bluuebunny/crossref_metadata_2025 huggingface dataset:
The decay dynamics of photoexcited rare gas cluster ions
Authors: Jones A. B. , Jukes P. R. , Stace A. J.
Published: July 2002

The kinetic energies of fast neutrals ejected from photoexcited rare gas cluster ions have been measured for the following systems: Arn+, Krn+, Xen+ at two photon wavelengths: 355 and 532 nm, and for n in the range 2–19. New data are presented for xenon at both wavelengths, and for argon and krypton cluster ions at 355 nm. For argon and krypton cluster ions at 532 nm, new data have been recorded which are more accurate than those presented previously. A Monte Carlo model of the experiment has been used to simulate the kinetic energy releases and also to investigate variations in the scattering anisotropy parameter (β) as a function of photon energy and cluster composition and size. Significant fluctuations in β are observed, and these are attributed to a combination of structural variation and changes to the nature of the central chromophore. For small cluster ions the kinetic energy release data show evidence of being influenced by the final spin-orbit state of the atomic ion. Overall, there is a gradual decline in kinetic energy release as a function of increasing cluster size; however, there are marked variations within this trend. For all three rare gas systems the results show that the primary response to photoexcitation is the ejection of a single atom with a high kinetic energy on a time scale that is short compared with the rotational period of a cluster.
The relaxation from linear to triangular Ag3 probed by femtosecond resonant two-photon ionization
Authors: Leisner Thomas , Vajda Stefan , Wolf Sebastian , Wöste Ludger , Berry R. Stephen
Published: July 2002

We present extended NeNePo (negative to neutral to positive) measurements on the ultrafast dynamics in the ground state of neutral, mass-selected Ag3 molecules. A vibrational wave packet in the neutral molecule is created with an ultrashort laser pulse by photodetachment of the excess electron from the corresponding mass-selected anion. The subsequent molecular rearrangement is probed by photoionization after a selected time delay. Complementary to our previous investigations of this process, we now use two-photon photoionization via a resonant state in the probe step. Here, a bound–bound excitation to a well-known state followed by one-photon ionization is used instead of the nonresonant bound/free transition into the ionic continuum. Using radiation with wavelengths near 370 nm for resonant ionization, we observe a fast bending motion of the initially linear Ag3, followed by an ultrafast intramolecular vibrational energy redistribution, interpretable as an intramolecular collision process. The signal shows an apparent loss of vibrational coherence after the collision, which can be explained by the finite temperature of the anionic clusters in our experiment. Additionally, we describe a previously unknown resonance in the linear neutral molecule around 500 nm.
Modified Robertson projection operator method and irreversible thermodynamics
Authors: Eu Byung Chan
Published: July 2002

A modified Robertson projection operator is used to obtain the evolution equation for the projected distribution function as well as various macroscopic evolution equations. These evolution equations, although not as yet proved to be consistent with the thermodynamic laws, form a basis for a formal theory of macroscopic processes. On introducing some approximations to the projected propagator we construct an approximate, thermodynamically consistent evolution equation (kinetic equation) and develop a thermodynamically consistent theory of irreversible processes with the approximate evolution equation so obtained. The mathematical structure of the theory of irreversible processes thus formulated can be brought into harmony with the theory based on the Boltzmann equation and the generalized Boltzmann equation, which was previously developed and reported in the literature. The Maxwell–Cattaneo–Vernotte type constitutive equations are derived on making a number of approximations on the exact evolution equations for the stress and the heat flux.
Photodissociation dynamics of tert-butyl hydroperoxide at 213 nm via degenerate four-wave mixing spectroscopy
Authors: Lee Keon Woo , Kim Dong-Chan , Jung Kyung-Hoon , Hahn Jae Won
Published: July 2002

The photodissociation dynamics of t-BuOOH at 213 nm has been studied using degenerate four-wave mixing spectroscopy. The internal energy distribution, Λ-doublet ratio and spin-orbit state ratio of OH (X2Π, v″=0) fragments were extracted. The OH radicals were found to be vibrationally cold with an average rotational energy of 1726 cm−1, indicating that 5.0% of the available energy was transferred into the OH rotational degree of freedom. A Gaussian distribution of product rotational energy was observed. The population was found to be distributed statistically between the two spin-orbit states. A preferential population of the π+ Λ-doublet was observed irrespective of N without inversion. The observed Λ-doublet nonequilibrium implies that splitting of energy levels may occur because of the breaking of symmetry due to substitution. We suggest that the hydroxyl part should be the dominant chromophore for the absorption of t-BuOOH at 213 nm.
Electron transfer reactions on Cs/MoS2(0002) with chlorine, oxygen, and water: High resolution x-ray photoelectron spectroscopy and theoretical study
Authors: Park Ken T. , Hess James S. , Klier Kamil
Published: July 2002

