this densely oxygen-covered surface with CO, H2, and propene.
Photofragment translational spectroscopy with state-selective “universal detection:” The ultraviolet photodissociation of CS2
Authors: McGivern W. Sean , Sorkhabi Osman , Rizvi Abbas H. , Suits Arthur G. , North Simon W.
Published: July 2002

We have investigated the photodissociation of CS2 at 193 nm using the technique of photofragment translational spectroscopy. The utilization of vacuum ultraviolet synchrotron radiation for product photoionization has permitted a determination of the vibrationally resolved translational energy distribution for the CS+S(1D) channel and the translational energy distribution for the CS+S(3P) channel. A simulation of the coincident S(1D) translational energy distribution is consistent with a CS vibrational distribution of 0.02:0.17:0.19:0.46:0.15 in ν=0:1:2:3:4 and an average rotational energy of ∼1–3 kcal/mol. We find that the S(3P)/S(1D) branching ratio is 3.0±0.2, in good agreement with previous reports. Both asymptotic channels exhibit similar velocity dependent anisotropy parameters that decrease with decreasing translational energy release. The results extend earlier reports and provide further insight into the dissociation dynamics at 193 nm.
Verification of the insertion mechanism of N(2 2D) into H–H bonds by the vibrational state distribution measurement of NH(X  3Σ−,0⩽v″⩽3)
Authors: Umemoto Hironobu , Terada Naoki , Tanaka Kunikazu
Published: July 2002

The nascent vibrational state distribution of NH(X 3Σ−) radicals produced in the reaction of N(2D) with H2 was determined by employing a pulsed laser technique. N(2D) was produced by two-photon dissociation of NO, while NH(X 3Σ−) was detected by laser-induced fluorescence. Off-diagonal transitions of the A–X system were employed to probe NH(X 3Σ−,v″⩾2) because of the predissociative nature of the upper state. The vibrational distribution was determined to be 10.0(v″=0): 8.0±1.0(v″=1): 5.0±0.7(v″=2): 2.5±0.5(v″=3). This distribution is much cooler than that obtained by infrared emission measurements, but is similar to that of recent quasiclassical trajectory calculations as well as that of three dimensional quantum calculations based on an ab initio potential energy surface. The agreement with theoretical results suggests that the reaction proceeds via an insertive process.
OH vibrational activation and decay dynamics of CH4–OH entrance channel complexes
Authors: Wheeler Martyn D. , Tsiouris Maria , Lester Marsha I. , Lendvay György
Published: July 2002

Infrared spectroscopy has been utilized to examine the structure and vibrational decay dynamics of CH4–OH complexes that have been stabilized in the entrance channel to the CH4+OH hydrogen abstraction reaction. Rotationally resolved infrared spectra of the CH4–OH complexes have been obtained in the OH fundamental and overtone regions using an IR-UV (infrared-ultraviolet) double-resonance technique. Pure OH stretching bands have been identified at 3563.45(5) and 6961.98(4) cm−1 (origins), along with combination bands involving the simultaneous excitation of OH stretching and intermolecular bending motions. The infrared spectra exhibit extensive homogeneous broadening arising from the rapid decay of vibrationally activated CH4–OH complexes due to vibrational relaxation and/or reaction. Lifetimes of 38(5) and 25(3) ps for CH4–OH prepared with one and two quanta of OH excitation, respectively, have been extracted from the infrared spectra. The nascent distribution of the OH products from vibrational predissociation has been evaluated by ultraviolet probe laser-induced fluorescence measurements. The dominant inelastic decay channel involves the transfer of one quantum of OH stretch to the pentad of CH4 vibrational states with energies near 3000 cm−1. The experimental findings are compared with full collision studies of vibrationally excited OH with CH4. In addition, ab initio electronic structure calculations have been carried out to elucidate the minimum energy configuration of the CH4–OH complex. The calculations predict a C3v geometry with the hydrogen of OH pointing toward one of four equivalent faces of the CH4 tetrahedron, consistent with the analysis of the experimental infrared spectra.
F
19
/
23
Na
multiple quantum cross polarization NMR in solids
Authors: Lim Kwang Hun , Grey Clare P.
Published: July 2002

