bluuebunny/crossref_metadata_2025 huggingface dataset:
Multiple quantum nuclear magnetic resonance in one-dimensional quantum spin chains
Authors: Fel’dman Edward B. , Lacelle Serge
Published: July 2002

Multiple quantum (MQ) nuclear magnetic resonance (NMR) spin dynamics are investigated analytically in infinite one-dimensional (1D) chains of spins 1/2. The representation of spin 1/2 operators with fermion field operators allows to calculate exactly the spin density operator, and hence NMR observables, under a variety of different conditions for 1D spin systems. The exact expressions are valid for all times and for a macroscopic number of coupled spins. The calculations for a 1D spin system initially at thermal equilibrium, and evolving under a 2-quantum/2-spin average dipolar Hamiltonian, in the presence of nearest-neighbor dipolar interactions yield MQ NMR spectra with 0- and 2-quantum coherences only. For a nonequilibrium initial condition with transverse magnetization, the analogous spin dynamics calculations produce MQ NMR spectra with all possible coherences of odd orders. Calculations at the level of perturbation theory, which include next-nearest-neighbor dipolar interactions, generate MQ spectra with higher even order coherences for equilibrium initial condition and evolution under a 2-quantum/2-spin propagator. Consideration of multiple spin correlations, 0-quantum coherences, and rf pulse imperfections are also presented. The relevance and implications of these theoretical results for comparison with the recent MQ NMR experiments of Yesinowski et al. on materials with quasi-one-dimensional distributions of spins, and for MQ NMR of solids in general are discussed.
Differential cross section polarization moments: Location of the D-atom transfer in the transition-state region for the reactions Cl+C2D6→DCl(v′=0,J′=1)+C2D5 and Cl+CD4→DCl(v′=0,J′=1)+CD3
Authors: Rakitzis T. Peter , Kandel S. Alex , Lev-On Topaz , Zare Richard N.
Published: July 2002

The photoloc technique can permit the measurement of not only the state-to-state differential cross section but also its complete product polarization dependence for all moments of orientation and alignment with k⩽2. We have realized this possibility for the reaction Cl+C2D6→DCl(v′=0,J′=1)+C2D5 at a collision energy of 0.25 eV, for which we have measured the differential cross section, 1/σ(dσ00/dΩr), and the four polarization-dependent moments of the differential cross section, A1(1)stf, A0(2)stf, A1(2)stf, and A2(2)stf, in the stationary target frame (STF), which are defined by Aq(k)stf=(dσkqstf/dΩr)/(dσ00/dΩr). For the Cl+CD4→DCl(v′=0,J′=1)+CD3 reaction at a collision energy of 0.28 eV we have also determined 1/σ(dσ00/dΩr) and A0(2)stf. The laboratory speed distributions of the DCl(v′=0,J′=1) products are measured using 2+1 resonance-enhanced multiphoton ionization (REMPI) and the core-extraction technique. The polarization-dependent differential cross sections are determined from the dependence of the core-extracted profiles on the photolysis and probe polarizations. Recent studies have shown that the Cl+CD4 and Cl+C2D6 both show scattering behavior described by the line-of-centers model and both yield rotationally cold DCl products with little energy in the alkyl fragments. Despite these similarities, we measure DCl(v′=0,J′=1) product polarizations that differ greatly for these two reactions. For the Cl+CD4 reaction, we find that JDCl is maximally aligned perpendicular to an axis close to the product scattering direction, uDCl. For the Cl+C2D6 reaction, we find that JDCl is half-maximally aligned perpendicular to the line-of-centers direction. We interpret these results in terms of the location of the D-atom transfer along the reaction coordinate, positing that the D-atom transfer for the Cl+CD4 reaction occurs late in the reactive process and the D-atom transfer for the Cl+C2D6 reaction occurs earlier near the distance of closest approach. We interpret the difference in the locations of the D-atom transfer to be the cause of the large differences in the Arrhenius pre-exponential factors of the Cl+CD4 and Cl+C2D6 reactions.
Application of the effective valence shell Hamiltonian method to accurate estimation of oscillator strengths and excitation energies of Mg-like ions
Authors: Chaudhuri Rajat K. , Das B. P. , Freed Karl F.
Published: July 2002

The ab initio effective valence shell Hamiltonian (Hυ) method is used to compute the excitation energies and oscillator strengths for resonance transitions in Mg-like ions, as well as their lowest ionization potentials. The computed excitation energies and oscillator strengths from the Hυ method are in excellent agreement with experiment and with the best values from other high level correlated computations, where available. Several previous discrepancies between theory and experiment are now removed. The present work also investigates the dependence of the calculated Hυ oscillator strengths on the nature and choice of the valence orbitals and provides a comprehensive study of the convergence of Hυ calculations with respect to the enlargement of the valence space.
Comment on “Thermochemistry of gaseous SiO(OH), SiO(OH)2, and SiO2,”[J. Chem. Phys. 101, 6076 (1994)]
Authors: Hildenbrand D. L. , Lau K. H.
Published: July 2002

