bluuebunny/crossref_metadata_2025 huggingface dataset:
Solvation dynamics of benzonitrile excited state in polar solvents: A time-dependent reference interaction site model self-consistent field approach
Authors: Ishida Tateki , Hirata Fumio , Kato Shigeki
Published: July 2002

The solvation dynamics of benzonitrile (C6H5CN) after the 21A1←1 1A1 vertical transition in water (H2O), methanol (CH3OH), and acetonitrile (CH3CN) solvents is studied with the reference interaction site model self-consistent field (RISM-SCF) method. The evolution of solute electronic states associated with the solvent relaxation is described by a time-dependent RISM-SCF method, incorporating the time-dependent solute–solvent site–site radial distribution functions, which are derived from the surrogate linear response theory. Ab initio electronic structure calculations reveal that the 2 1A1 state is of ionic nature whose dipole moment is larger by 2.41 D than that of the ground state. It is found that the excited state dipole moment is enhanced in the solutions, which provides the red shift of ∼6000 cm−1 in the vertical excitation energy. The solvent relaxation further increases the charge polarization in solute, indicating the electronic state of excited C6H5CN is sensitive to the electrostatic field coming from the solvent. The dynamic Stokes shift is characterized by the solvation time correlation function (STCF). The calculated STCFs show that the solvent relaxation exhibits a nonexponential behavior and almost completes within 5 ps in H2O and CH3CN while a long-time tail is observed up to 20 ps in CH3OH. The slow component of the decay rate is consistent with other simulation calculations though the fast one is smaller. In order to analyze the solute charge polarization during the solvent relaxation, the solute charge time correlation function (CTCF) is calculated and the resultant CTCFs are discussed in terms of the solvent charge polarization in the vicinity of solute molecule.
New empirical rate expression for reactions without a barrier: Analysis of the reaction of CN with O2
Authors: Hessler Jan P.
Published: July 2002

The rate coefficients of reactions that occur on potential energy surfaces without a barrier often exhibit a negative temperature dependence at low temperatures. Generally, this behavior is modeled with either the Harcourt–Essen equation, k(T)=AT−m, or a “negative” activation energy, k(T)=ATm exp{ΔE/kBT}. Neither of these expressions is consistent with the Wigner threshold law. The general expression k(T)=(1+T/TW)−m∑l=0∞Al(1+T/TW)−l(T/TW)l is proposed where the relative angular momentum of the reacting species is l, TW and m are independent parameters to be extracted from the data, and the amplitude of each partial wave is Al. This expression may be approximated by k(T)=A0(1+T/TW)−m exp[(T/TW)/(1+T/TW)]. For CN+O2→ NCO+O and CO+NO the above expression reproduces the rate data, the branching ratio to the CO+NO channel, and the reactive cross section for the NCO+O channel. The rate coefficient for the NCO+O channel is given by k(cm3 s−1)=1.79×10−10(+T/21.7)−1.38{exp[(T/21.7)/(1+T/21.7)]−1}+4.62×10−12 exp[(T/21.7)/(1+T/21.7)] while for CO+NO we obtain k(cm3 s−1)=1.79×10−10(1+T/21.7)−1.38. An analytic form of the C–O bonding potential and the electric dipole–quadrupole interaction is used to show that the quantum threshold region extends up to 7 K. These results demonstrate the need of a complete quantum treatment for reactions that proceed on potential surfaces without a barrier.
Intrinsic reaction coordinate analysis of the conversion of methane to methanol by an iron–oxo species: A study of crossing seams of potential energy surfaces
Authors: Yoshizawa Kazunari , Shiota Yoshihito , Yamabe Tokio
Published: July 2002

Crossing seams between the potential energy surfaces and possible spin inversion processes for the direct conversion of methane to methanol by the bare FeO+ species are discussed by means of the intrinsic reaction coordinate (IRC) approach. There are three crossing seams between the sextet and the quartet potential energy surfaces, and spin inversion should occur twice in the entrance and the exit channels; FeO+(6Σ+)+CH4(1A1)→OFe+(CH4)(6A)→TS1(4A′)→HO–Fe+–CH3(4A)→TS2(4A)→Fe+(CH3OH)(4A)→Fe+(6D)+CH3OH(1A′). The first crossing seam exists in prior to TS1, a four-centered transition state for the cleavage of a C–H bond of methane. This crossing seam is the most important aspect in this reaction pathway because the molecular system should change its spin multiplicity from the sextet state to the quartet state near this crossing region, leading to a significant decrease in the barrier height of TS1 from 31.1 to 22.1 kcal/mol at the B3LYP level of density functional theory. The second crossing seam occurs in the vicinity of the hydroxy intermediate (HO–Fe+–Ch3), but this crossing seam would not play a significant role because the quartet IRC valley always lies below the sextet one in this region of reaction coordinate and accordingly the molecular system would preferentially move on the quartet potential energy surface. The third crossing seam exists in the exit channel in which the elimination of methanol occurs from the product complex. This crossing seam will again lead to spin inversion from the quartet to the sextet state, by which the elimination energy can be decreased from 57.2 to 37.4 kcal/mol in the FeO+/CH4 system.
A second rhomboidal isomer of SiC3
Authors: McCarthy M. C. , Apponi A. J. , Thaddeus P.
Published: July 2002