F 19 → 23 Na triple quantum (TQ) cross polarization (TQCP) experiments and numerical simulations have been performed on the oxyfluoride NaMoO3F. Due to the orientation dependence of the quadrupolar tensor and thus the TQ nutation frequency (ωs,nut), only a fraction of the spins in the powder can match the Hartmann–Hahn condition at the same time, for a fixed F19 rf field strength (ω1I). Numerical simulations of the static TQCP process, for different single crystallite orientations, demonstrate that the most efficient TQCP occurs for parts of the powder where the quadrupolar splitting, Q′, is largest, and where the TQ coherences are pure eigenstates of the system, even though ωs,nut is smallest for these orientations. Under magic angle spinning (MAS) conditions, ωs,nut becomes time dependent and again, efficient TQCP is observed at times during the rotor period where Q′ is largest. TQCP intensities for different crystallites were calculated as a function of ω1I, for fixed Na23 rf field strengths, to obtain TQCP matching profiles and to determine optimum Hartmann–Hahn conditions. The TQCP matching profiles vary significantly with crystallite orientation and with spinning speed, due to the different time dependences of the quadrupolar interaction for the different orientations. Centerband matching conditions are observed at F19 rf fields, close to the minimum values of ωs,nut observed during the rotor period. Two different centerbands are observed for crystallite orientations where there are two different local minima for ωs,nut. The time dependence of ωs,nut results in higher-order (>2) sideband matching conditions. The experimentally observed static and MAS TQCP NMR matching profiles, and changes in the Na23 static and MAS second-order quadrupolar NMR lineshapes, could be rationalized on the basis of the calculated distributions of ωS,nut that occur within the powder. Optimum TQCP intensities were obtained with high Na23 rf power, to maximize ωs,nut, and slow MAS, to ensure efficient spin-locking; a further increase in intensity could be achieved by ramping the F19 rf field during the contact time. The efficiencies of the single quantum cross polarization (SQCP) multiple quantum (MQ) MAS and TQCP-MQMAS experiments were compared and were found to be very similar for NaMoO3F. Finally, the two-dimensional TQCP-MQMAS experiment was illustrated.
Understanding the anomalous 1/t3 time dependence of velocity correlation function in one dimensional Lennard-Jones systems
Authors: Srinivas Goundla , Bagchi Biman
Published: July 2002

One dimensional Lennard-Jones fluids are known to exhibit an interesting 1/t3 time (t) dependence of the velocity correlation function. The origin of this decay is apparently not well understood. We have studied this problem both by molecular dynamic simulations and by mode coupling theory. We find that this t−3 decay of the velocity autocorrelation function (VACF) arises from the coupling of the tagged particle’s motion to the longitudinal current mode of the fluid. Interestingly such a decay is intern rendered possible by the Gaussian time dependence of the coherent dynamic structure factor at the relevant times. This is confirmed by the simulations of Lennard-Jones rods. The t−3 dependence is found to be dominant at low and intermediate densities. We show that the mode coupling theory provides an accurate description of the VACF both at short and long time limits.
A helium atom scattering study of the adsorption of NO on Pt(111)
Authors: Fouquet P. , Graham A. P. , Witte G.
Published: July 2002

The low frequency vibrational modes of NO adsorbed on a Pt(111) surface have been investigated with helium atom scattering (HAS). At low coverages (Θ=0.03) NO forms a dilute phase of isolated molecules which have a characteristic frequency of ℏω=8.0 meV. Based on isotope exchange measurements this mode is assigned to the parallel frustrated translational mode (T-mode) of NO at on top sites. At saturation a well ordered p(2×2) structure (Θ=0.25) appears, for which two different dispersionless modes with frequencies of ℏω=9.5 meV and 12.3 meV were observed. Isotope substitution revealed that the higher frequency mode corresponds to a vibration of the NO molecules in specific threefold hollow sites, as shown by the asymmetric helium diffraction peak intensities. A lattice dynamical analysis identified the lower frequency mode as a back-folded substrate surface phonon, emphasizing that the surface phonon Umklapp processes must be properly identified in order to assign the low energy adsorbate vibrations correctly.
Investigation of steric effects in inelastic collisions of NO(X 2Π) with Ar
Authors: Alexander Millard H. , Stolte Steven
Published: July 2002

Cross sections were determined for collisions of Ar with oriented NO(X 2Π), based on full close-coupled calculations and new ab initio potential energy surfaces (PESs). Collisions in which the NO molecules are initially oriented so that the O end preferentially points toward the Ar atom are more effective in promoting spin–orbit changing transitions. The magnitude of the steric asymmetry is consistent with earlier calculations based on a previous PES, and agrees well with experiment. Various modifications of the full PESs were used to explore the origin of the observed features in the steric asymmetries, in particular the striking oscillatory pattern seen in the variation of the steric asymmetry with final state.
Quantized dynamical bottlenecks and transition state control of the reaction of D with H2: Effect of varying the total angular momentum
Authors: Chatfield David C. , Mielke Steven L. , Allison Thomas C. , Truhlar Donald G.
Published: July 2002

Accurate quantum mechanical scattering calculations for the reaction of D with H2 are analyzed for evidence that quantized transition states control the reaction dynamics over a wide range of total angular momenta. We find that quantized transition states control the chemical reactivity up to high energy and for values of the total angular momentum (J) up to at least nine. We show that the average transmission coefficient for individual dynamical bottlenecks up to 1.6 eV is greater than 90% for all four of the values of J considered (J=0,3,6,9). We assign energies, widths, level-specific transmission coefficients, and quantum numbers to eleven transition state levels for J=0 and two for J=1, and we show how a separable rotation approximation (SRA) based on these data predicts thermal rate constants for temperatures between 500 and 1500 K that are within 0.3%–5.0% of the values obtained from accurate quantal scattering calculations up to high J. This implementation of the SRA enables us to quantify the contribution of each transition state level to the thermal rate constant, and to separately quantify the influence of recrossing and of quantum mechanical tunneling and nonclassical reflection on the thermal rate constant. Finally, we demonstrate the influence of two supernumerary transition states on both the overall and the state-selected dynamics.
Squeezing lubrication films: Layering transition for curved solid surfaces with long-range elasticity
Authors: Persson B. N. J. , Ballone P.
Published: July 2002