Previously published data for a gaseous reaction equilibrium involving the species SiO(OH) have been re-interpreted, based on other information suggesting a very weak OSi–OH bond. This reinterpretation leads to a revised value of −85 kcal mol−1 for the standard enthalpy of formation at 298 K of gaseous SiO(OH).
Product rotational polarization in the photoinitiated bimolecular reaction A+BC→AB+C on attractive, mixed and repulsive surfaces
Authors: Wang Ming-Liang , Han Ke-Li , He Guo-Zhong
Published: July 2002

The product rotational polarization is reported using the quasiclassical trajectory method for the photoinitiated bimolecular reaction A+BC→AB+C. The model takes the form of a 3D quasiclassical trajectory study of a hypothetical exothermic reaction employing combinations of (a): three different potential energy surfaces (attractive, mixed and repulsive), (b): three markedly different reagent mass combinations (H+HL, H+LL and H+HH, where L≡1 amu and H≡80 amu). Four PDDCSs (2π/σ) (dσ00/dωt), (2π/σ) (dσ20/dωt), (2π/σ) (dσ22+/dωt), and (2π/σ) (dσ21−/dωt) which are usually sensitive to many photoinitiated bimolecular reaction experiments are presented. Furthermore, the distribution of dihedral angle P(φr) and the distribution of angle between K and J′ P(θr) are discussed. Moreover, the angular distribution of product rotational vectors in the form of polar plots in θr and φr is calculated.
Path integrals for Fokker–Planck dynamics with singular diffusion: Accurate factorization for the time evolution operator
Authors: Drozdov Alexander N. , Talkner Peter
Published: July 2002

Fokker–Planck processes with a singular diffusion matrix are quite frequently met in Physics and Chemistry. For a long time the resulting noninvertability of the diffusion matrix has been looked as a serious obstacle for treating these Fokker–Planck equations by various powerful numerical methods of quantum and statistical mechanics. In this paper, a path-integral method is presented that takes advantage of the singularity of the diffusion matrix and allows one to solve such problems in a simple and economic way. The basic idea is to split the Fokker–Planck equation into one of a linear system and an anharmonic correction and then to employ a symmetric decomposition of the short time propagator, which is exact up to a high order in the time step. Just because of the singularity of the diffusion matrix, the factors of the resulting product formula consist of well behaved propagators. In this way one obtains a highly accurate propagation scheme, which is simultaneously fast, stable, and computationally simple. Because it allows much larger time steps, it is more efficient than the standard propagation scheme based on the Trotter splitting formula. The proposed method is tested for Brownian motion in different types of potentials. For a harmonic potential we compare to the known analytic results. For a symmetric double well potential we determine the transition rates between the two wells for different friction strengths and compare them with the crossover theories of Mel’nikov and Meshkov and Pollak, Grabert, and Hänggi. Using a properly defined energy loss of the deterministic particle dynamics, we obtain excellent agreement. The methodology is outlined for a large class of processes defined by generalized Langevin equations and processes driven by colored noise.
Femtosecond hole-burning spectroscopy with stimulated emission pumping and supercontinuum probing
Authors: Kovalenko S. A. , Ruthmann J. , Ernsting N. P.
Published: July 2002

A novel broadband femtosecond version of the stimulated emission pumping (SEP) technique is demonstrated. A nonstationary ground state of a molecular sample in the condensed phase is prepared by two optical pulses. The first picosecond PUMP pulse resonantly excites the sample. The second femtosecond DUMP pulse, which is tuned to the molecular fluorescence band, is applied after relaxation in the excited state and creates a “particle” in the ground state and a “hole” in the excited state. The relaxation of this system is probed by a femtosecond supercontinuum. An advantage of the proposed scheme is that the hole contribution is constant for certain conditions, and hence, the transient absorption spectrum of the particle may be isolated. As an application of the technique, the ground-state evolution of coumarin 102 in acetonitrile is studied. Intramolecular vibrational redistribution (IVR), with a characteristic time τIVR∼10 fs, is observed in the frequency domain. Subsequently, the absorption band shifts to the blue and shows isosbestic points in the course of relaxation.
A classical molecular dynamics study of recombination reactions in a microporous solid
Authors: Delogu Francesco , Demontis Pierfranco , Suffritti Giuseppe B. , Tilocca Antonio
Published: July 2002

Classical molecular dynamics calculations have been applied to the study of the recombination reaction of photodissociated radical species. Within a simplified reaction scheme it has been possible to get qualitative information about the influence of the environment. A comparison has been made between reactions in a liquid solvent and in a complex structured environment, such as a microporous silicate. Marked differences in the recombination yield and in the energy relaxation mechanism have been observed.
Excited state polarizabilities in solution obtained by cubic response theory: Calculations on para-, ortho-, and meta-nitroaniline
Authors: Jonsson Dan , Norman Patrick , Ågren Hans , Luo Yi , Sylvester-Hvid Kristian O. , Mikkelsen Kurt V.
Published: July 2002