A second low-lying cyclic isomer of SiC3 has been detected in a supersonic molecular beam by Fourier transform microwave spectroscopy. Calculated to lie about 5 kcal above the ground state rhomboid, the new isomer is also a planar rhomboid with a transannular bond, C2v symmetry, and a singlet electronic ground state. The transannular bond, however, is between the Si and the opposite C, and the rotational spectrum as a result is that of an oblate, not a prolate, asymmetric rotor. Both rhomboidal isomers of SiC3 are produced with comparable abundance under a wide range of experimental conditions, which suggests that cyclic isomers of longer silicon carbides may now be observable with the present techniques. Oblate SiC3 is a plausible molecule for astronomical detection because it is calculated to be fairly polar, and because radio emission lines of the ground state rhomboid have already been detected in the circumstellar shell of the evolved carbon star IRC+10216.
Comment on: “The hindered rotor density-of-states interpolation function” [J. Chem. Phys. 106, 6675 (1997)] and “The hindered rotor density- of-states” [J. Chem. Phys. 108, 2314 (1998)]
Authors: McClurg Richard B.
Published: July 2002

There has been some confusion regarding the various approximations for the hindered rotor partition function and its associated thermodynamic functions and density of states. This comment seeks to clarify the situation by comparing and contrasting the various functions, particularly with regard to the consistent use of reference energies. Only the tabular data of Pitzer and Gwinn [J. Chem. Phys. 10, 428 (1942)] and our analytic function [J. Chem. Phys. 106, 6675 (1997)] have consistent reference energies. The main contribution of our publication is the set of simple, asymptotically correct expressions for the thermodynamic functions. There are similar, but different approximations to the density of states given by Knyazev and co-workers [J. Phys. Chem. A 102, 3916 (1998)] and by me [J. Chem. Phys. 108, 1748 (1998)].
Intracluster hydrogen transfer followed by dissociation in the phenol–(NH3)3 excited state: PhOH(S1)–(NH3)3→PhO•+(NH4)(NH3)2
Authors: Pino G. A. , Dedonder-Lardeux C. , Grégoire G. , Jouvet C. , Martrenchard S. , Solgadi D.
Published: July 2002

The study of the phenol–(NH3)3 cluster with two-color two-photon ionization shows that the main ion observed with delays between the lasers up to a few hundred nanoseconds is the (NH4)+(NH3)2 fragment, resulting from direct ionization of the (NH4)(NH3)2 product coming from the reaction: PhOH(S1)–(NH3)3→PhO•+(NH4)(NH3)2.
Optimization of quantum Monte Carlo wave functions using analytical energy derivatives
Authors: Lin Xi , Zhang Hongkai , Rappe Andrew M.
Published: July 2002

An algorithm is proposed to optimize quantum Monte Carlo (QMC) wave functions based on Newton’s method and analytical computation of the first and second derivatives of the variational energy. This direct application of the variational principle yields significantly lower energy than variance minimization methods when applied to the same trial wave function. Quadratic convergence to the local minimum of the variational parameters is achieved. A general theorem is presented, which substantially simplifies the analytic expressions of derivatives in the case of wave function optimization. To demonstrate the method, the ground-state energies of the first-row elements are calculated.
Detection of the millimeter wave spectra of the weakly bound complexes 3He–CO and 4He–CO
Authors: Surin Leonid A. , Roth Daniel A. , Pak Igor , Dumesh Boris S. , Lewen Frank , Winnewisser Gisbert
Published: July 2002

For the first time, millimeter wave absorption spectra of the van der Waals complexes 3He–CO and 4He–CO were detected in a supersonic jet. Altogether four rotational transitions of 3He–CO and six rotational transitions of 4He–CO were recorded between 110 GHz and 127 GHz with an intracavity spectrometer based on the millimeter wave generator, called OROTRON. The obtained results were included in a global fit together with previously known data enabling a more precise determination of the energy levels of the 3He–CO and 4He–CO complexes. In extremely cold, dark, and dense interstellar clouds the He–CO complex may have astrophysical relevance.
The tricontinuous double-gyroid structure from a three-component polymer system
Authors: Suzuki Jiro , Seki Motohiro , Matsushita Yushu
Published: July 2002

The tricontinuous structure of ABC-type triblock copolymer in bulk at equilibrium was studied by both transmission electron microscopy (TEM) and small-angle x-ray scattering (SAXS). Sample is an anionically polymerized isoprene-styrene-2-vinylpyridine triblock copolymer whose volume fraction is 0.22–0.59–0.19 and total molecular weight is 64 000. It was found that computer-simulated images based on tricontinuous structure with two parallel surfaces to the gyroid surface, which is one of the three-dimensionally infinite minimal surfaces agree well with the observed TEM images. Further, calculated diffraction patterns for the same tricontinuous structure well represent the observed SAXS intensity maps on imaging plates. These facts imply that the structure of the present triblock copolymer is the tricontinuous double gyroid structure, whose space group is I4132.
Theoretical description of the nonlinear response functions associated with eight distinctive three-dimensional vibrational spectroscopies
Authors: Park Kisam , Cho Minhaeng
Published: July 2002