The properties of an atomic lubricant confined between two approaching solids are investigated by a model that accounts for the curvature and elastic properties of the solid surfaces. Well defined atomic layers develop in the lubricant film when the width of the film is of the order of a few atomic diameters. An external squeezing-pressure induces discontinuous, thermally activated changes in the number n of lubricant layers. The precise mechanism for these layering transitions depends on n, and on the lubricant-surface pinning barriers. Thus, in the absence of sliding, unpinned or weakly pinned incommensurate lubricant layers give rise to fast and complete layering transitions. Strongly pinned incommensurate and commensurate layers give rise to sluggish and incomplete transformations, resulting in trapped islands. In particular, for commensurate layers it is often not possible to squeeze out the last few lubricant layers. However, lateral sliding of the two solid surfaces breaks down the pinned structures, greatly enhancing the rate of the layering transitions. In the case of sliding, an important parameter is the barrier for sliding one lubricant layer with respect to the others. When this barrier is larger than the lubricant-surface pinning barrier, the lubricant film tends to move like a rigid body with respect to the solid surface. In the opposite case, slip events may occur both within the lubricant film and at the lubricant–solid interface, making the squeeze-out process much more complex. In some of the simulations we observe an intermediate phase, forming immediately before the layering transition. This transient structure has a lower 2D density than the initial phase, and allows the system to release elastic energy, which is the driving force for the phase transformation.
Vibronic spectroscopy and lifetime of S1 acrolein
Authors: Paulisse Kevin W. , Friday Tyson O. , Graske Margaret L. , Polik William F.
Published: July 2002

The S1 vibronic spectrum of acrolein (CH2CHCHO) was obtained in a supersonic free-jet expansion using cavity ringdown spectroscopy. Comparison of room temperature and free-jet spectra was used to assign vibronic transitions. Computations using the configuration interaction-singles method were used to predict the values of the S1 fundamental vibrational frequencies. The current set of assignments increases the number of identified bands from 27 to 59, corrects 16 misassignments in the previous literature, and identifies two new fundamental bands. A lower limit for the lifetime of the S1 vibronic origin was determined from linewidth measurements to be 1.8–2.1 ps.
Pressure broadening of NH3 by H2 from 15 to 40 K
Authors: Willey Daniel R. , Timlin Robert E. , Deramo Melinda , Pondillo Peter L. , Wesolek Danielle M. , Wig Ryan W.
Published: July 2002

Pressure broadening of the (J,K)=(1,1), (2,2), and (3,3) inversion transitions of NH3 was measured using normal- H2 as the broadening agent at kinetic temperatures of 15 to 40 K. Measurements were taken in a quasiequilibrium cell using the collisional cooling technique. H2 pressure broadening cross sections were compared to low-temperature He pressure broadening of the same transitions and found to be from 2.5 to 8 times larger than corresponding He cross sections. Measured normal- H2 and He cross sections were also compared to calculated J=0, para-H2 cross sections.
A reduced dimensionality quantum calculation of the reaction of H2 with diamond (111) surface
Authors: Skokov Sergei , Bowman Joel M.
Published: July 2002

We present a reduced dimensionality quantum dynamics study of the hydrogen abstraction reaction on a semirigid (111) diamond surface, Cd+H2(v,j,m)→CdH+H. A nine-dimensional potential energy surface is developed by combining a London–Eyring–Polanyi–Sato potential based on ab initio data with nonbonded and surface interactions. Four reactive degrees of freedom are treated explicitly using a recently developed wave packet approach in a real L2 basis, and the total reaction probabilities for initial states v=0–1, j=0–11, and m=0–4 are calculated over a large total energy range. The remaining five degrees of freedom are treated using energy-shift approximations, and the full cumulative reaction probability is obtained and from it the full thermal rate constant. Comparison with conventional transition state theory indicates that at 300 K tunneling accounts for 90% of the rate constant and remains significant even at high temperatures. Dynamical corrections to transition state theory become important above 1000 K. At 1200 K the tunneling and dynamical corrections nearly cancel each other and the transition state theory rate constant agrees very well with quantum rate constant. The coupling of surface and reactive modes has only a minor, less then 15%, effect on the rate constants, provided that the energetics for the relaxed surface are incorporated into the potential. The thermal rate for H abstraction from diamond, obtained from detailed balance, is in good agreement with experimental data. Under typical chemical vapor deposition conditions the thermal rate for H abstraction by diamond active sites is found to be 100 slower than the rate of competitive reaction, H addition to diamond active sites.
Nucleation and growth of AgCl clusters in a sodium borate glass: Numerical analysis and SAXS results
Authors: Schmelzer Jürn , Lembke Ulrich , Kranold Rainer
Published: July 2002

By solving a set of differential rate equations the precipitation of AgCl clusters in the glass system 30Na2O–70B2O3/AgCl has been modeled. Using a parallel algorithm on a CRAY T3E it was possible to investigate the process of homogeneous nucleation and growth, which starts after an initial quench of the glass melt into the miscibility gap of the phase diagram, even including the onset of the Ostwald ripening stage. The method has been applied to the examination of the intermediate stage between independent growth and Ostwald ripening. In particular, the influence of the interfacial tension and the temperature of heat treatment on the evolution of the silver halide clusters has been investigated. The results are in qualitative agreement with those of in situ measurements of small-angle x-ray scattering. Furthermore, general consequences for the interpretation of experimental data on nucleation and growth have been derived.
Chain length scaling of protein folding time: Beta sheet structures
Authors: Dimitrievski K. , Kasemo B. , Zhdanov V. P.
Published: July 2002