We show that response theory implemented with a self-consistent reaction field theory model is a viable approach to simulate excited state polarizabilities of molecules in solution. The excited state polarizabilities are in this approach given by the double residue of the ground state cubic response functions, accounting for both equilibrium and nonequilibrium contributions to the interaction with the outer medium. The effects of the inertial polarization of the solvent on the polarizabilities of the solutes are shown to strongly depend on the solvent configuration, whether the solvent is in equilibrium or in nonequilibrium with the charge distribution of the investigated compound. The inertial polarization vector in the nonequilibrium solvent configuration represents the equilibrated solvent configuration when solvating the ground state of the solute. This inertial polarization vector is not in equilibrium with any of the excited states and therefore one observes a rather different behavior between nonequilibrium and equilibrium solvent descriptions of the solute. Illustrative calculations are presented for para-, meta-, and ortho-nitroanilines in gas and solution phases. Results have been compared with experimental data where available.
Segment connectivity, chain-length breathing, segmental stretch, and constraint release in reptation models. II. Double-step strain predictions
Authors: Hua Chi C. , Schieber Jay D. , Venerus David C.
Published: July 2002

Predictions for double-step strain flows are presented using a newly proposed reptation theory that accounts for segment connectivity, chain-length breathing, segmental stretch and constraint release in a self-consistent, full-chain theory. In this part of the work emphasis is on double-step shear strains where the second step is reversed and the imposition time of the second strain is earlier than the estimated retraction time, for which the Doi–Edwards model and single-integral models have been found to be incapable of describing experimental trends. Transient stress relaxation properties of two types of reversing flows, types B and C, have been examined and compared to the predictions obtained from the Doi–Edwards model and a single-integral model. The simulations show excellent agreement with the experimental trends based on recent mechanical and optical measurements.
Dynamical quenching of laser-induced dissociations of heteronuclear diatomic molecules in intense infrared fields
Authors: Abou-Rachid Hakima , Nguyen-Dang T. Tung , Atabek O.
Published: July 2002

This article explores the influence of permanent dipole moments, i.e., of direct vibrational excitations, on the dynamical dissociation quenching (DDQ) effect, a mechanism for laser-induced vibrational trapping in the infrared (IR) spectral range which was recently demonstrated for the homonuclear H2+ ion, and was shown to result from a proper synchronization of the molecular motions with the oscillations of the laser electric field [see F. Châteauneuf, T. Nguyen-Dang, N. Ouellet, and O. Atabek, J. Chem. Phys. 108, 3974 (1998)]. To this end, the wave packet dynamics of the HD+ and, to a lesser extent, the HCl+ molecular ions are considered in an intense IR laser field of variable frequency. Variations in the absolute phase of the laser electric field, a form of variations in the initial conditions, reveal new signatures of the DDQ effect due to the presence of nonzero permanent dipole moments in these molecules. The added permanent dipole/field interaction terms induce a discrimination between parallel and antiparallel configurations of the aligned molecule with respect to the laser’s instantaneous electric field. As a result, molecules that are prepared antiparallel to the field at peak intensity find their dissociation quenched most efficiently, while those that are prepared parallel to the field are strongly dissociative.
Thermodynamically consistent reptation model without independent alignment
Authors: Öttinger Hans Christian , Beris Antony N.
Published: July 2002

The Poissonian character of the reversible part of nonequilibrium dynamics is exploited here in order to determine a dynamically consistent expression for a reptation model without the independent alignment assumption. It is shown that the previously proposed form by Doi and Edwards for such a model is compatible with the GENERIC formalism of nonequilibrium thermodynamics [Phys. Rev. E 56, 6620 (1997); 56, 6633 (1997)] only after two changes are made: (a) the production term in the evolution equation involves an average of the orientation dyadic uu over the entire internal phase space, and (b) the extra stress tensor involves an additional term, qualitatively different from the one representing the original Doi–Edwards expression. The predictions of the new model for the stress after double shear strain with flow reversal are shown to be realistic, demonstrating irreversibility effects, in contrast to the model with the independent alignment approximation.
Dielectric response of polymer films confined between mica surfaces
Authors: Cho Yoon-Kyoung , Watanabe Hiroshi , Granick Steve
Published: July 2002

The thin-film dielectric response of organic films confined within a surface forces apparatus (SFA) and also between parallel sheets of atomically smooth mica is reported for the first time. Analysis is presented to infer dielectric properties of the organic film from the measured capacitance of the total system: sample, and mica sheets intervening between sample and electrodes. Measurements concerned the frequency dependence of normal-mode dielectric relaxation of cis-polyisoprene having dipoles aligned in the same direction along the chain backbone. We find that in thin-film geometries the peak frequency, fpeak, of normal mode dielectric loss (ε″) is moderately lower than for bulk samples and that, more important, the expected terminal tail, observed in the bulk sample (ε″∝f for f<fpeak), is not observed even at the lowest frequency examined. Thus the slow normal mode distribution is much broader and the terminal relaxation time is much longer for chains in the thin layers. These dielectric features are attributed to spatial constraints on global chain motion in the thin layers and also to adsorption of chains on mica surfaces when the layer thickness is comparable to the unperturbed chain dimension. Independent measurements of shear relaxation, performed using a SFA modified for measurement of dynamical mechanical shear rheology, found a tremendously retarded viscoelastic response relative to bulk samples. There is the possibility that the broad distribution of the dielectric response of individual polymer chains may correspond to the observed retarded viscoelastic relaxation. However, we cannot rule out the other possibility that the dielectrically detected relaxation of individual chains is still faster than the terminal viscoelastic relaxation and that the latter thus corresponds to the collective motion of many confined chains.
A concerted assessment of potential-dependent vibrational frequencies for nitric oxide and carbon monoxide adlayers on low-index platinum-group surfaces in electrochemical compared with ultrahigh vacuum environments: Structural and electrostatic implications
Authors: Weaver Michael J. , Zou Shouzhong , Tang Catherine
Published: July 2002