The three-dimensional (3D) vibrational spectroscopies are theoretically considered in terms of the associated nonlinear response functions. Since the 3D vibrational spectroscopy involves three vibrational coherence evolutions in the ground electronic state, it is found that there are eight distinctive possibilities when a vibrational coherence state can be created via an infrared field–matter interaction or two off-resonant optical field–matter interactions via Raman. The nonlinear response functions associated with eight distinctive 3D vibrational spectroscopies, where seven of them are novel methods, are presented and expressed in terms of the linear response functions by taking the lowest-order contributions. The analytic expressions of the 3D Fourier spectra are obtained. By using the results, how to utilize the 3D vibrational spectroscopic methods to measure the higher-order vibrational mode coupling arising from the anharmonicity of the multidimensional potential energy surface as well as from the nonlinearity of the dipole moment or polarizability with respect to the vibrational degrees of freedom is discussed. Numerical calculations of the results for a three-oscillator model system are presented, and a few characteristic peaks uniquely appearing in the 3D vibrational spectra are discussed in detail. Finally, the third-order nonlinear terms of dipole moment and polarizability are found to be of critical use in the structure determination, assuming that the collective dipole moment and polarizability is mainly determined by the dipole-induced–dipole interaction effect.
Electronic structure and short-range recombination dynamics of S2 in solid argon
Authors: Kiljunen Toni , Eloranta Jussi , Kunttu Henrik , Khriachtchev Leonid , Pettersson Mika , Räsänen Markku
Published: July 2002

Potential energy curves for 13 lowest electronic states of S2 and 6 lowest states of ArS are computed at the MRCI level utilizing the CASSCF orbitals. The electronic structure of S2 is described by the correlation consistent cc-pVQZ basis set, whereas for ArS the augmented version of this basis is combined with ten electron-core pseudopotential basis set for S and Ar, respectively. Thermal and shock wave induced recombination dynamics of sulfur atoms trapped in Ar lattice are investigated by classical Molecular Dynamics simulations. It is observed that atoms separated by nearest neighbor distance of the lattice do immediately recombine even at 1 K with no thermal activation. While separated by one lattice constant, the S atoms stay stable up to 80 K and no recombination is observed in the classical trajectories. Consequently, the simulation was able to reproduce the experimental S+S glow curve only by lowering the reaction barrier by introducing lattice vacancies in the four atom plane separating the S–S pair. Local 1.1 eV kinetic excitation of a lattice atom next to the trapped S–S pair or artificial shock waves initiated by more distant excitation at 2 eV or more greatly enhanced the probability for recombination. Nonradiative D1–3P relaxation of sulfur provides a mechanism for such phonon emission and is discussed as a potential reason for the observed photoinduced recombination in low temperature Ar matrix.
A close look on single quantum dots
Authors: Zrenner A.
Published: July 2002

Quantum dots, often referred to as artificial atoms, open the field of quantum resolved spectroscopy to semiconductor physics. The current article is designed to review the field of interband optical spectroscopy on single semiconductor quantum dots.
Thermodynamics of electrolyte solutions in the modified mean spherical approximation
Authors: Varela L. M. , Perez-Rodriguez M. , Garcia M. , Mosquera V.
Published: July 2002

The exact Ornstein–Zernike formalism for ionic fluids is seen to be equivalent to the dressed-ion theory (DIT), therefore proving the exact character of this mean-field formalism. The modified mean spherical approximation (MMSA) [Varela et al., J. Chem. Phys. 109, 1930 (1998)] is a modified version of the mean spherical approximation, which corrects some of the deficiencies of the original version of this closure relation in the prediction of the effective screening length. The MMSA effective non-Debye decay length, developed in the framework of the dressed-ion transport theory (DIT) of Kjellander and Mitchell, is an improvement on those of other theoretical and numerical schemes, which include self-consistent second moment approaches, asymptotic expansions, and nonlinear Debye–Hückel approximations. The MMSA screening length is used to analyze thermodynamic magnitudes of the charged fluid such as the internal energy and the osmotic coefficient and the results are seen to fit accurately to hypernetted chain calculations.
Microwave studies of three alkylbenzenes: Ethyl, n-propyl, and n-butylbenzene
Authors: Maté Belén , Suenram Richard D. , Lugez Catherine
Published: July 2002

The rotational spectra of ethyl, n-propyl, and n-butylbenzene have been observed and analyzed using a high-resolution Fourier transform microwave spectrometer. Only one stable conformation was found for ethylbenzene, in agreement with previous results from Caminati et al. [Mol. Phys. 74, 885 (1991)]. The high sensitivity of the technique allows observation of the rotational spectra of the six C13 isotopes of ethylbenzene in natural abundance. The structural analysis indicates that the dihedral angle between the ethyl group and the ring plane is 88.7°±0.9°. Two conformers have been found for n-propylbenzene as predicted by ab initio calculations while four of the five theoretically predicted conformers [Dickinson et al., J. Chem. Soc., Faraday Trans. 93, 1467 (1997)] have been found for n-butylbenzene.
Biased Monte Carlo optimization of protein sequences
Authors: Cootes Adrian P. , Curmi Paul M.G. , Torda Andrew E.
Published: July 2002

We demonstrate the application of a biased Monte Carlo method for the optimization of protein sequences. The concept of configurational-biased Monte Carlo has been used, but applied to sequence/composition rather than coordinates. Sequences of two-dimensional lattice proteins were optimized with the new approach and results compared with conventional Monte Carlo and a self-consistent mean-field (SCMF) method. Biased Monte Carlo (MC) was far more efficient than conventional MC, especially on more complex systems and with faster cooling rates. Biased MC did not converge as quickly as SCMF, but often found better sequences.
Riccati equations and perturbation expansions in quantum mechanics
Authors: Rogers George W.
Published: July 2002