We present comprehensive 3D lattice Monte Carlo simulations of the folding kinetics of two-turn antiparallel β sheets. The model employed takes into account isotropic nonspecific interactions as in previous flexible heteropolymer models and also orientation-dependent monomer–monomer interactions, mimicking the formation of hydrogen bonds and chain rigidity. The chain length is varied from N=15 to 33. For each chain length, we calculate the fastest folding temperature, Tfast, folding temperature, Tfold, and glass-transition temperature, Tg. The time-averaged occupation probability of the native state is found to be nearly independent of N at all temperatures. The dependence of Tfast and Tfold on N is accordingly relatively weak. The temperature interval where the folding is fast rapidly decreases with increasing N. For the chain lengths chosen, Tfold slightly exceeds Tg. The dependence of the folding time τf on N is well fitted by using the power law, τf∝Nλ. The exponent λ is found to depend on temperature and on the distribution of nonspecific interactions in the chain. In particular, λ=2.7–4.0 at T=Tfast and 5.2 at T slightly below Tfold. Evaluating τf in real units at T near Tfold yields physically reasonable results.
Electrically induced dynamic processes in nematic liquid crystals: H1 nuclear magnetic resonance investigations
Authors: Bender Michael , Holstein Peter , Geschke Dieter
Published: July 2002

The director reorientation of some nematic liquid crystals in the presence of both magnetic and electric field is described by a modified from of the Leslie equation. Proton nuclear magnetic resonance experiments observing static director orientations in different angles between the director and the magnetic field are described together with reorientation experiments driven by various electric fields. A new technique to measure Δχ/Δε is presented which gives direct access to the anisotropies without any influence of elastic properties. Using electric fields of different strength and in different angles with respect to the magnetic field the dynamic processes in liquid crystals can be investigated in a very flexible way. A number of experiments investigating the homogeneous director reorientation in the electric field is presented. As one result the rotational viscosity was determined. As a surprising result we found a homogeneous reorientation in the electric field and an inhomogeneous reorientation back in the magnetic field even though the initial angles between the director and the external field were the same.
Regular maximal slicings in asymptotically flat space-times
Authors: Carfora Mauro
Published: July 2002

An estimate is provided for the lapse function defining asymptotically Euclidean maximal slicings in asymptotically flat space-times. This estimate is found to be in agreement with a similar estimate suggested, on heuristic grounds, by Smarr and York. It is also shown that in vacuum space-times the scalar curvature of maximal slices remains uniformly bounded in time provided that suitable conditions on the rate of growth of the (negative) lower bound of the Ricci curvature of the slices are satisfied.
Brownian dynamics approximation to the decay rate of a metastable state
Authors: Weaver D. L.
Published: July 2002

An integrodifferential equation for the time dependence of the unabsorbed fraction in a finite diffusion system is derived and solved approximately. The lowest-order approximate solution is equivalent to the first-passage time approximation to the decay rate of the system whether or not the absorbing boundary probability of absorption varies with time.
Cauchy system for resolvent of Milne’s integral equation with anisotropic scattering
Authors: Ueno S.
Published: July 2002

It has been shown previously that the resolvent of the inhomogeneous truncated Milne’s integral equation with isotropic scattering enables us to reduce dimensionally the above auxiliary equation via Chandrasekhar’s X- and Y-functions. In the present paper, extending the above procedure to the case of anisotropic scattering, we show how to use effectively the Bellman–Krein–Sobolev-like formula for the dimensional reduction of the Cauchy system of the source function via the generalized Chandrasekhar X- and Y-functions.
Bound and radiation fields of a pointlike SO(3) monopole
Authors: Sorg M.
Published: July 2002

The macroscopic field of a pointlike, arbitrarily moving monopole is split up into its bound and radiation parts. The SO(2) fiber bundle, having the total monopole field as its curvature, is embedded into an SO(3) bundle (Georgi–Glashow model) such that the SO(2) monopole field is composed in an SO(3) invariant manner by the microscopic gauge and Higgs fields: The Higgs field constitutes the bound part and the gauge field (Yang–Mills field) is responsible for the radiation part of the macroscopic monopole field. The role played by the field equations for the validity of separate local energy-momentum conservation laws is discussed extensively.
Symmetries of gauge fields
Authors: Molelekoa Moshe
Published: July 2002

The concept of homogeneity for a gauge field is introduced as an appropriate geometrical interpretation of the symmetric properties of the gauge field relative to a group of space-time transformations. It is more general than the formulation in terms of an invariant connection, as illustrated by an example on translational symmetries. Sufficient conditions are given for invariance to be equivalent to homogeneity. Both finite and infinitesimal symmetries are treated.
Linearly and nonlinearly transforming fields on homogeneous spaces of the (4,1)-de Sitter group
Authors: Drechsler W.
Published: July 2002