Electrode potential-dependent intramolecular stretching frequencies, νNO, for nitric oxide adlayers on ordered low-index Pt, Rh, Ir, and Pd electrodes in acidic aqueous solution measured by infrared reflection-absorption spectroscopy (IRAS) are compared with corresponding data obtained in ultrahigh vacuum (UHV) environments in order to assess the manner and degree to which the chemisorbate vibrational properties are controlled by electrostatic factors. For most of the seven surfaces for which corresponding UHV-based data are also available, the coverage-dependent νNO spectral fingerprints observed in the corresponding electrochemical case are closely comparable, suggesting the occurrence of the same (or similar) binding sites and adlayer structures. The νNO frequencies at a given coverage are typically 10–15-fold more sensitive to the electrostatic potential (or field) at the Pt-group electrodes than for isolated (gas-phase) NO, highlighting the importance of potential-dependent surface bonding. The νNO frequencies in the electrochemical and UHV interfacial environments are compared at an equivalent metal-vacuum “surface potential,” φvM, deduced from work-function data for the latter systems, together with the “absolute” potential of the hydrogen reference electrode, Eab(ref). This procedure is facilitated by the stability of adsorbed NO toward electro-oxidation even at high electrode potentials in acidic media. In view of the piecemeal analyses along these lines undertaken previously for carbon monoxide, vibrational data for CO as well as NO are included so as to provide a comprehensive compilation for 14 surface-adsorbate pairs. Most systems selected exhibit a single dominant chemisorbate binding site as gleaned from the spectral form. For saturated adlayers, where the adsorbate coverages and binding geometries are known (or are likely) to be similar within the two environments, the vibrational frequencies are found to be remarkably concordant, within 5–10 cm−1, when the comparison is undertaken at equivalent φvM values deduced by presuming that Eref(abs) is 4.8 (±0.1) V. This value is consistent with the “higher” Eref(abs) estimates quoted in the literature. Although the νNO and νCO values are anticipated to be sensitive only to the potential drop across the chemisorbed adlayer, the inclusion of corrections to the electrochemical potentials for φvM components located spatially outside this region does not substantially alter this conclusion. Some adlayer structural implications are considered, along with the value of such well-defined electrochemical systems to explore systematically electrostatic-field effects on surface bonding.
Molecular dynamics simulation of an activated transfer reaction in zeolites
Authors: Demontis Pierfranco , Suffritti Giuseppe B. , Tilocca Antonio
Published: July 2002

The activated transfer of a light particle between two heavier species in the micropores of silicalite and ZK4 zeolites has been studied through molecular dynamics (MD) simulations. A three-body potential controls the exchange of the light particle between the heavier ones; an effective barrier of a few kBT separates the two stable regions corresponding to symmetric “reactant” and “product” species. Harmonic forces always retain the reactants at favorable distances so that in principle only the energetic requirement must be fulfilled for the transfer to occur. The rate constant for the process (obtained from a correlation analysis of equilibrium MD trajectories) decreases by more than one order of magnitude when the barrier height is increased from 2kBT to 5kBT following an Arrhenius-type behavior. The transfer rates are always lower in ZK4. When the reaction is studied in a liquid solvent the calculated rate constants are closer to those obtained in silicalite. Since with this model the diffusive approach of the reactants is almost irrelevant on the reactive dynamics, only the different ability of each environment to transfer the appropriate energy amount to the reactants and then promote the barrier passage could be invoked to explain the observed behavior. We found that structural, rather than energetic, effects are mainly involved on this point. The lower efficiency of ZK4 seems to arise from the frequent trapping of the reactive complex in the narrow ZK4 windows in which the transfer is forbidden and from the weaker interaction of the reactive complex with the host framework compared to silicalite.
HF stretching–bending combination bands for small complexes in solid argon
Authors: Andrews Lester , Souter Philip F.
Published: July 2002

Infrared spectra of HF (with DF substitution) in solid argon contain weak HF stretching–bending combination bands for N2–HF, (HF)2, and (HF)3 that are higher than the sum of fundamentals. This is in accord with stronger hydrogen bonds upon vibrational excitation of the H–F stretching mode, as observed in the gas phase. Overtone bands were also observed for DF and (DF)2 in solid argon.
Molecular-level description of temperature and pressure effects on the viscosity of water
Authors: Cho C. H. , Urquidi J. , Robinson G. Wilse
Published: July 2002