Supra-valence electron transfer from surface Cs-doped MoS2(0002) to electron acceptor adsorbates was investigated by high resolution x-ray photoelectron spectroscopy (HRXPS) in the valence band region and above the valence band maximum (VBM). Deposition of a sub-monolayer amount of Cs onto the basal plane of MoS2 introduced a new electron density of states at ca. 1.25 eV above VBM. Angle-resolved HRXPS and theoretical analysis located this electron density in the MoS2 layer. Upon the reaction with Cl2, this Cs-induced photoelectron almost completely disappeared and the Cs 3d and Cl 2p core levels indicated the formation of a surface Cs-chloride species. The Cs-covered MoS2(0002) surface also reacted with O2 to form surface peroxides and superoxides, as evidenced by two distinct binding energies of the O 1s core level peaks. However, the reaction with water proved to be more difficult: Exposure of the Cs-covered MoS2(0002) surface to H2O at 10−5 Torr did not result in electron transfer reaction, but the Cs/MoS2(0002) surface exposed to H2O at 1 Torr showed a substantial decrease in the density of states above VBM as well as formation of a surface-hydroxide, indicated by the O 1s core level position. Theoretical calculations using a full-potential linearized augmented plane wave density functional theory (FLAPW-DFT) confirm the conclusion based on experimental intensity anisotropy of the new peak: the Cs 6s electron transfers into the MoS2 substrate, forming the Cs/MoS2 electron donor–acceptor complex with Csδ+. In addition, all phenomena observed during the adsorption of electron donor–acceptor molecules are quantitatively accounted by the theory.
From molecular states to band structure: Theoretical investigation of momentum dependent excitations in phenylene based organic materials
Authors: Zojer E. , Shuai Z. , Leising G. , Brédas J. L.
Published: July 2002

The electronic states in conjugated organic materials are usually characterized either by quantum-chemical approaches relying on a molecular picture, or by solid-state band structure models requiring infinite periodicity of the chains. In this contribution we present calculations showing that a band structure like character is inherent also in molecular systems and discuss the gradual evolution of a full band structure upon increasing the number of repeat units in oligomer molecules. The main feature of a band structure approach is the description of the electronic eigenstates in momentum space. We have therefore developed a method to describe momentum dependent excitation processes in conjugated organic materials based on a post-Hartree–Fock approach including electron–electron correlation effects. The results of the simulations performed for oligo(phenylene)s of different chain lengths agree very well with experimental electron energy loss spectroscopy (EELS) data.
Hermite polynomial expansions of the error function and related F(w) integral
Authors: Kovacevic K.
Published: July 2002

Hermite polynomial expansions of the error function and the related F0(w) integral is presented. Expansion in even Hermite polynomials is convergent in the whole argument space of interest, with a smaller number of terms necessary to achieve the desired accuracy than in usual calculation methods of F0(w). Hermite polynomial asymptotic expansion is presented too. It is compared with the standard asymptotic expansion as well as with the interpolation method of P. M. Gill.
Effect of solvent density and species on static and dynamic fluorescence Stokes shifts of coumarin 153
Authors: Kimura Y. , Hirota N.
Published: July 2002

Solvent density dependence of the absorption and fluorescence spectra of coumarin 153 in argon (Ar), ethane (C2H6), carbon dioxide (CO2), and trifluoromethane (CF3H) has been studied at 323.2 K over a wide density region up to ρr∼3, where ρr is the reduced density by the critical density (ρc) of the solvent (ρr≡ρ/ρc). By analyzing the line shape functions of the absorption and fluorescence spectra, the first moment and the full width of the half maximum (FWHM) have been determined. Both the free energy difference (ΔG) between the ground and the S1 states and the fluorescence Stokes shift (Δν), evaluated by the first moments of the absorption and fluorescence line shape functions, show larger shift to the values in vapor in the order of Ar, C2H6, CO2, and CF3H if compared at the same ρr. There are three characteristic density regions on the density dependence of ΔG and Δν; these values show larger dependence in the lower-density region (ρr<0.5) and the higher-density region (ρr>2), than that in the medium-density region. The solvent density and species dependence of the FWHM of the absorption spectrum is quite similar to that of Δν. The density dependence of Δν and FWHM in Ar and C2H6 indicates that the intramolecular reorganization energy decreases with increasing the solvent density, while the effect is small. We have estimated the solvent reorganization energy (λS) in CO2 and CF3H by assuming no contribution of λS in C2H6 and Ar. We have demonstrated that the dielectric continuum model makes a good prediction on the relation between ΔG and λS, while it is poor on their density dependence. The invariance of ΔG and λS in the medium-density region can be interpreted as the density saturation around the solute molecule. In the lower-density region (ρr<∼0.5), the way of the solvation is suggested to be different from those in the medium- and high-density regions. The lifetime of S1 shows a large dependence on the solvent density and species in the very low-density region (ρr∼0.05). We have also found that slow solvation dynamics exists in the lower-density region of CF3H. The origin of the dynamics is discussed in relation with the static Stokes shift.
Femtosecond fluorescence depletion spectroscopy of NO2 multiphoton dissociation dynamics
Authors: López-Martens R. B. , Schmidt T. W. , Roberts G.
Published: July 2002

Two-color femtosecond pump–probe spectroscopy has been applied to the multiphoton dissociation of NO2 with a time resolution of ⩽350 fs. At laser intensities in the range ≃3×1012–2×1013 W cm−2 and a wavelength of 400 nm, NO2 absorbs three photons before dissociation. Nascent NO A 2Σ+ product in its n′=0 and 1 vibrational levels is probed by single-photon fluorescence depletion at 800 nm. Analyses of the ultrafast transient behavior at different intensities leads to an estimate of ⩽600 fs for formation of NO A 2Σ+ n′=0 and 1.
Vibrational state-resolved study of the O−+H2 reaction: Isotope effects on the product energy partitioning
Authors: Lee Susan Troutman , Farrar James M.
Published: July 2002