Scalar functions on the homogeneous spaces ℋR of the de Sitter group G=SO(4,1) are studied, where the spaces ℋR are of the form G/K with K being a subgroup of the Lorentz group H=SO(3,1) contained in SO(4,1). The spaces ℋR can be regarded as fiber bundles ER=ER(G/H,H/K), with the base V′4 =G/H being a space of constant negative curvature characterized by a fundamental length parameter R[(4,1)-de Sitter space], and the fiber S=H/K being a homogeneous space of the Lorentz group. The action of G on the spaces ER is a linear action on V4 and a nonlinear action on S, where the latter action is defined by a generalized Wigner rotation. A gauge theory based on the (4,1)-de Sitter group is investigated with matter represented in terms of a generalized wave function Φ(x;ξ,ỹ) [with x∈U4 (Riemann–Cartan space-time), ξ∈V′4, and ỹ∈S] which is defined as a map from a cross section on the bundle E=E(U4, F=ER, G=SO(4,1)) over space-time U4 with fiber F=ER =G/K and structural group G=SO(4,1) into the complex numbers. The introduction of purely nonlinearly transforming fields (N)Φ(x;ỹ) is discussed as well as the nonlinear realization of the SO(4,1) symmetry in terms of transformations of the Lorentz subgroup H (generalized Wigner rotations). The geometric implications of symmetry breaking are pointed out.
Proof of the Levinson theorem by the Sturm–Liouville theorem
Authors: Ma Zhong-Qi
Published: July 2002

The Levinson theorem is proved by the Sturm–Liouville theorem in this paper. For the potential ∫10r‖V(r)‖dr <∞,V(r)→b/r2 when r→∞, the modified Levinson theorem is derived as nl=(1/π)δl(0) +(a−l)/2− 1/2  sin2{δl(0)+[(a−l)/2]π}, if a(a+1)≡b+l(l+1)> 3/4 or a=0. Two examples which violate the Levinson theorem and satisfy the modified Levinson theorem are discussed.
Some exact solutions of Einstein–Dirac–Maxwell fields and a massive neutrino
Authors: Patra Amar Chandra , Ray Dipankar
Published: July 2002

The field equations obtained by Krori, Chaudhury, and Bhattacharjee for Einstein–Dirac–Maxwell fields for several different metrics with a time-independent and a time-dependent Dirac field for a massless neutrino and for a massive neutrino are completely integrated. It is also noted that one of the cases, the particular solutions given by Krori, Chaudhury, and Bhattacharjee, is not correct. All other particular solutions are the special cases of the solutions obtained here.
The generalized Morse oscillator in the SO(4,2) dynamical group scheme
Authors: Barut A. O. , Inomata A. , Wilson R.
Published: July 2002

A family of the Morse oscillators with certain quantized coupling constants are described as composite objects in the framework of the SO(4,2) dynamical group scheme. Although a single Morse oscillator can be solved by the subgroup SO(2,1) of SO(4,2) this SO(2,1) is not the spectrum generating group], the set of all energy levels is given by the representation of another particular one-parameter subgroup of SO(4,2), which is the dynamical group of a single Morse oscillator. The continuous spectra of this oscillator and other variations of the Morse potential are also discussed by making an analytic continuation from the Morse potential well to the Morse barrier.
Colliding gravitational plane waves with noncollinear polarization. II
Authors: Ernst Frederick J. , García D. Alberto , Hauser Isidore
Published: July 2002

A simple criterion for colliding gravitational plane waves is developed. This colliding wave condition is preserved by a new realization of the Geroch group augmented by a Kramer–Neugebauer involution. A three-parameter generalization of a two-parameter family of solutions with noncollinear polarization discovered recently by Ferrari, Ibañez, and Bruni is presented, and two additional solutions are derived that demonstrate that much larger families are likely to be constructed in the near future.
Commutation properties of cyclic and null Killing symmetries
Authors: Szabados L. B.
Published: July 2002

In a space-time admitting cyclic and nonspacelike Killing symmetries the commutation properties of the Killing vectors are examined. It is shown that cyclic and null Killing vectors can be noncommuting only if a Killing vector of stationarity is also admitted. Two consequences of this commutativity are also discussed.
N=2 supertori and their representation as algebraic curves
Authors: Melzer Ezer
Published: July 2002

N=2 supertori (N=2 super-Riemann surfaces of genus 1) are classified according to their superconformal equivalence classes. A detailed description of the corresponding supermoduli space is based on this classification. Superelliptic functions are constructed and used for representing the supertori as algebraic varieties in projective superspace. The boundary of N=2, genus 1 supermoduli space is discussed.
Integral equations with symmetrical kernel applied to a system with a Dirac-type spectrum
Authors: Ma Zhong-Qi , Dai An-Ying
Published: July 2002

The generalized Sturm–Liouville problem for a system with a Dirac-type spectrum was converted to that of a linear integral operator with a symmetrical kernel by Yang [Commun. Math. Phys. 112, 205 (1987)]. A supplementary case is discussed in this paper.
Four-momentum and angular momentum in classical electrodynamics
Authors: Lozada Abraham , Torres P. L.
Published: July 2002

The total four-momentum Pμ and the total angular momentum tensor Mλμ for a classical point charged particle and its field are considered. The standard definition of Pμ and Mλμ is used as the integrals of their respective densities over a spacelike hyperplane orthogonal to the four-velocity of the particle. It is shown that the integral defining Pμ exists and is a conserved quantity, but that the integral defining Mλμ does not exist. The last result is due to the asymptotic behavior of the Coulomb field at spatial infinity.
Coefficients of fractional parentage in the L–S coupling scheme
Authors: Novoselsky Akiva , Katriel Jacob , Gilmore Robert
Published: July 2002