The steep non-Arrhenius temperature dependence at low temperatures of the shear viscosity of water and its backwards-sounding increased fluidity under pressure for temperatures below 33 °C are two of the anomalies of this liquid that have been known for a very long time. The purpose of the present paper is to show how these two important characteristics of water emerge quantitatively from an explicit two-state outer-neighbor mixture model that we have used to explain many other properties of this substance. It will be shown here that both of these viscosity anomalies are directly related to the steep variations with temperature and pressure of the fractional compositions of ice-Ih-type bonding and ice-II-type bonding in the two-state mixture. This compositional dependence has already been obtained in earlier work from the variations of the density and the isothermal compressibility of water with temperature. The viscosity analysis presented here thus helps to unify further all the properties of this liquid under a single, very simple structural characteristic.
Proton-transport catalysis and proton-abstraction reactions: An ab initio dynamical study of X+HOC+ and XH++CO (X=Ne, Ar, and Kr)
Authors: Collins Michael A. , Petrie Simon , Chalk Andrew J. , Radom Leo
Published: July 2002

Ab initio potential energy surfaces have been constructed and used to carry out classical simulations of the reactions of X with HOC+ and of XH+ with CO (X=Ne, Ar, and Kr). The competition between rearrangement, X+HOC+→OCH++X, and abstraction, X+HOC+→XH++CO, has been examined, and found to favor abstraction in the cases where both processes are energetically allowed. The reaction of XH+ with CO is found to produce highly vibrationally excited [CHO]+ products.
Modeling proton mobility in acidic zeolite clusters. I. Convergence of transition state parameters from quantum chemistry
Authors: Fermann Justin T. , Blanco Cristian , Auerbach Scott
Published: July 2002

We have applied electronic structure methods to the calculation of transition state parameters for the O(1)→O(4) proton transfer in H-Y zeolite. We arrive at a set of recommendations for calculating these transition state parameters accurately and efficiently. Density functional theory using the B3LYP functional and basis sets of triple-ζ quality in the valence space, and including polarization functions on all atoms, is the most efficient method for converging structures and vibrational frequencies. For converging classical barrier heights, we find it necessary to augment MP2 barrier heights calculated using large basis sets with MP4 energies obtained in more limited basis sets. We obtain an O(1)→O(4) barrier height of 86.1 kJ mol−1, and find the curvature of the barrier at the transition state to be 1570 cm−1. Including long range effects from the work of Sauer et al. [ACS Symp. Ser. 721, 358 (1999)] results in a higher barrier, which we estimate to be 97.1 kJ mol−1. We attribute the fact that our barriers are significantly larger than those reported in the experimental literature to the neglect of tunneling in the interpretation of experimental data.
Predissociation of the F(4) 1Σg+ state of Li2
Authors: Antonova Stiliana , Lazarov Guenadiy , Urbanski Ken , Lyyra A. Marjatta , Li Li , Jeung Gwang-Hi , Stwalley William C.
Published: July 2002

This paper reports measurements of the homogeneous predissociation of the Li2 F 1Σg+ state due to electrostatic interaction with the E 1Σg+ state. Ab initio potential energy curves have been calculated for both states which in the adiabatic representation show two avoided crossings. However, predissociation was not previously predicted. Our experimental results show that the three isotopomers Li27, Li76Li, and Li26 all strongly predissociate above the 2s+3s atomic limit. We report high resolution measurements of linewidths for a large number of F–state levels spread across the 2600 cm−1 energy region between the 2s+3s and 2p+2p atomic limits, which yield systematic information regarding the rotational, vibrational, and isotopomer dependence of the predissociation rate. An experimental RKR potential energy curve for the F state is derived and used to calculate predissociation rates whose trends show good agreement with the experimental values. This paper presents the first complete data set of observations on the predissociation rate of a diatomic molecule and its variation with v and J when the interaction with the perturbing state takes place at two distinct internuclear distances.
Chain dynamics in steady shear flow
Authors: Dua Arti , Cherayil Binny J.
Published: July 2002

Recent experimental measurements of the static and dynamic properties of single fluorescently labeled molecules of DNA in steady shear flow are compared with the predictions of a theoretical model of chain dynamics. The model is based on a set of coupled kinetic equations for the evolution of chain conformations and solvent fluctuations. The polymer is represented as a continuous curve with no excluded volume or hydrodynamic interactions, while the solvent is described by a time and space-varying velocity field. In the absence of constraints that enforce the finite extensibility of the chain at large shear rates, the calculated curves of the normalized dynamic autocorrelation function of the mean extension reproduce the qualitative features of the measured curves, but otherwise deviate significantly from them. We develop an analytically tractable finitely extensible model of the Gaussian chain that is more successful in reproducing the experimental data.
Theoretical investigation of water formation on Rh and Pt Surfaces
Authors: Wilke Steffen , Natoli Vincent , Cohen Morrel H.
Published: July 2002