The deuterium isotope effect on product energy partitioning in the O−+H2 particle transfer reaction is investigated in a crossed molecular beam experiment. Vibrational-state-resolved angular distributions are measured at six collision energies between 0.20 and 0.77 eV for the O−+H2 reaction and at seven collision energies between 0.22 and 1.20 eV for the O−+D2 reaction. The fraction of the total available energy deposited into product vibration is significantly larger in the deuterium system than in the hydrogen system. This effect is greatest at the lowest collision energies where OD− products are formed with more than twice as much vibrational energy as OH− products. The isotopic systems display similar trends in the product angular distributions, which extend over the full range of scattering angles at low energies and shift towards the forward direction as the collision energy is increased. These observations are discussed in terms of a competition between reaction mechanisms. An insertion-migration mechanism, yielding products with moderate vibrational excitation, is especially important at the lower energies. The insertion process leads to the isotope effect in the product energy partitioning which is explained in terms of Franck–Condon factors. As the energy increases, larger impact parameter collisions are able to proceed through a direct mechanism, yielding more tightly forward-scattered, vibrationally excited products. Since direct mechanisms show isotopically independent energy partitioning, the overall isotope effect diminishes with increasing energy as more collisions become purely direct. Bimodal rotational state distributions help strengthen the claim that two distinct reaction mechanisms produce the particle transfer product.
A theoretical study of hole induced desorption
Authors: Katz Gil , Kosloff Ronnie , Zeiri Yehuda
Published: July 2002

A two-dimensional quantum mechanical model describing hole induced desorption is developed and discussed. The model is used for a detailed study of hole induced molecular oxygen desorption and dissociation dynamics on a silver surface. The O2–substrate interaction is described by four diabatic semiempirical potential energy surfaces. These potentials describe physisorption of O2 on the substrate together with two molecular ion states (superoxide and peroxide) and a dissociative adsorption state. The model is used to correlate desorption and dissociation yields with various parameters of the system such as: excitation scheme, substrate work function (φm) and isotope used (Mad). In all cases examined, both desorption and dissociation channels were found to be active. It is demonstrated that experimental measurements of the branching ratio between these two channels and the variation of this ratio as a function of φm and Mad allows determination of the excitation route induced by the hole.
Comment on “A comparison of the efficiency of Fourier- and discrete time-path integral Monte Carlo” [J. Chem. Phys. 109, 2123 (1998)]
Authors: Doll J. D. , Freeman David L.
Published: July 2002

We examine the efficiency of the partial averaged Fourier path integral method for a model of the (H2)22 system. We show errors in thermodynamic average energies asymptotically approach zero as the inverse of the square of the number of path variables. Using common estimators, we also find the efficiency of the Fourier method for the (H2)22 application comparable to that reported recently [J. Chem. Phys. 109, 2123 (1998)] for effective-potential, discretized approaches.
Evolution of density fluctuations to lamellar crystals in linear polyethylene
Authors: Akpalu Yvonne A. , Amis Eric J.
Published: July 2002

Structure formation during the isothermal crystallization of a linear polyethylene (Mw=32 100 g/mol, Mw/Mn=1.1) has been monitored by simultaneous real time small-angle x-ray scattering (SAXS) and wide angle x-ray scattering (WAXS) with synchrotron radiation. Changes in the crystalline and amorphous scattering in WAXS occur simultaneously with the changes observed in the SAXS intensity profile, suggesting that the resulting scattering is a consequence of forming crystals. At the early stage of crystal growth, the SAXS intensity at q<0.02 Å−1 increases while that at higher wave vectors remains constant. Meanwhile, the apparent crystallinity from WAXS increases to about 10% before two peaks in the SAXS intensity profile can be resolved. As lamellar stacks develop, the period corresponding to the first SAXS peak, L1, decreases initially. After reaching a minimum, L1 further increases with crystallization time. On the other hand, the period corresponding to the second SAXS peak increases with crystallization time. At late times, the rate of increase is very slow. Changes in the crystallinity obtained from WAXS and the total scattering power from SAXS were evaluated and compared with a model for the crystallizing system which accounts for changes in the fraction of lamellar aggregates. The relative importance of two secondary crystallization processes, namely the formation of new lamellar stacks and increase in the crystallinity within lamellae, were evaluated during and after primary crystallization.
Polarizability tensor theory based upon a Bayley–Nielsen–Schellman-type model Hamiltonian: Circular dichroism calculations of polypeptides
Authors: Ito Hirotoshi
Published: July 2002

In our previous article based upon the usual Fano–DeVoe model Hamiltonian, the partial polymer polarizability tensor equation for describing visible and ultraviolet (VIS/UV) absorption and circular dichroism (CD) spectra was represented in terms of transition moments and a partial polymer Green’s function matrix equation, which is constructed from partial monomer Green’s matrix elements and inter(sub)molecular interaction energies. Here, on the basis of the extended Fano–DeVoe model Hamiltonian similar to the Bayley–Nielsen–Schellman secular Hamiltonian matrix, we represent a partial polymer polarizability tensor matrix equation in terms of transition moments and a partial polymer Green’s function matrix equation, which is constructed from partial monomer Green’s matrix elements, inter(sub)molecular interaction energies, and inter(sub)molecular electrostatic interaction energies. The last ones are newly taken into account. Computing the amide monomer spectroscopic parameters by the CNDO/S method and substituting them into the polymer polarizability tensor matrix equation derived, we have successfully carried out the CD band shape calculations on polypeptides having α-helix and β-sheet structures and on a tripeptide, N-acetyl-Pro-Gly-Leu-OH having a type II β-turn conformation.
Reduced dynamics in spin-boson models: A method for both slow and fast bath
Authors: Golosov Andrei A. , Friesner Richard A. , Pechukas Philip
Published: July 2002