An efficient procedure for the evaluation of the coefficients of fractional parentage (cfp’s) for L–S coupled wave functions is presented. The cfp’s are calculated separately for N particles, each with angular momentum l (s), coupled into a total angular momentum L (S). The N-particle states formed can belong to any permutational symmetry. The procedure for the evaluation of the L and the S cfp’s for arbitrary permutational symmetry is a generalization of the procedure proposed by Bayman and Lande [Nucl. Phys. 77, 1 (1966)] for symmetric and antisymmetric states. It involves the construction and diagonalization of the matrices representing the quadratic Casimir operators for the appropriate special unitary and symplectic (or orthogonal) groups. The cfp’s of the antisymmetric L–S coupled states are obtained in terms of products of cfp’s for L and S corresponding to conjugate representations of the symmetric group. This method is demonstrated to provide cfp’s for L–S states for systems with a considerably larger number of particles than is feasible using the procedures heretofore available.
On a time-dependent extension of the Morse potential
Authors: Kondo Anne E. , Truax D. Rodney
Published: July 2002

A time-dependent extension of a Morse potential is formulated. Both the bound and unbound state wave functions are obtained algebraically for the resulting time-dependent Schrödinger equations, based upon the representations of su(2) and su(1,1), respectively. The method of R-separation of variables is instrumental in the analysis.
A new proof of the generalized Birkhoff theorem
Authors: Bona C.
Published: July 2002

A new proof of the generalized Birkhoff theorem in general relativity is presented. The partial results contained in previous proofs are recovered in a unified treatment of the different kinds of space-times to which the theorem applies. The proof is based on the fact that these space-times are conformal to the direct product of two two-dimensional manifolds (almost-product structure).
The S̄(a,b,c/m) metrics interpreted as colliding wave solutions
Authors: García D. Alberto
Published: July 2002

It is shown that the class of solutions S̄(a,0,−1/1), a real slice of the ‘‘complexified’’ Plebański S(a,b,c/m) metrics, is interpretable as colliding wave solutions and, for a=−s2, coincides precisely with the Ferrari–Ibañez colliding wave metrics.
Bäcklund transformations for the anti-self-dual Yang–Mills equations
Authors: Mason L. , Chakravarty S. , Newman E. T.
Published: July 2002

Beginning from any given (local) solution of the GL(n,C) anti-self-dual Yang–Mills (ASDYM) equations on Minkowski space, a simple technique for the generation of large classes of solutions (perhaps in some sense all) is given. The origin of this technique is described in terms of two versions of the Ward construction. The resulting description of Bäcklund transformations is sufficiently simple that it is then possible to identify the group generated by the collection of all such Bäcklund transformations and the space on which it acts in terms of concrete functions.
Conformally Ricci-flat perfect fluids. II
Authors: Van den Bergh N.
Published: July 2002

A review is given of the perfect fluid solutions which can be constructed by conformal transformations of nonflat vacuum solutions of Einstein’s field equations. In addition a proof is given that (a) under physically reasonable restrictions all solutions for which the gradient of the scalar field is orthogonal to the fluid velocity and (b) all solutions sharing with the corresponding vacuum solution a symmetry group of dimension n≥2 are necessarily shear- or vorticity-free and hence are explicitly known.
Effective conductivity and average polarizability of random polycrystals
Authors: Avellaneda Marco , Bruno Oscar
Published: July 2002

A third-order expansion for the effective thermal conductivity tensor K* of anisotropic polycrystalline cell materials is derived. The coefficients of the expansion are given in terms of the average polarizability tensor, a nondimensional quantity determined from the grain shape and crystallographic orientation distributions independent of other details of the microgeometry such as two (or more) particle correlation functions. Explicit numerical results for a wide variety of microgeometries made of ellipsoidal cells are obtained. This calculation uses a new method that exploits the symmetry properties of the effective conductivity tensor of a cell material as a function of the single-crystal conductivities.
Some symmetries of quantum dimensions
Authors: Fuchs Jürgen , van Driel Peter
Published: July 2002

Several useful properties of the quantum dimensions of representations of 𝒰q(sl(n)) for q a root of unity are established. The results can be used to calculate truncated Kronecker products of these representations and hence to investigate the isomorphism between these truncated tensor products and the fusion rules of the WZW theories associated with 𝒰q(sl(n)).
Multivariable biorthogonal continuous–discrete Wilson and Racah polynomials
Authors: Tratnik M. V.
Published: July 2002

Several families of multivariable, biorthogonal, partly continuous and partly discrete, Wilson polynomials are presented. These yield limit cases that are purely continuous in some of the variables and purely discrete in the others, or purely discrete in all the variables. The latter are referred to as the multivariable biorthogonal Racah polynomials. Interesting further limit cases include the multivariable biorthogonal Hahn and dual Hahn polynomials.
Relations between hyperspherical harmonic transformations and generalized Talmi–Moshinsky transformations
Authors: Liu Xian-hui
Published: July 2002