General perturbation expansions, which allow corrections to any order to be written in quadrature, are presented for Riccati and other nonlinear first-order equations. These results are valid for eigenfunctions which are free of poles and zeros. A Riccati equation suitable for a Schrödinger or Klein–Gordon particle in a central field is expanded for a general state, with corrections to all orders expressed in quadrature. A general Riccati equation for a meromorphic eigenfunction leads to a similar expansion with corrections to all orders, including corrections to the zeros and simple poles, expressed in quadrature. This form is suitable for a Dirac particle in a central field but is more general. The general results are applied to specific examples from the literature.
Evolution loops
Authors: Mielnik Bogdan
Published: July 2002

The problem of manipulating Schrödinger’s particle by time-dependent external fields is discussed. New solutions of the evolution problem, called evolution loops, are found. They correspond to the ‘‘particle memory’’ in the sense of Brewer and Hahn [Sci. Am. 251(12), 50 (1984)]. A technique of generating the unitary operations by perturbing the evolution loops is outlined.
Reconstruction of dynamics from an eigenstate
Authors: Vilela Mendes R.
Published: July 2002

For Hamiltonians that have a formal (canonical) decomposition H=− 1/2 Δ+V(x), V(x) being a multiplication operator, the definition of the dynamics by a ground state measure leads to an energy (Dirichlet) form formulation of quantum mechanics that is more general than the operator Schrödinger approach. Here, the question of reconstruction of the dynamics from an eigenstate when the potential is not restricted to the class of multiplication operators is analyzed. By explicit analysis of several examples, it is found that, once a particular operator class is chosen, the potential and the energy form are, to some extent, determined by the eigenstate. However, depending on the type of operator the potential is chosen to be, many distinct dynamics can be associated to the same fixed eigenstate. The nature of the stochastic processes associated with each reconstructed dynamic is also discussed, as well as a generalization of the stochastic dynamics formalism allowing for nonlocal potentials.
Symmetries of linear systems of second-order ordinary differential equations
Authors: González López A.
Published: July 2002

In this paper, several problems concerning the Lie algebra structure of symmetries and variational symmetries of a general linear system of second-order ordinary differential equations are studied. In particular, a necessary and sufficient condition is obtained, in terms of the coefficients of the system, for the system’s symmetry algebra to be of maximal dimension (i.e., n2+4n+3) and isomorphic to sl(n+2,R), the well-known symmetry algebra of the free-particle equation x″=0. When this condition is satisfied, it is proved that the system is Lagrangian and that its variational symmetry algebra is isomorphic to a fixed, (n2+3n+6)/2- dimensional Lie algebra, whose structure (Levi–Mal’cev decomposition and realization by means of a matrix algebra) is determined. For the particular case of isotropic systems (which includes, as far as is known, all the examples treated in the literature), explicit formulas for the generators of both the symmetry algebra and the variational symmetry algebra are obtained.
Extended Weinberg–Witten theorem
Authors: L/opuszański Jan
Published: July 2002

A new method of proving the Weinberg–Witten theorem is presented. It is shown that this theorem can be extended to currents that, being carriers of a charge, cause simultaneously a flip of the helicity of the massless one-particle state.
New integrable nonlinear integrodifferential equations and related solvable finite-dimensional dynamical systems
Authors: Matsuno Y.
Published: July 2002

A new integrable nonlinear integrodifferential equation (NIDE) is proposed. This equation may be interpreted as a model equation for deep-water waves. The N-periodic and N-soliton solutions for the equation are constructed by means of the bilinear transformation method. These solutions have the same structure as that for the Benjamin–Ono equation which describes internal waves in stratified fluids of great depth. Furthermore, it is shown that the motion of the positions of the poles of solutions is related to certain solvable finite-dimensional dynamical systems described by first-order nonlinear ordinary differential equations. The discussion is also made on a more general NIDE that may be interpreted as a model equation describing nonlinear waves in fluids of finite depth.
Finite geometries and Clifford algebras
Authors: Shaw R.
Published: July 2002

The Clifford algebra in dimension d=2m+1−1, m≥2, is treated using the finite m-dimensional projective geometry PG(m,2) over the field of order 2. The incidence properties of the geometry help in the problem of finding a complete commuting set of operators with which to label the 2(d−1)/2 spinor states of an irreducible representation. Full details are given in the case m=3, d=15, thus generalizing previous work for the m=2, d=7 case, and various conjectures are made concerning the cases m>3.
A dynamical formalism of singular Lagrangian system with higher derivatives
Authors: Saito Yoshihiko , Sugano Reiji , Ohta Tadayuki , Kimura Toshiei
Published: July 2002

The singular Lagrangian system with higher derivatives is analyzed with the aid of the Ostrogradski transformation and the Dirac formalism. The formulation of canonical theory is developed so that the equivalence between the Lagrange formalism and the Hamilton one is maintained. As a practical example, the acceleration-dependent potentials appearing in the Lagrangian of two-point particles interacting gravitationally are dealt with and the equivalence between the two Hamiltonians that follow from the two Lagrangians which are related by the coordinate transformations is shown. It is also shown, when the constraints are all first class, that a consistent generator of gauge transformation is constructed. Typical examples are given.
Finite geometries and Clifford algebras. II
Authors: Shaw R. , Jarvis T. M.
Published: July 2002