We study a model for treating dissipative systems, a one dimensional quantum system coupled to a harmonic bath. The dynamics of such a system can be described by Feynman’s path integral expression for the reduced density matrix. In this formulation the interaction of the system with the environment is stored in the influence functional. Recently we showed that fast environmental modes that give rise to correlations in the influence functional which are short range in time can be treated efficiently by a memory equation algorithm, which is a discretized version of a master equation. In this work we extend this approach to treat slow environmental modes as well, thereby efficiently linking adiabatic and nonadiabatic regimes. In this extended method the long range correlations in the influence functional arising from slow bath modes are taken into account through Stock’s semiclassical self-consistent-field approach.
Vector correlation in molecular photodissociation: Quantum mechanical expression and comparison with the formal expansion formula
Authors: Mo Yuxiang , Suzuki Toshinori
Published: July 2002

The quantum mechanical expression for the angle-dependent photofragment multipole moments is derived with only the dipole approximation. The angular momentum coupling between the two fragments is taken into account for the first time. The result is also compared with the formal expansion method assuming fixed μ–v–J vector correlation for all scattering angles [Y. Mo and T. Suzuki, J. Chem. Phys. 108, 6780 (1998)]. The condition that reduces the rigorous formula to the approximate formula is examined.
Photoelectron spectroscopy of autoionizing Rydberg states of ammonia
Authors: Bacon J. A. , Pratt S. T.
Published: July 2002

Photoelectron spectroscopy was used to determine the ionic vibrational distributions following vibrational autoionization of Rydberg states of NH3. Two-color, two-photon resonant, three-photon excitation via selected rotational levels of the NH3 C̃′ 1A1′(0200) intermediate state was employed to populate vibrationally autoionizing Rydberg states between the v2+=1 and v2+=2 ionization thresholds of the NH3+ X̃ 2A2″ ground electronic state. As expected from the propensity rule for vibrational autoionization, ionization with Δv2=−1 was found to be the dominant process. The observed vibrational distributions appear to be independent of the rotational quantum number of the autoionizing state. Partially resolved rotational structure was exhibited within the photoelectron spectra providing information on the assignments of the Rydberg states and on the mechanism for vibrational autoionization.
H-bond spectroscopy as the level crossing problem: Evolution of nonstationary probe spectra
Authors: Burshtein A. I. , Sivachenko A. Yu.
Published: July 2002

The previously developed level crossing model has been employed to study the relaxation of transmission spectra of hydrogen-bonded species. We investigated the spectral transformation after the saturation of intramolecular vibrational transition by a strong light pulse as well as the signal accumulation in the course of light action. From the shape of the transmission spectrum, composed from the negative (“superabsorption”) and positive (“bleaching”) components, the first moment of the latter was calculated whose shift in time provides the information about the relaxation of the H-bond to the equilibrium length. The limiting cases of long and short exciting pulse as well as fast and slow vibrational relaxation were investigated. When the latter is slow the kinetics of the first moment relaxation is similar to that obtained experimentally, especially after short pumping. On the contrary, the kinetics of signal accumulation and dissipation is better to study at long pumping when it is closer to stationary response, at any time. From this response, the signal dependence on light power can be obtained, which is the main characteristic of the saturation phenomenon.
Surface diffusion of long chainlike molecules: The role of memory effects and stiffness on effective diffusion barriers
Authors: Hjelt T. , Vattulainen I.
Published: July 2002

We study the coverage dependence of surface diffusion for chainlike molecules by the fluctuating-bond model with a Monte Carlo dynamics. The model includes short-ranged excluded volume interactions between different chains as well as an intrachain bond angle potential to describe the chain stiffness. Our primary aim is to consider the role played by chain stiffness and the resulting memory effects in tracer diffusion, and in particular their role in the effective tracer diffusion barrier EAT extracted from the well-known Arrhenius form. We show that the memory effects in tracer diffusion become more pronounced at an increasing coverage as a result of packing requirements. Increasing the chain flexibility furthermore has the same overall effect as increasing the chain length, namely, they both increase EAT. We then analyze the influence of memory effects on EAT and find that, for a single diffusing chain, about 20% of EAT arises from temperature variations in the memory effects, while only the remaining part comes from thermally activated chain segment movements. At a finite coverage, the memory contribution in EAT is even larger and is typically about 20%–40%. Further studies with chains of different lengths lead to a conclusion that, for a single diffusing chain, the memory contribution in EAT decreases along with an increasing chain length and is almost negligible in the case of very long chains. Finally, we close this work by discussing our results in light of recent experimental work as regards surface diffusion of long DNA molecules on a biological interface.
Photolysis of CH3I on Cu(110) at 337 nm: Direct and charge-transfer photodissociation
Authors: Johnson C. C. , Jensen E. T.
Published: July 2002