Catalytic water formation from adsorbed H and O adatoms is a fundamental reaction step in a variety of technologically important reactions involving organic molecules. In particular, the water-formation rate determines the selectivity of the catalytic partial oxidation of methane to syngas. In this report we present a theoretical investigation of the potential-energy diagram for water formation from adsorbed O and H species on Rh(111) and Pt(111) surfaces. The study is based on accurate first-principles calculations applying density-functional theory. Our results are compared to the potential-energy diagram for this reaction inferred from experimental data by Hickman and Schmidt [AIChE. J. 39, 1164 (1993)]. The calculations essentially reproduce the scheme of Hickman and Schmidt for water formation on Rh(111) with the important difference that the OH molecule is significantly more stable than assumed by Hickman and Schmidt. On Pt(111) surfaces, however, the calculations predict a barrier to OH formation very similar to that found on Rh(111). In particular, the calculated barrier to OH formation of about 20 kcal/mol seems to contradict the small 2.5 kcal/mol barrier assumed in the Hickman–Schmidt scheme and the observed large rate of water formation on Pt. A possible explanation for the apparent discrepancy between the large calculated barrier for OH formation on Pt and the experimentally observed rapid formation of water even at low temperatures is that the active sites for water formation on Pt are at “defect” sites and not on the ideally flat terraces. A similar conclusion has been reached by Verheij and co-workers [Surf. Sci. 371, 100 (1997); Chem. Phys. Lett. 174, 449 (1990); Surf. Sci. 272, 276 (1991)], who did detailed experimental work on water formation on Pt surfaces. Analyzing our results, we develop an explicit picture of the interaction processes governing the formation of OH groups. This picture rationalizes the calculated weak dependence of OH formation on substrate material. An important conclusion from this work is that “good” catalysts for the partial oxidation of hydrocarbons should resist defect formation at their surfaces.
Dielectric study of supercooled 2D water in a vermiculite clay
Authors: Bergman R. , Swenson J. , Börjesson L. , Jacobsson P.
Published: July 2002

We report results of dielectric spectroscopy on water confined in a two-dimensional layer-structured Na-vermiculite clay. Several relaxation processes of different origin can be discerned in the spectra. A strong dielectric loss peak is observed in the clay with two layers of water molecules between the rigid clay platelets at temperatures between 125 and 215 K. This loss peak is neither observed in bulk ice, nor in the dry clay or clay with only one water layer between platelets. The relaxation time is shown to have an Arrhenius temperature dependence which does not extrapolate to the high-temperature behavior. This behavior is in accordance with the proposed so-called “fragile-strong” transition of supercooled bulk water, which implies a change in the temperature dependence of the relaxation time from a high-temperature non-Arrhenius to low-temperature Arrhenius behavior. However, this transition is experimentally elusive as it would occur in an inaccessible (due to the ease of crystallization) temperature range of the supercooled bulk water.
Uncertainty relations in stochastic mechanics
Authors: Golin S.
Published: July 2002

Position–momentum uncertainty in Nelson’s stochastic mechanics [Phys. Rev. 150, 1079 (1966)] has previously been investigated by de la Peña-Auerbach and Cetto [Phys. Lett. A 39, 65 (1972)]. In this paper their result is generalized, and full equivalence between the uncertainty relations in stochastic mechanics and conventional quantum mechanics is established. Force–momentum uncertainty is also considered.
A theorem on Lyapunov stability for dynamical systems and a conjecture on a property of entropy
Authors: Beretta Gian Paolo
Published: July 2002

For a general dynamical system, it is proved that an equilibrium state belonging to a continuous family of conditionally stable equilibrium states is stable. The result is applied to quantum thermodynamics to clarify in what restricted sense the entropy functional s( ρ)=−k Tr ρ ln ρ can provide a Lyapunov criterion for the stability of thermodynamic equilibrium. A conjecture on a special positive-definiteness property of −k Tr ρ ln ρ remains to be proved.
Exact solution of the Schrödinger equation with noncentral parabolic potentials
Authors: Guha Asok , Mukherjee S.
Published: July 2002

The Schrödinger equation with a class of parabolic potentials has been studied. A constant of motion related to angular momentum has been calculated. It has been shown that the scattering states for these potentials can be defined only in some special cases. The Hartmann potential and the Aharonov–Bohm potential are studied as special cases.
Quantum observables: Compatibility versus commutativity and maximal information
Authors: Busch Paul , Schonbek Thomas P. , Schroeck Franklin E.
Published: July 2002

Two different approaches to a characterization of the degree of (in)compatibility of quantum observables are investigated. First, recent examples of the (partial) commutativity of spectral measures of incompatible observables are proved to be generic. The analysis is extended to the case of compatible or incompatible unsharp, or stochastic observables, leading to a general criterion for commutativity of position and momentum effects. Further, a recently proposed information theoretic quantification of the (in)compatibility of noncommuting observables is generalized, and the relation between ‘‘maximal information,’’ ‘‘minimal uncertainty,’’ partial commutativity, and strict correlation is further clarified. Both approaches are illustrated in a number of examples.
Geodesic deviation in the Schwarzschild space-time
Authors: Bażański Stanisl/aw L. , Jaranowski Piotr
Published: July 2002

A general solution of the geodesic deviation equations in the Schwarzschild space-time is presented. It is found in a rigorous form with the aid of a recently formulated method of integration of the Hamilton–Jacobi type, and is applied to a study of the behavior of a cloud of particles freely falling into the Schwarzschild singularity. Presuming that the cloud of such particles provides one with a measure of strength of the singularity of a field, a similar problem of freely falling particles is also solved in the Newtonian theory. It has turned out that the behavior of the cloud of particles freely falling into the center of attraction is, contrary to what one would rather expect, in each of the two theories exactly the same. A possible reason for obtaining such a result is briefly discussed.
Hamilton–Jacobi formalism for geodesics and geodesic deviations
Authors: Bażański Stanisl/aw L.
Published: July 2002