The correlations between the hyperspherical harmonic transformations and the generalized Talmi–Moshinsky transformations are studied for the three-body and four-body systems. An optical approach for solving few-body problems through diagonalizing the Hamiltonian of a system in an optimal subset of the basis functions of harmonic oscillators in hyperspherical coordinates is proposed. The evaluations of the interaction matrix elements are achieved with the aid of the transformation properties of hyperspherical harmonics.
Summational invariants in systems of mass points and rigid bodies
Authors: Huber Wolfgang
Published: July 2002

For systems of rigid bodies and mass points, the general form of summational invariants will be derived using some results of Amigó and Reeh [J. Math. Phys. 24, 1594 (1983)].
The Dirac equation in Robertson–Walker spaces: A class of solutions
Authors: Kovalyov M. , Légaré M.
Published: July 2002

Exact solutions of the Dirac equation in open and closed Robertson–Walker spaces are presented. A set of massive solutions is given for static metrics. In the case of nontrivial and arbitrary expansion factors, massless solutions are obtained via a conformal transformation. The set of massless solutions in open Robertson–Walker spaces is shown to be complete.
Transversal affine connection and quantization of constrained systems
Authors: Hajicek Petr , Kuchar Karel V.
Published: July 2002

The Dirac quantization of a finite-dimensional relativistic system with a quadratic super-Hamiltonian and linear supermomenta is investigated. In a previous work, the operator constraints were consistently factor-ordered in such a way that the resulting quantum theory was invariant under all relevant transformations of the classical theory. The method was based on a special choice of coordinates and gauge. Here, coordinate-independent methods are worked out and a quite general gauge is used. A new mathematical concept, the so-called ‘‘transversal affine connection,’’ is introduced. This connection is not a linear connection and is associated with a degenerate metric. The corresponding curvature tensor is defined and its components are calculated. The formalism is used to reconstruct the operator constraints, clarify their geometric meaning, and calculate their commutators.
On the covariant quantization of a first-class superparticle
Authors: Lindström U. , Roček M. , Siegel W. , van Nieuwenhuizen P. , van de Ven A. E.
Published: July 2002

The Batalin–Vilkovisky formalism is used to quantize covariantly a formulation of the superparticle with only first-class constraints. Towers of ghosts are found that split into ghosts-for-ghosts and ghost gauge fields. Subsolutions to the master equation with spinor and bispinor ghosts contain terms cubic in antifields and lead to free gauge-fixed BRST-invariant actions. The final formulation with multispinor ghosts is nilpotent only on the classical shell.
Covariant Lax operators and Kac–Moody algebras
Authors: Das Ashok , Roy Shibaji
Published: July 2002

It will be shown that covariantizing the Lax operators with a ‘‘time’’ independent non-Abelian gauge connection leaves the dynamical equations invariant. However, the symmetries associated with the Schrödinger equation in such a case is enlarged. This is used to give a simple derivation of various Kac–Moody algebras associated with such Lax operators.
Kac–Moody and new infinite-dimensional Lie algebras
Authors: Okubo Susumu
Published: July 2002

It will be shown that general polynomials of the Kac–Moody field can generate either a new infinite-dimensional Lie algebra or W3 -type algebra, at least for the classical field case. For the case of the infinite dimensional Lie algebra, it leads to an infinite number of conserved classical quantities which generate hierarchy equations analogous to that of the KdV system. The chiral boson equation emerges as the lowest-order equation of the hierarchy.
Momentum operators with gauge potentials, local quantization of magnetic flux, and representation of canonical commutation relations
Authors: Arai Asao
Published: July 2002

Commutation properties of two-dimensional momentum operators with gauge potentials are investigated. A notion of local quantization of magnetic flux is introduced to characterize physically the strong commutativity of the momentum operators. In terms of the notion, a necessary and sufficient condition is given for the position and the momentum operators to be equivalent to the Schrödinger representation of the canonical commutation relations.
Natural bundles. II. Spin and the diffeomorphism group
Authors: Swift S. Timothy
Published: July 2002

In this, the second of a sequence of papers dealing with the geometry and applications of natural infinite dimensional bundles, a framework is described in which the interaction between spinors, metrics, and diffeomorphisms can be discussed. In this framework, a coupled metric–spinor field configuration manifold and a grand spin frame bundle can be constructed geometrically. In addition, a notion of infinite dimensional spin structure is defined and an example of such a structure is provided. Applications of these ideas to general relativity and other field theories are suggested.
On the Riemann–Hilbert problem for the one-dimensional Schrödinger equation
Authors: Aktosun Tuncay , Klaus Martin , van der Mee Cornelis
Published: July 2002

A matrix Riemann–Hilbert problem associated with the one-dimensional Schrödinger equation is considered, and the existence and uniqueness of its solutions are studied. The solution of this Riemann–Hilbert problem yields the solution of the inverse scattering problem for a larger class of potentials than the usual Faddeev class. Some examples of explicit solutions of the Riemann–Hilbert problem are given, and the connection with ambiguities in the inverse scattering problem is established.
Two-dimensional reductions of the self-dual Yang–Mills equations in self-dual spaces
Authors: Tafel Jacek
Published: July 2002