The photochemistry of methyl iodide adsorbed on Cu(110) surfaces has been studied using time-of-flight mass spectrometry, temperature programmed desorption, and retarding potential spectroscopy. The λ=337 nm photodissociation of CH3I adsorbed on clean and iodided Cu(110) is found to have an increased cross section (by ∼2 orders of magnitude) and altered dynamics from that of the gas phase at the same wavelength. On the clean Cu(110) surface both enhanced neutral photodissociation and charge-transfer photodissociation processes are observed, the latter being ascribed to hot photoelectrons generated in the substrate. On the Cu(110)–I surface, only enhanced neutral photodissociation is observed and the CH3I molecules are found to be orientationally ordered with a 20° tilt in the [11̄0] azimuth. Further evidence of altered neutral photodissociation dynamics is found in the observed I/I* branching ratio. In contrast to earlier studies of adsorbed CH3I, the branching ratio is found to favor the higher energy I* dissociation pathway as compared to the gas phase. The altered neutral photodissociation dynamics are ascribed to changes in the CH3I excited state potential energy surfaces, caused by interactions with the copper–iodine interface.
Measurement of radiation damping rate constants in nuclear magnetic resonance by inversion recovery and automated compensation of selective pulses
Authors: Chen Jin-Hong , Cutting Brian , Bodenhausen Geoffrey
Published: July 2002

A method is proposed to measure the radiation damping rate constant based on the analysis of the nonexponential recovery of the magnetization after inversion. It is applicable when the recovery is dominated by radiation damping rather than by relaxation processes. The accurate measurement of the radiation damping rate constant can be used to simplify a recent method for the compensation of radiation damping effects during the application of selective pulses [Chen, Jerschow, and Bodenhausen, Chem. Phys. Lett. 308, 397 (1999)]. This procedure can now be automated, as illustrated by applications to selective inversion and excitation.
Theoretical investigation of the eight low-lying electronic states of the cis- and trans-nitric oxide dimers and its isomerization using multiconfigurational second-order perturbation theory (CASPT2)
Authors: Sayós R. , Valero R. , Anglada J. M. , González Miguel
Published: July 2002

In this work we have carried out ab initio electronic structure calculations, CASSCF/CASPT2 and CASSCF/MRCI-SD+Q with several Pople’s and correlation-consistent Dunning’s basis sets, of the planar cis- and trans-NO dimers for the lowest eight electronic (singlet and triplet) states. The geometry, frequencies, dipole moment, binding energy, and vertical excitation energies are predicted with an accuracy close to or even better than the best reported ab initio previous results for some of these properties, and in very good agreement with the available experimental data. CASPT2 optimized geometries show the existence of at least four shallow NO-dimers (i.e., two cis-(NO)2 (1A1 and 3B2) and two trans-(NO)2 (1Ag and 3Au)), although CASSCF optimization with CASPT2 pointwise calculations indicate the existence of other less stable dimers, on the excited states. Vertical excitation energies were calculated for these four dimers. For the cis-NO dimer, the ordering and the energy spacings between the excited states (i.e., 1A1, 3B2, 1B2, 2nd 1A1, 1A2, 3A2, 3B1, 2nd 3B1) are very similar to those found in a recent MRCI-SD study. The singlet cis-NO dimer (1A1) is the most stable one in almost quantitative accord with the experimental data, and in disagreement with previous density functional theory studies. A nonplanar transition state for the singlet trans ↔ cis isomerization has also been fully characterized. This leads to an almost negligible energy barrier which would originate a rapid isomerization to the most stable cis-NO dimer at low temperatures, in accord with the experimental difficulties to measure the properties of the trans-NO dimer. Not only are basis set superposition error corrections necessary to evaluate accurately the binding energies, but also to determine the NN distance of these symmetrical dimers. Some problems regarding the symmetry of the wave function were found for the symmetrical NO dimers and for the NO+NO asymptote, and several approximate solutions were proposed.
Semiclassical approximations to real-time quantum-mechanical effects in correlation functions of complex molecular systems
Authors: Sun Sean X.
Published: July 2002

Semiclassical approximation of real-time quantum effects is analyzed with the aid of the semiclassical initial value representation (SC-IVR) and Wigner distribution functions. We utilize these two ingredients to propose a new version of the semiclassical correlation function that contains, in principle, all quantum-mechanical effects. The advantage of this formulation is that it allows for a stepwise approximation specifically for real-time quantum effects based on a gradual inclusion of more degrees of freedom into the integral responsible for interference. From numerical calculations, this procedure does not seem to depend significantly on the choice coordinates if all degrees of freedom are coupled. This freedom from the coordinate choice removes possible ambiguities in applying this method. Several example cases are presented to demonstrate the usefulness of this approach.
Concertedness and solvent effects in multiple proton transfer reactions: The formic acid dimer in solution
Authors: Kohanoff J. , Koval S. , Estrin D. A. , Laria D. , Abashkin Y.
Published: July 2002