The Clifford algebra in dimension d=2m+1−1, m≥2, is treated using the finite m-dimensional projective geometry PG(m, 2) over the field of order 2. Full details are given for the case m=4, d=31, generalizing previous work for m=2 and 3. Details are given of some configurations that arise in PG(4, 2).
Quaternionic gauge fields and the geometric phase
Authors: Lévay Péter
Published: July 2002

The quaternionic representation of the SU(2) non-Abelian, nonadiabatic geometric phase for Fermi systems with time reversal invariance is investigated. The underlying differential geometric structure originating from the Riemannian metric on HPn (the quaternionic projective space) is studied in detail. For two simple model Hamiltonians corresponding to the cases of adiabatic, and nonadiabatic cyclic evolutions, the gauge fields are shown to be identical with Yang’s SU(2) monopole solutions. This example of nonadiabatic cyclic evolution turns out to be useful in the context of Polyakov’s spin factors also. Employing bosonic degrees of freedom interacting with the fermionic ones, it is found that the gauge structures are also present in the bosonic effective action. However, this topological part of the effective action cannot solely be interpreted as a Wess–Zumino term unlike the one in the complex case.
On the application of maximum entropy to the moments problem
Authors: Ciulli S. , Mounsif M. , Gorman N. , Spearman T. D.
Published: July 2002

The use of the maximum entropy condition to obtain a solution to the moments problem, in which one seeks to reconstruct a function from the values of a finite set of its moments, is of interest in a variety of physical applications. Unfortunately, the standard analysis which is available, and on which these applications are based, takes as its starting point precise values of the moments whereas the physical applications involve imprecise data. In this paper it will be shown how to solve the moments problem, using the maximum entropy condition, starting from imprecise data values with errors specified by a χ2 -function.
The Stratonovich–Weyl correspondence for one-dimensional kinematical groups
Authors: Gadella Manuel , Martin Miguel A. , Nieto Luis M. , del Olmo Mariano A.
Published: July 2002

The Stratonovich–Weyl correspondence is a restatement of the Moyal quantization where the phase space is a manifold and where a group of transformations acts on it transitively. The first and most important step is to define a mapping from the manifold into the set of self-adjoint operators on a Hilbert space, under suitable conditions. This mapping is called a Stratonovich–Weyl kernel. The construction of this mapping is discussed on coadjoint orbits of the one-dimensional Galilei, Poincaré, and Newton–Hooke groups as well as the two-dimensional Euclidean group.
Conformal invariance in a Dirac oscillator
Authors: Martínez-y-Romero R. P. , Salas-Brito A. L.
Published: July 2002

The conformal invariance properties of a Dirac oscillator are established. A set of operators is constructed whose algebra shows that it can be considered as a conformal system. The operators are then used to solve the problem using algebraic techniques. The superconformal generalization of the algebra is also worked out, and some consequences of these invariances for the properties of the model are mentioned.
The problem of exact interior solutions for rotating rigid bodies in general relativity
Authors: Wahlquist H. D.
Published: July 2002

The (3+1) dyadic formalism for timelike congruences is applied to derive interior solutions for stationary, axisymmetric, rigidly rotating bodies. In this approach the mathematics is formulated in terms of three-space-covariant, first-order, vector-dyadic, differential equations for a and Ω, the acceleration and angular velocity three-vectors of the rigid body; for T, the stress dyadic of the matter; and for A and B, the ‘‘electric’’ and ‘‘magnetic’’ Weyl curvature dyadics which describe the gravitational field. In the paper it is shown how an appropriate ansatz for the forms of these dyadics can be used to discover exact rotating interior solutions such as the perfect fluid solution first published in 1968. By incorporating anisotropic stresses, a generalization is found of that previous solution and, in addition, a very simple new solution that can only exist in toroidal configurations.
The projective unitary irreducible representations of the Poincaré group in 1+2 dimensions
Authors: Grigore D. R.
Published: July 2002

A complete analysis is given of the projective unitary irreducible representations of the Poincaré group in 1+2 dimensions applying the Mackey theorem and using an explicit formula for the universal covering group of the Lorentz group in 1+2 dimensions. Explicit formulas are given for all representations.
Differential geometric Poisson bivectors in one space variable
Authors: Doyle Philip W.
Published: July 2002

The connection of a nondegenerate k-weight differential geometric Poisson bivector is proved to be symmetric and integrable, for any k≥1. In the cases k=1,2,3, it is shown that the bivector has constant form if and only if its (2,0)-tensor is parallel. This is always the case if k=1, but is not generally true if k≥2. The normal forms for k=2 are described. A class of nondegenerate three-weight Poisson bivectors without constant form is described. Finally, it is proved that if the sum of two homogeneous bivectors is Poisson, then the bivectors are separately Poisson.
On the Bogoliubov transformation for quadratic boson observables
Authors: Maldonado Osvaldo
Published: July 2002

The diagonalization of Hermitian quadratic boson operators is studied in the equation of motion approach. The existence of a canonical transformation that diagonalizes such operators is discussed and an algorithm is sketched.
On the application of maximum entropy to the moments problem
Authors: Tagliani Aldo
Published: July 2002