Many completely integrable equations have been shown to be reductions of the Yang–Mills equations in a flat space. In this paper two-dimensional symmetry reductions of the self-dual Yang–Mills equations, together with the corresponding linear equations, in an arbitrary self-dual space are classified. The reduced equations are given in different forms. Some new equations are found, in particular one which generalizes the sine-Gordon equation and the Liouville equation.
Finslerian structures: The Cartan–Clifton method of the moving frame
Authors: Vargas José G. , Torr Douglas G.
Published: July 2002

A theory of Finslerian structures is presented using an unpublished method of Clifton. It consists of using Cartan’s moving frame method with fields of special bases, and the Cartan calculus of tensor-valued forms with nonredundant coordinates on sphere bundles (which are the base spaces of the Finsler bundles). The formulation only requires a modicum of new concepts and does not involve Lagrangians at any fundamental level, including the definitions of metrics and connections. Finslerian connections on Riemannian (and even flat) metrics are discussed. The invariant forms of the sphere bundle of Minkowski space are obtained. The possibility of describing equations of motion through autoparallels, rather than extremals, is illustrated.
Mass spectra from field equations
Authors: Good R. H.
Published: July 2002

A type of field quantization is developed which, in some cases, leads directly from a field equation to a mass spectrum. The starting point is a field-Hamiltonian setup of the field equations. A Schrödinger-type wave function, a function of the field variables, is postulated and a Hamiltonian operator is inferred from the Hamiltonian function. A wave equation is suggested which has particle-type solutions only for special values of the rest mass. As examples, the spectra for the linear wave equation and for an equation with a sharply limited range of the field variable are discussed.
Integrable mechanical systems related to the Harry–Dym hierarchy
Authors: Ragnisco O. , Rauch-Wojciechowski S.
Published: July 2002

It is shown that all stationary and restricted flows of the Harry–Dym hierarchy have a parametrization as a set of Newton equations. They are new classes of integrable mechanical systems. Properties of the Harry–Dym hierarchy are used for deriving systematically spectral-parameter-dependent Lax representations and bi-Hamiltonian formulation for some of these systems. They yield complete sets of integrals in involution which render these systems to be completely integrable.
Long-range interaction of electromagnetic field induced by Chern–Simons field
Authors: Ma Zhong-shui , Xue Xun
Published: July 2002

The canonical quantization to a Ginzburg–Landau-like theory is shown by considering the potentials of the electromagnetic field and the Chern–Simons field independently. The operator of matter fields which carries fractional spin and obeys the fractional statistics is constructed. The transportation of flux between those of the corresponding gauge field and Chern–Simons field is found. This leads to a striking conclusion that the electromagnetic field induced a topological term, which gives photon mass and leads to a Meissner effect different than happens in ordinary Ginzburg–Landau theory. The induction of a Chern–Simons term for the electromagnetic field is considered the origin of fractional statistics in general, through the transportation of flux is equivalent to the transportation of the long-distance interaction in the text. That the Chern–Simons field is hidden in the constructed matter field gives rise to a theoretical interpretation of the off-diagonal long-range order in the theory.
Note on Kantowski–Sachs universes
Authors: Da̧browski Mariusz P.
Published: July 2002

It is shown that the conformal time parameter η for closed dust-filled Kantowski–Sachs models [J. Math. Phys. 7, 443 (1966)] cannot be taken as growing to infinity in subsequent cycles of evolution regardless of the values of the integration constants. This forces the energy density to remain constant in each subsequent cycle rather than decrease, which contradicts the original Kantowski and Sachs statement.
Scattering by singular potentials. A. Wave function expansion
Authors: Dolinszky T.
Published: July 2002

The series of the radial wave functions is developed by iterating a Volterra-type integral equation with a modified Wentzel–Kramers–Brillouin problem supplying the reference system. The expansion proved to be convergent for exponentially singular scattering potentials in general while for the case of power singularity r−p it was convergent only at p≥4.
Scattering theory for the Belavkin equation describing a quantum particle with continuously observed coordinate
Authors: Kolokol’tsov Vassili N.
Published: July 2002

In the article, the complete investigation is given of the large times behavior of the solutions of the Belavkin quantum filtering equation describing a quantum particle with continuously observed coordinate. It turns out that these solutions have an extraordinary property, namely: as t → ∞, any solution will tend to a Gaussian function (for almost all realizations of innovating Wiener process). As a consequence, it follows that the dispersion of coordinate will always tend to the same limit, as t → ∞, not depending on initial data.
Topological BF theories in 3 and 4 dimensions
Authors: Cattaneo Alberto S. , Cotta-Ramusino Paolo , Fröhlich Jürg , Martellini Maurizio
Published: July 2002

In this paper we discuss topological BF theories in 3 and 4 dimensions. Observables are associated to ordinary knots and links (in 3 dimensions) and to 2-knots (in 4 dimensions). The vacuum expectation values of such observables give a wide range of invariants. Here we consider mainly the 3 dimensional case, where these invariants include Alexander polynomials, HOMFLY polynomials and Kontsevich integrals.
Identities of the scalars of the four-dimensional Riemannian manifold
Authors: Harvey Alex
Published: July 2002

A general algorithm is presented for the calculation of identities relating scalars constructed from appropriate contractions of the Riemann tensor, Ricci tensor, and curvature scalar. The algorithm is applied to determining the identities among the quartic scalars.