The issue of multiple proton transfer (PT) reactions in solution is addressed by performing molecular dynamics simulations for a formic acid dimer embedded in a water cluster. The reactant species is treated quantum mechanically, within a density functional approach, while the solvent is represented by a classical model. By constraining different distances within the dimer we analyze the PT process in a variety of situations representative of more complex environments. Free energy profiles are presented, and analyzed in terms of typical solvated configurations extracted from the simulations. A decrease in the PT barrier height upon solvation is rationalized in terms of a transition state which is more polarized than the stable states. The dynamics of the double PT process is studied in a low-barrier case and correlated with solvent polarization fluctuations. Cooperative effects in the motion of the two protons are observed in two different situations: when the solvent polarization does not favor the transfer of one of the two protons and when the motion of the two protons is not synchronized. This body of observations is correlated with local structural and dynamical properties of the solvent in the vicinity of the reactant.
van der Waals bending bands of the ArDCN cluster observed by millimeter-wave spectroscopy combined with a pulsed supersonic jet technique
Authors: Tanaka Keiichi , Bailleux Stephane , Mizoguchi Asao , Harada Kensuke , Baba Takeshi , Ogawa Ikuyo , Shirasaka Mitsuaki
Published: July 2002

Millimeter-wave absorption spectroscopy combined with a pulsed-jet expansion technique was applied to the measurement of the rovibrational transitions of the van der Waals (vdW) bending bands of the ArDCN cluster in the frequency region of 182∼294 GHz. Sixteen and thirty-seven rovibrational lines were observed for the Σ1–Σ0 and Π1–Σ0 bands, respectively, split into hyperfine structure due to the nitrogen nucleus. A set of accurate molecular constants, including the band origins, rotational constants, nuclear quadrupole coupling constants, and the Coriolis interaction constant between the Σ1 and Π1 bending substates, was determined. The band origins for the Σ1–Σ0 and Π1–Σ0 bands of ArDCN, 189.017 380(7) GHz and 195.550 736(12) GHz, are larger by 24.126 585(9) and 13.566 314(16) GHz than the corresponding values of ArHCN, respectively. The abnormal isotopic effect on the vibrational frequencies is attributed to the characteristic potential energy surface of ArH(D)CN, which has two minima, corresponding to the linear configuration and a much shallower minimum at the T-shaped configuration. The rotational and quadrupole coupling constants for the excited states are quite different from those of the ground state. For example, the rotational constants 1926.8863(16) and 1967.8768(9) MHz for the excited Σ1 and Π1 states are significantly larger than that of the ground Σ0 state, 1574.793 16(24) MHz. It indicates the shrinkage of the bond length of the cluster by about 0.402∼0.440 Å on the excitation of the vdW bending mode, together with the change from the linear form in the ground (j=0) state to the T-shaped form in the first excited (j=1) state. The determined molecular constants were compared with those calculated with the potential energy surface calculated at CCSD(T) level.
Unified approach to the Bloch–Redfield theory and quantum Fokker–Planck equations
Authors: Yan YiJing , Shuang Feng , Xu Ruixue , Cheng Jixin , Li Xin-Qi , Yang Chen , Zhang Houyu
Published: July 2002

By using a rather simple algebraic approach, we revisit and further bridge between two most commonly used quantum dissipation theories, the Bloch–Redfield theory and a class of Fokker–Planck equations. The nature of the common approximation scheme involving in these two theories is analyzed in detail. While the Bloch–Redfield theory satisfies the detailed-balance relation, we also construct a class of Fokker–Planck equations that satisfy the detailed-balance relation up to the second moments in phase-space. Developed is also a generalized Fokker–Planck equation that preserves the general positivity of the reduced density operator. Both T1-relaxation and pure-T2 dephasing are considered, and their temperature dependence is shown to be very different. Provided is also an analogy between the quantum pure-T2 dephasing and the classical heat transport.
On the commutant of an irreducible set of operators in real Hilbert space
Authors: Castrigiano D. P. L. , Mutze U.
Published: July 2002

The relation between irreducibility and the structure of the commutant is studied for a set of linear bounded operators on a real Hilbert space of arbitrary dimension. The results are applied to the investigation of irreducible sets of semilinear operators on a complex or quaternionic Hilbert space.
Topological properties of unbounded bicommutants
Authors: Mathot Françoise
Published: July 2002

We consider different possible definitions of unbounded commutants and unbounded bicommutants of a set or an algebra of unbounded operators. We investigate their behavior with respect to various topologies. In particular we give sufficient conditions in order that bicommutants be the closure of the original set of operators with respect to some of those topologies. We investigate some special classes of algebras (symmetric, self-adjoint, regular, V* algebras) for which several or all of the bicommutants coincide and are the closure of the algebra with respect to some or all of the considered topologies.
A local limit theorem for strongly dependent random variables and its application to a chaotic configuration of atoms
Authors: Reichert P. , Schilling R.
Published: July 2002

We investigate one-dimensional chaotic configurations of atoms, which are generated by the Baker transformation or, equivalently, by the Bernoulli shift. The problem of calculating the distribution of the jth nearest-neighbor distances of these configurations is shown to be equivalent to the task of finding the limit distribution of the sum of the strongly dependent random variables Xl:([0,1),μL)→[0,1), x→(2lx)mod 1 (l∈N0, μL is the Lebesgue measure). We prove the validity of a local limit theorem for this sequence of random variables and conclude, therefore, that the distribution density Gj of the jth nearest-neighbor distances is asymptotically (as j→∞) a Gaussian distribution, the width of which grows as (j)1/2. With the aid of this result, we prove that the pair distribution function G of our configurations, which is the sum of the Gj’s, tends to unity in the limit of large distances.
Harmonic analysis on the Euclidean group in three-space
Authors: Rno Jung Sik
Published: July 2002