The maximum-entropy approach to the solution of classical inverse problem of moments, in which one seeks to reconstruct a function p(x) [where x∈(0,+∞)] from the values of a finite set N+1 of its moments, is studied. It is shown that for N≥4 such a function always exists, while for N=2 and N=3 the acceptable values of the moments are singled out analytically. The paper extends to the general case where the results were previously bounded to the case N=2.
The half-Hartley and the half-Hilbert transform
Authors: Paveri-Fontana Stefano L. , Zweifel Paul F.
Published: July 2002

Inversion formulas are obtained for the restrictions of the Hartley and Hilbert transforms to R+. Regularity results are derived, and an illustrative example presented.
Partial fractions and bilateral summations
Authors: Chu Wenchang
Published: July 2002

Bilateral extensions of the hypergeometric formulas due to Minton (1970), Karlsson (1971), and Gasper (1981) are established through the decomposition of products of gamma functions into partial fractions. Some exceptional cases are demonstrated and a hypergeometric transformation from a bilateral series to a unilateral series is shown to contain Dougall’s summation formula for 2H2 as its special case.
Classification and construction of unitary topological field theories in two dimensions
Authors: Durhuus Bergfinnur , Jonsson Thordur
Published: July 2002

It is proven that unitary two-dimensional topological field theories are uniquely characterized by n positive real numbers λ1,...,λn, which can be regarded as the eigenvalues of a Hermitian handle creation operator. The number n is the dimension of the Hilbert space associated with the circle, and the partition functions for closed surfaces have the form Zg=∑ni=1λg−1i, where g is the genus. The eigenvalues can be arbitrary positive numbers. It is shown how such a theory can be constructed on triangulated surfaces.
Improved inequalities for one-electron moments of r
Authors: Brownstein K. R.
Published: July 2002

Let 〈r k〉=∫r kρr 2 dr be the kth moment of r for the one-electron radial density ρ(r). One obtains improved (Schwarz-like) inequalities for these moments if ρ is Nth-order monotonic, i.e., if dNρ/dr n is of one sign. These are of the form 〈r a〉〈rb〉≥GN(a,b)〈r(a+b)/2〉, where GN(a,b) increases with N. In particular for (a,b)=(1,−1), one obtains G0=1 (Schwarz inequality), G1=9/8 (as obtained by Gadre), and G∞=3/2 in the limit N→∞. One also obtains similarly improved (Gram-like) determinantal inequalities for r moments in terms of the order of monotonicity N. Several examples using published r moments are presented.
Geometric phase, bundle classification, and group representation
Authors: Mostafazadeh Ali
Published: July 2002

The line bundles that arise in the holonomy interpretations of the geometric phase display curious similarities to those encountered in the statement of the Borel–Weil–Bott theorem of the representation theory. The remarkable relationship between the mathematical structure of the geometric phase and the classification theorem for complex line bundles provides the necessary tools for establishing the relevance of the Borel–Weil–Bott theorem to Berry’s adiabatic phase. This enables one to define a set of topological charges for arbitrary compact connected semisimple dynamical Lie groups. These charges signify the topological content of the phase. They can be explicitly computed. In this paper, the problem of the determination of the parameter space of the Hamiltonian is also addressed. It is shown that, in general, the parameter space is either a flag manifold or one of its submanifolds. A simple topological argument is presented to indicate the relation between the Riemannian structure on the parameter space and Berry’s connection. The results about the fiber bundles and group theory are used to introduce a procedure to reduce the problem of the nonadiabatic (geometric) phase to Berry’s adiabatic phase for cranked Hamiltonians. Finally, the possible relevance of the topological charges of the geometric phase to those of the non-Abelian monopoles is pointed out.
Dually charged mesoatom on the space of constant negative curvature
Authors: Ivashchuk V. D. , Melnikov V. N.
Published: July 2002

The discrete spectrum solutions corresponding to dually charged mesoatom on the space of constant negative curvature are obtained. The discrete spectrum of energies is finite and vanishes when the magnetic charge of the nucleus exceeds the critical value.
Lagrangian dynamics for classical, Brownian, and quantum mechanical particles
Authors: Pavon Michele
Published: July 2002

In the framework of Nelson’s stochastic mechanics [E. Nelson, Dynamical Theories of Brownian Motion (Princeton University, Princeton, 1967); F. Guerra, Phys. Rep. 77, 263 (1981); E. Nelson, Quantum Fluctuations (Princeton University, Princeton, 1985)] we seek to develop the particle counterpart of the hydrodynamic results of M. Pavon [J. Math. Phys. 36, 6774 (1995); Phys. Lett. A 209, 143 (1995)]. In particular, a first form of Hamilton’s principle is established. We show that this variational principle leads to the correct equations of motion for the classical particle, the Brownian particle in thermodynamical equilibrium, and the quantum particle. In the latter case, the critical process q satisfies a stochastic Newton law. We then introduce the momentum process p, and show that the pair (q,p) satisfies canonical-like equations.
Quantization of a loop extended SU(2) affine Kac–Moody algebra
Authors: Lipiński Z.
Published: July 2002

A quantization of a Lie bialgebra structure on a loop extended SU■(2) algebra is considered. An asymptotic expansion for R-matrix is given.
Lie-series approach to the evolution of resonant and nonresonant anharmonic oscillators in quantum mechanics
Authors: Sáenz A. W.
Published: July 2002