A formalism of integrating the equations of geodesics and of geodesic deviation is examined based upon the Hamilton–Jacobi equation for geodesics. The latter equation has been extended to the case of geodesic deviation and theorems analogous to Jacobi’s theorem on the complete integral has been proved. As a result, a straightforward algorithm of integrating the geodesic deviation equations on Riemannian (or pseudo-Riemannian) manifolds is obtained.
Graviton fluctuations in de Sitter space
Authors: Antoniadis I. , Mottola E.
Published: July 2002

The two-point correlation function of metric fluctuations in de Sitter space is calculated. The results are expressed in a gauge-invariant and O(4,1)-invariant form in terms of elementary functions of z(x,x′) (a biscalar variable simply related to the invariant distance between x and x′). The Feynman functions for the transverse, trace-free, and scalar metric fluctuations grow without bounds, as ln z and z ln z, respectively, for large z. The consequences of this bad infrared behavior are discussed and it is shown that it leads to divergences in physical quantities at both the classical and quantum levels.
On the elementary Schrödinger bound states and their multiplets
Authors: Znojil M. , Leach P. G. L.
Published: July 2002

The problem of the existence of elementary bound states is discussed. A−trivial−observation that every elementary wave function ψ[i](r) is an exact bound state for an appropriate potential, V(r)=V[i][ψ(r),r], is shown to lead to a very transparent form of the ‘‘quasiexact’’ (QE) solvability condition V[i]=V[j] for doublets and multiplets of the ψ’s. In this sense, the particular class of elementary ansätze, ψ[i](r)=rλpolynomial(r2) ×exp[rμpolynomial(r2)], also defines the particular class of QE-solvable potentials. They have an elementary nonpolynomial (rational) form, possibly also with a strongly singular−repulsive−core at the origin. The properties of these forces are discussed in detail.
Sources for McVittie’s mass particle in an expanding universe
Authors: Nolan Brien
Published: July 2002

Among the large class of spherically symmetric solutions of Einstein’s field equations for a shear-free perfect fluid with spatially homogeneous energy density given by Kustaanheimo, solutions which can be interpreted as sources for McVittie’s mass particle in the three families of expanding universes were identified.
The two-fermion relativistic wave equations of constraint theory in the Pauli–Schrödinger form
Authors: Mourad J. , Sazdjian H.
Published: July 2002

The two-fermion relativistic wave equations of constraint theory are reduced, after expressing the components of the 4×4 matrix wave function in terms of one of the 2×2 components, to a single equation of the Pauli–Schrödinger type, valid for all sectors of quantum numbers. The potentials that are present belong to the general classes of scalar, pseudoscalar, and vector interactions and are calculable in perturbation theory from Feynman diagrams. In the limit when one of the masses becomes infinite, the equation reduces to the two-component form of the one-particle Dirac equation with external static potentials. The Hamiltonian, to order 1/c2, reproduces most of the known theoretical results obtained by other methods. The gauge invariance of the wave equation is checked, to that order, in the case of QED. The role of the c.m. energy dependence of the relativistic interquark confining potential is emphasized and the structure of the Hamiltonian, to order 1/c2, corresponding to confining scalar potentials, is displayed.
On position and momentum operators in the q-oscillator algebra
Authors: Chung Won-Sang , Klimyk Anatoli U.
Published: July 2002

The aim of this paper is to study the position and momentum operators in q-deformed oscillator algebras. The natural form of the position operator is Xp=qpN(a++a)qpN, where p is a real number. This operator is an operator representable by a Jacobi matrix. Using the theory of Jacobi matrices, the theory of classical moment problem and the theory of basic hypergeometric functions, it is shown that, depending on values of q and p, Xp can be unbounded symmetric operator [which has the deficiency indices (1,1) and, hence, is not self-adjoint, but has self-adjoint extensions], bounded self-adjoint operator with continuous simple spectrum or self-adjoint operator of trace class (therefore, with discrete spectrum with zero as the point of accumulation of eigenvalues). The connection of the q-deformed Heisenberg relation PX−qXP=1 for the position and momentum operators with a q-deformation of the quantum harmonic oscillator is also considered.
On a nonlinear stationary problem arising in transport theory
Authors: Latrach Khalid
Published: July 2002

In this article a nonlinear one-dimensional stationary transport equation with general boundary conditions is considered where an abstract boundary operator relates the incoming and the outgoing fluxes. Existence results are proved in the case where the collision operator is of the Hammerstein type. In particular, it is shown that these results remain valid for multidimensional geometry with vacuum boundary conditions. Sufficient conditions are given in terms of collision frequency and scattering kernel assuring the existence and uniqueness of solutions. The article ends with the discussion of the case of multiplying boundary conditions.
A second invariant for one-degree-of-freedom, time-dependent Hamiltonians given a first invariant
Authors: Bouquet Serge , Lewis H. Ralph
Published: July 2002

An explicit formula for a second invariant of a one-degree-of-freedom time-dependent Hamiltonian is derived in terms of the Hamiltonian and an assumed first invariant. If the first invariant is expressed as a function of two canonical functions, a transformation to an autonomous Hamiltonian system is possible.
Scattering in one dimension: The coupled Schrödinger equation, threshold behaviour and Levinson’s theorem
Authors: Kiers K. A. , van Dijk W.
Published: July 2002