We develop the extensive harmonic analysis on the universal covering group of the Euclidean group in three-space.
On the projective representations of finite Abelian groups. II
Authors: Saeed-ul-Islam M.
Published: July 2002

Complete sets of inequivalent irreducible projective representations of Cnm ={w1,⋅⋅⋅,wn; wmi =1, i=1,...,n; wiwj =wjwi, i, j=1,...,n} with respect to a class of factor sets α are determined, where α(wi,wj) =θα(wj,wi), 1≤i<j≤n and θ is a fixed mth root of unity. A single irreducible projective representation of Cnm for each factor set α is constructed and called the basic projective representation. The rest of the representations are obtained by tensoring the basic projective representations with some ordinary representations of Cnm. Projective representations of Cnm are thus parametrized in terms of its ordinary representations.
Anisotropic cosmological model in Nordtvedt’s scalar–tensor theory of gravitation
Authors: Banerjee A. , Banerjee N. , Santos N. O.
Published: July 2002

Anisotropic cosmological models are considered in the light of the scalar–tensor theory of gravitation proposed by Nordtvedt. Special attention is paid to Bianchi type I models. The models consist of perfect fluid with the equation of state p=ερ. The solutions are obtained in Dicke’s conformally transformed units for empty space, as well as for ε=1 and (1)/(3) , assuming two separate functional relationships between ω and φ. Their properties are also compared with those of the models given in Brans–Dicke theory.
Relativistic, stationary, axisymmetric perfect fluids. I. Reduction to a system of two equations
Authors: Bonanos S. , Sklavenites D.
Published: July 2002

The introduction of a new system of coordinates permits a partial solution of Einstein’s field equations for the interior of a uniformly rotating, stationary, axisymmetric perfect fluid, and reduces the problem to two second-order partial differential equations for two unknown functions.
Bloch oscillations in one-dimensional solids and solitary wave packets
Authors: Luban Marshall
Published: July 2002

We derive the exact solution of a single-band time-dependent Schrödinger equation for an electron in an idealized one-dimensional periodic solid in the presence of a constant uniform electric field. We show that all wave functions are necessarily periodic in time. This result is the fully quantum-mechanical analog of the well-known Bloch oscillations predicted by quasiclassical dynamics. Our method of solution consists of mapping the electron Schrödinger equation to the exactly solvable problem of a quantum planar rotor in the eikonal limit subject to an arbitrary angular and time-dependent external potential. The time periodicity of the electron wave functions is due to the fact that all of the rotor wave functions have the form of solitary wave packets.
Cumulant expansions for thermal density matrices and ground state logarithmic perturbation series
Authors: Royer Antoine
Published: July 2002

We express the logarithm of the thermal density matrix ρH,β (X,X′)≡〈X‖e−βH‖X′〉, where H=H0+V, as a cumulant expansion in powers of the perturbation V, by associating with {H0,‖X〉,‖X′〉} a stochastic process. If the ground state of H0 is isolated, this stochastic process is of finite memory; it then follows from the properties of cumulants that the above expansion of ln ρ is nonsecular as β→∞ (all its terms ∼β), and is thus usable down to zero temperature, unlike the direct expansion of ρ in powers of V, whose nth term ∼βn. To determine explicitly the low-temperature behavior, we apply an analysis familiar in the theory of relaxation, and obtain the form ln ρH,β(X,X′)=h(X,X′,β) +a(X)+a(X′)°−bβ, where a,b,h are cumulant expansions in powers of V; a(X), b are independent of β; and h(X,X′,β)→0 as β→∞. Comparing with ρ→〈X‖ψ0〉e−βE0〈ψ0‖X′〉 as β→∞, where ψ0 and E0 are the ground state and energy of H, we deduce E0=b, ln〈X‖ψ0〉=a(X), i.e., the Rayleigh–Schrödinger perturbation series for E0 and ln〈X‖ψ0〉 (with 〈ψ0‖ψ0〉=1) emerge as cumulant expansions. In the case of a many-body system, the properties of cumulants immediately imply linked cluster theorems for ln ρ, as well as for E0 and ln〈X‖ψ0〉.
Quantum electrodynamic perturbation theory based on semiclassical representation
Authors: Gordov E. P. , Fazliev A. Z.
Published: July 2002

A perturbation theory-based procedure for calculating mean values of quantum electrodynamic operators is proposed. Analytical solutions to similar electrodynamic problems are used as zero-order approximations for the above approach.
Weak rigidity in almost-thermodynamic material schemes
Authors: del Olmo V. , Olivert J.
Published: July 2002

To avoid the restrictions that the Born rigidity supposes for the motions in relativity, the definition of a weakly rigid almost-thermodynamic material scheme is proposed. From it the relativistic incompressibility condition given by Ferrando and Olivert is obtained. Moreover, it is proved that, for the weakly rigid irrotational and geodesic almost-thermodynamic material schemes, the scalar curvature of the Landau manifolds is constant along the streamlines.
The vacuum Einstein equations and deformations of the Bianchi identity
Authors: Chinea F. J. , Guerrero F. Guil
Published: July 2002