A version of a normal-form method of Kummer and Gompa, analogous to the Lie-series methods of classical mechanics, is used to rigorously construct uniform long-time approximations to the quantum evolution of a system of resonant or nonresonant anharmonic oscillators. The Hamiltonian Hε governing the system is a self-adjoint operator in the Hilbert space H=L2(Rν) (ν⩾2), given formally by H0+εV. Here, H0 denotes the Hamiltonian of ν one-dimensional simple harmonic oscillators and εV their anharmonic coupling, ε⩾0 being a small parameter and V an operator of multiplication by a smooth function of polynomial growth at infinity. We treat the case in which an arbitrary number ρ⩾1 of the frequencies of these oscillators are rationally independent, imposing a standard diophantine condition on the independent frequencies if ρ⩾2. Under these assumptions, stated precisely in the paper, an Nth-order approximant ψN(t,ε) to the exact solution ψ(t,ε) of the Schrödinger equation idψ(t,ε)/dt=Hεψ(t,ε), satisfying the initial condition ψ(0,ε)=ψ0, is constructed recursively, where the initial state ψ0 belongs to a family of smooth functions dense in ℋ. The main result is that ψN(t,ε) differs in ℋ-norm from ψ(t,ε) by ⩽const εN+1|t| for t∈R and ε in an arbitrary compact interval [0,ε0]. This result is obtained by an approach simpler and quite different from that of Kummer and Gompa, and extends their work to oscillators with nonpolynomial couplings, under very general resonance conditions.
Vacuum expectation value asymptotics for second order differential operators on manifolds with boundary
Authors: Branson Thomas P. , Gilkey Peter B. , Vassilevich Dmitri V.
Published: July 2002

Let M be a compact Riemannian manifold with smooth boundary. We study the vacuum expectation value of an operator Q by studying TrL2Qe−tD, where D is an operator of Laplace type on M, and where Q is a second order operator with scalar leading symbol; we impose Dirichlet or modified Neumann boundary conditions.
Schlesinger–Bäcklund transformations for the N-component KP
Authors: van de Leur Johan
Published: July 2002

The n-component Kadomtsev–Petviashvili (KP) hierarchy was introduced by Sato as the set of deformation equations, i.e., Lax equations, of n+1n×n-matrix pseudodifferential operators. On such a set of operators we define a Schlesinger–Bäcklund transformation, which produces from a set of solutions of the KP hierarchy a new set of solutions. Applying such transformations recursively we obtain a whole family of solutions, from which we can then derive the KP tau function.
A generalized Hirota equation in 2+1 dimensions
Authors: Maccari Attilio
Published: July 2002

Using an asymptotically exact reduction method based on Fourier expansion and spatiotemporal rescaling, a new integrable and nonlinear partial differential equation (PDE) in 2+1 dimensions is obtained starting from the Kadomtsev–Petviashvili equation. We apply the reduction technique to the Lax pair of the Kadomtsev–Petviashvili equation and demonstrate the integrability property of the new equation, because we obtain the corresponding Lax pair. The new equation reduces to the Hirota equation in the 1+1-dimensional limit.
A general BRST approach to string theories with zeta function regularizations
Authors: Hwang Stephen , Marnelius Robert , Saltsidis Panagiotis
Published: July 2002

We propose a new general BRST approach to string and string-like theories that have a wider range of applicability than, e.g., the conventional conformal field theory method. The method involves a simple general regularization of all basic commutators, which makes all divergent sums expressible in terms of zeta functions from which finite values then may be extracted in a rigorous manner. The method is particularly useful in order to investigate possible state space representations to a given model. The method is applied to three string models: The ordinary bosonic string, the tensionless string, and the conformal tensionless string. We also investigate different state spaces for these models. The tensionless string models are treated in detail. Although we mostly rederive known results, they appear in a new fashion that deepens our understanding of these models. Furthermore, we believe that our treatment is more rigorous than most of the previous ones. In the case of the conformal tensionless string we find a new solution for d=4.
Derivation of the wave function collapse in the context of Nelson’s stochastic mechanics
Authors: Pavon Michele
Published: July 2002

The von Neumann collapse of the quantum mechanical wave function after a position measurement is derived by a purely probabilistic mechanism in the context of Nelson’s stochastic mechanics.
Cones and causal structures on topological and differentiable manifolds
Authors: Rainer M.
Published: July 2002

General definitions for causal structures on manifolds of dimension d+1>2 are presented for the topological category and for any differentiable one. Locally, these are given as cone structures via local (pointwise) homeomorphic or diffeomorphic abstraction from the standard null cone variety in Rd+1. Weak (𝒞) and strong (Cm) local cone (LC) structures refer to the cone itself or a manifold thickening of the cone, respectively. After introducing cone (C-)causality, a causal complement with reasonable duality properties can be defined. The most common causal concepts of space–times are generalized to the present topological setting. A new notion of precausality precludes inner boundaries within future/past cones. LC-structures, C-causality, a topological causal complement, and precausality may be useful tools in conformal and background independent formulations of (algebraic) quantum field theory and quantum gravity.
The structure, slip systems, and microhardness of C60 crystals
Authors: Lubenets S. V. , Natsik V. D. , Fomenko L. S. , Isakina A. P. , Prokhvatilov A. I. , Strzhemechny M. A. , Aksenova N. A. , Ruoff R. S.
Published: July 2002