We formulate scattering in one dimension due to the coupled Schrödinger equation in terms of the S matrix, the unitarity of which leads to constraints on the scattering amplitudes. Levinson’s theorem is seen to have the form η(0)=π(nb+1/2n−1/2N), where η(0) is the phase of the S matrix at zero energy, nb the number of bound states with nonzero binding energy, n the number of half-bound states, and N the number of coupled equations. In view of the effects due to the half-bound states, the threshold behaviour of the scattering amplitudes is investigated in general, and is also illustrated by means of particular potential models.
The source identification problem in electromagnetic theory
Authors: Magnoli N. , Viano G. A.
Published: July 2002

The problem of the identification of the electromagnetic source which produces an assigned radiation pattern is ill-posed: the solution is, in general, not unique and it does not depend continuously on the data. In this paper we treat in detail these two aspects of the problem. First of all we reconsider the radiation problem in the very general setting of the Sobolev spaces in order to make more acceptable, from a physical viewpoint, the conditions which have to be imposed on the electromagnetic sources. Then by the use of the Euclidean character of the Hilbert spaces we decompose the sources into a radiating and a non radiating component. We determine the subspace of the radiating sources and we find the basis spanning this subspace. Particular attention is then devoted to the case of the linear antenna. In this case the solution of the problem is unique but it does not depend continuously on the data. We may, however, implement the problem taking into account a bound on the ohmic losses. This is sufficient to restore the continuity. Finally a method of variational regularization (in the sense of Tikhonov) is discussed in detail.
The Hamiltonian (p2+m2)1/2−α/r near the critical value αc=2/π
Authors: Le Yaouanc A. , Oliver L. , Raynal J.-C.
Published: July 2002

We elucidate the behavior of the operator (p2+m2)1/2−α/r near the critical value α=αc where it ceases to be bounded below, by obtaining a family H(z) of operators which is self-adjoint holomorphic in a domain including all real z>−αc−αc′, and such that H(αc−α)(α⩽αc) is just the operator (p2+m2)1/2−α/r or its Friedrich extension, while H(−αc−α)(αc′<α<αc) is another self-adjoint extension. The operators H(z) (z real) are shown to be positive, and to have only discrete spectrum below m. The eigenvalues are then analytic functions of αc−α near α=αc (and become the eigenvalues of a non-self-adjoint operator when α>αc). We show that these eigenvalues cannot vanish, but that the lowest eigenvalue of H(−αc−α) goes to zero when α→αc′. The L>0 eigenvalues are analytic in α at α=αc.
Discrete Riemannian geometry
Authors: Dimakis Aristophanes , Müller-Hoissen Folkert
Published: July 2002

Within a framework of noncommutative geometry, we develop an analog of (pseudo-) Riemannian geometry on finite and discrete sets. On a finite set, there is a counterpart of the continuum metric tensor with a simple geometric interpretation. The latter is based on a correspondence between first order differential calculi and digraphs (the vertices of the latter are given by the elements of the finite set). Arrows originating from a vertex span its (co)tangent space. If the metric is to measure length and angles at some point, it has to be taken as an element of the left-linear tensor product of the space of 1-forms with itself, and not as an element of the (nonlocal) tensor product over the algebra of functions, as considered previously by several authors. It turns out that linear connections can always be extended to this left tensor product, so that metric compatibility can be defined in the same way as in continuum Riemannian geometry. In particular, in the case of the universal differential calculus on a finite set, the Euclidean geometry of polyhedra is recovered from conditions of metric compatibility and vanishing torsion. In our rather general framework (which also comprises structures which are far away from continuum differential geometry), there is, in general, nothing like a Ricci tensor or a curvature scalar. Because of the nonlocality of tensor products (over the algebra of functions) of forms, corresponding components (with respect to some module basis) turn out to be rather nonlocal objects. But one can make use of the parallel transport associated with a connection to “localize” such objects, and in certain cases there is a distinguished way to achieve this. In particular, this leads to covariant components of the curvature tensor which allow a contraction to a Ricci tensor. Several examples are worked out to illustrate the procedure. Furthermore, in the case of a differential calculus associated with a hypercubic lattice we propose a new discrete analogue of the (vacuum) Einstein equations.
Interaction between vortices and waves in a simple model of geophysical flow
Authors: Bell George I.
Published: July 2002

A basic vortex–wave interaction in quasigeostrophic flows is investigated. Specifically, the interaction between a point vortex and an initially horizontal interface separating two regions of uniform potential vorticity is considered. In the asymptotic limit of small amplitude interface motions, the exact solution of the initial value problem is presented. If there exists an interface wave whose phase speed matches the drift speed of the point vortex, a spreading packet of such waves forms to the lee of the vortex, and these waves induce the vortex to drift toward or away from the interface. Such an interaction corresponds to a radiative transfer of momentum from the vortex to the interface. The effect is generalized to include more complex shear flows stabilized by variations in depth or Coriolis force with latitude. It is shown that a stable vortex strip repels or attracts point vortices according to their sign and that a pair of vortex strips focuses a vortex onto the line midway between them. The results support the hypothesis that in a stable shear flow, a positive (cyclonic) vortex drifts in the direction of increasing potential vorticity by radiating Rossby waves.