The Einstein equations in vacuum are written as a closed differential ideal of matrix-valued differential forms with constant coefficients. Several properties of the resulting equations, such as the existence of an associated integrability system and of conserved matrix currents, as well as the treatment of specific Petrov types, are briefly considered. We also show that the field equations can be expressed as a deformation (depending on a complex parameter λ) of the Bianchi identity for an adequate Poincaré or de Sitter connection.
Chiral and gravitational anomalies in any dimension
Authors: Delbourgo R. , Matsuki T.
Published: July 2002

Gravitational contributions to the chiral anomaly in 4N space-time dimensions as well as the purely gravitational anomaly in 4N−2 dimensions are expressed in terms of the Riemann–Christoffel tensor. Using this formula, we give a simple proof that if N≥4 there is no way to cancel the gravitational anomalies using fields of spin- 1/2 , - 3/2 , and -1.
On the geometric structure of gauge theories
Authors: Mangiarotti Luigi , Modugno Marco
Published: July 2002

In the framework of the adjoint forms over the jet spaces of connections and using a canonical jet shift differential, we give a geometrical interpretation of the Yang–Mills equations both in a direct and Lagrangian formulation.
Regular precession in Jacobi’s decomposition theorem
Authors: Yamada Katsuya
Published: July 2002

In this paper, Jacobi’s decomposition theorem, which states that the motion of a heavy symmetrical top can be decomposed into the motions of two torque-free triaxial tops (free asymmetrical tops), is applied to the case of a regular precession (no nutation) of the heavy symmetrical top, and it is found that the heavy top motion can be expressed as a composite motion consisting of two torque-free symmetrical tops with no nutation. A top motion without nutation is an extremely simple motion since it consists of only spin and precession, which are merely constant rotations. The dynamical relations among the three symmetrical tops are obtained. Quantum analysis of a torque-free top is completely known. Since the Hamiltonian of the regular precession of a heavy symmetrical top has the same form as that of the Stark effect of a symmetrical molecule, our result indicates a possibility of quantum treatment of Jacobi’s decomposition theorem.
Gauge theory of the post-Galilean groups
Authors: Dimakis A.
Published: July 2002

By means of an extension of the field of real numbers we construct post-Galilean groups, which in a sense lay between the Galilean group and the Lorentz group. By gauging these groups we obtain a frame theory of gravitation, which comprises Newton–Cartan theory, general relativity, and an infinite number of intermediate theories. This leads to a better understanding of how the structural differences of the two main theories of gravitation arise.
Perfect fluid models of Bianchi type-VI0 in modified Brans–Dicke cosmology
Authors: Ram Shri
Published: July 2002

The spatially homogeneous and anisotropic Bianchi type-VI0 cosmological solution for barotropic fluid in the context of modified Brans–Dicke theory is obtained. The general behavior of such an anisotropic homogeneous model has been discussed.
A simple construction of twist-eating solutions
Authors: van Baal Pierre , van Geemen Bert
Published: July 2002

A simple general construction of all solutions to the set of equations [Ωμ, Ων]=exp (2πinμν/N)I, where Ωμ∈SU(N) or U(N) and μ, ν=1, 2, ... , 2g, is given.
On the integration of the self-similar equations, and the meaning of the Cole–Hopf transformation
Authors: Gaffet B.
Published: July 2002

The existence of a first integral of the self-similar equations associated with a given partial differential system, in one space dimension, is shown, whenever there exists a conserved quantity Q whose scale remains time independent. That result is most conveniently derived through the introduction of Y≡exp Q as a new unknown. In the case of the Burgers equation, the velocity potential Φ has the required property, and the transformation to the new variable exp Φ is precisely the Cole–Hopf transform. The latter, as is well known, linearizes the Burgers equation.
Approach to equilibrium for random walks on graphs and for stochastic infinite particle processes
Authors: Thomas Lawrence E. , Yin Zhong
Published: July 2002

Associated with a finite connected graph g is a doubly stochastic (Laplacian) matrix G(g). A lower bound on the ‘‘mass gap’’ for G(g) is obtained, i.e., the first nonzero eigenvalue of G(g). This estimate is then used to estimate the mass gap for some infinite particle stochastic generators with corresponding processes that are closely related to Monte Carlo methods employed in statistical mechanics calculations.
Sites and googly twistor spaces. II. Yang–Mills fields
Authors: Helfer Adam D.
Published: July 2002

(Anti-) self-dual Yang–Mills fields may be described by twistors of the same or opposite handedness as the fields. These are called the leg-break and googly descriptions, respectively. The leg-break twistor space is a complex manifold; the Yang–Mills field is given by a vector bundle over this manifold; and massless fields minimally coupled to the Yang–Mills field are given by elements of certain sheaf cohomology groups on the manifold. In the previous paper, we analyzed the structure of the googly twistor space when no Yang–Mills field is present, and showed that it was a site. (Sites are generalizations of topological spaces, in which the primitive concept is that of an open set rather than that of a point.) In this paper, we treat the case where a gauge field is present. We show that the field is represented by a vector bundle over the site, and that massless fields minimally coupled to the Yang–Mills field are given by the elements of a sheaf cohomology group on the site. Also, this vector bundle is isomorphic to one over a leg-break twistor site. This provides a strong link between the googly and the leg-break spaces.