The structure and microplasticity of high-purity fullerite C60 have been investigated comprehensively. The crystalline structure, lattice parameters, and phase transitions have been studied by x-ray diffractometry in the temperature range 30–293 K. It is found that the temperature corresponding to the orientational order–disorder phase transition is Tc=260 K. A considerable number of regions with stacking faults discovered in the samples leads to blurring of the fcc→sc phase transition in the temperature interval Tc±3 K. The a(T) dependences of the lattice parameter display peculiarities at the following characteristic temperatures: Tc at which the lattice parameter jump Δa/a=3.3×10−3 is observed, and the temperatures T0≃155 K, and Tg≃95 K which are associated with the beginning and end of molecular orientation freezing. It is shown that the formation of orientational glass is accompanied by a considerable increase in the width of x-ray reflections. The slip geometry and the temperature dependence of microhardness HV are studied in the temperature interval 81–293 K. It is shown that a system of the {111}〈110〉 type is the only slip system in the fcc and sc phases. The value of HV depends on the indentation plane: HV111>HV100. Below Tc, the microhardness increases abruptly (by approximately 30%). The temperature interval of this anomaly decreases after annealing of the crystal in vacuum. At T<T0, the HV(T) dependence becomes much stronger. It is shown that the hardness of C60 normalized to the elastic shear modulus is higher than the hardness of typical molecular crystals at comparable homologic temperatures.
Analysis of decomposition of impurity–helium solid phase
Authors: Boltnev R. E. , Gordon E. B. , Krushinskaya I. N. , Martynenko M. V. , Pelmenev A. A. , Popov E. A. , Khmelenko V. V. , Shestakov A. F.
Published: July 2002

The elemental composition of the impurity–helium solid phase (IHSP) grown by injecting of a gas jet containing Ne, Ar, Kr, and Xe atoms and N2 molecules into superfluid HeII is studied. The measured stoichiometric ratios S=NHe/NIm are much larger than the values predicted by the model of frozen together monolayer helium clusters. The theoretical possibility of freezing together of two-layered clusters is justified in the continual model of the helium subsystem of IHSP which fills the space between rigid impurity centers. Regularities of decomposition of “dry” samples (extracted from liquid helium) are analyzed in the temperature range 1.5–12 K under pressures from 10 to 500 torr. Two stages of sample decomposition are discovered: a slow stage accompanied by cooling and a rapid stage accompanied by heat release. These results suggest the presence of two types of helium in IHSP, viz., weakly bound and strongly bound helium which can be attributed respectively to the second and first coordination spheres of helium formed around heavy impurity particles. A tendency to elevation of the thermal stability of impurity–helium (IH) samples upon an increase in the mass of impurity center has been observed. An increase in the helium vapor pressure above the samples also increases their stability. It is found that the decomposition of IH samples containing nitrogen atoms in the temperature range 3–4.5 K is accompanied with luminescence induced by recombination of atoms. This indicates the possibility of a wide range of chemical reactions in solidified helium.
The structure and the orientational order parameter of Ar–CO2 solid solutions
Authors: Strzhemechny M. A. , Solodovnik A. A. , Kovalenko S. I.
Published: July 2002

Electron diffraction studies of the structural characteristics of Ar–CO2 solid solutions are carried out over the entire range of their mutual concentrations. The regions of low concentrations of both components are analyzed in detail and the relative excess volumes Δv/v are determined for the CO2 impurity in solid Ar (Δv/v≃0.8), and for the Ar impurity in solid CO2 (Δv/v≃0.28). The experimental results and relationships are compared with the results obtained from the semi-quantitative theory on the basis of known atom–atom potentials. An expression relating the intensity of superstructural reflections I(super) (including the reflection 210) with the long-range orientational order parameter η is obtained. It is found that I210∝η2 to a high degree of precision. The experimental dependence of the orientational order parameter η on the argon concentration in solutions rich in CO2 is obtained.
Influence of an orthodeuterium impurity on the thermal conductivity of solid parahydrogen
Authors: Korolyuk O. A. , Gorodilov B. Ya. , Krivchikov A. I. , Manzhelii V. G.
Published: July 2002

The thermal conductivity of solid parahydrogen with orthodeuterium impurity at an impurity concentration from 0.01 to 1% has been studied in the temperature range from 1.8 to 9 K. The nonlinear concentration dependence of the thermal resistivity of the investigated samples is explained by the fact that the intensity of normal three-phonon scattering processes is comparable to that of resistive processes. The analysis of the experimental results has been made in the framework of the Callaway model by using different models for the impurity phonon scattering. It has been found that the intensity of phonon impurity scattering in parahydrogen with orthodeuterium impurity is essentially higher than classical theory predicts and it is close to analogous scattering in solutions of helium isotopes with the equal reduced molar volume given. It is considered that additional impurity scattering of phonons is connected with the change of force constants and lattice distortion in the vicinity of impurity molecules. The quantitative estimation of the mentioned effects has been made.
Simulations of turbulent thermal convection
Authors: Sirovich L. , Balachandar S. , Maxey M. R.
Published: July 2002

A direct numerical simulation of thermal convection between horizontal plane boundaries has been performed, at a Rayleigh number Ra=9800 Rac, where Rac is the critical Rayleigh number for the onset of convection (Pr=0.72). The flow is found to be fully turbulent and analysis of the probability distributions for temperature fluctuations indicates that this is within the ‘‘hard turbulence’’ regime, as defined by the Chicago group. Good agreement is shown to exist between their experiments and the present simulation.