bluuebunny/crossref_metadata_2025 huggingface dataset:
Molecular hyperpolarizabilities of retinal derivatives
Authors: Bezerra A. G. , Gomes A. S. L. , da Silva-Filho D. A. , Acioli L. H. , de Araújo Cid B. , de Melo C. P.
Published: July 2002

We report measurements of the third-order optical susceptibilities of 13-cis and all-trans retinal derivatives in chloroform liquid solutions using the Z scan and the optical Kerr gate techniques, with laser pulses of 70 ps and 60 fs, at 532 and 800 nm, respectively. The corresponding second hyperpolarizabilities of those molecules are estimated and the results compared to those obtained from semiempirical time-dependent Hartree–Fock calculations. The observed trends for the values of the nonlinear response are explained in terms of the π electron delocalization along the polyenic chain of the molecules.
Modeling chain stiffness, fusion and specific interaction using hard nonadditive size interactions
Authors: Hamad Esam Z.
Published: July 2002

We suggest a general method of representing chain stiffness, segment fusion, ring rigidity, and specific forces using only nonadditive size interactions. The initial results of molecular dynamics simulations indicate ordering of stiff chains and micelle formation for chains with specific site–site interactions.
Quadrupolar and polar anisotropy in end-grafted α-helical poly(γ-benzyl-L-glutamate) on solid substrates
Authors: Chang Ying Chih , Frank Curtis W. , Forstmann Gerd G. , Johannsmann Diethelm
Published: July 2002

Using grazing incidence reflectance Fourier transform infrared spectroscopy (GIR-FTIR) and electro-optic (EO) measurements, we have determined the degree of quadrupolar and polar anisotropy in end-grafted α-helical poly(γ-benzyl-L-glutamate) (PBLG) chains. The results are compared to data obtained on spin-cast and on Langmuir–Blodgett–Kuhn (LBK) films. End-grafted films were prepared by a vapor-deposition-polymerization (VDP) scheme and have thicknesses of up to 70 nm. The quadrupolar order of VDP films, as estimated by the nematic order parameter S, is higher than in spin-cast and LBK films. This result indicates a preferentially perpendicular alignment of PBLG chains in VDP films. Furthermore, after the removal of the physisorbed chains from the grafted films by intensive washing with solvent, the quadrupolar order is lowered while the polar order increases significantly, suggesting that the physisorbed chains might form anti-parallel pairs with the surface-grafted chains.
CO-oxidation model with superlattice ordering of adsorbed oxygen. I. Steady-state bifurcations
Authors: James E. W. , Song C. , Evans J. W.
Published: July 2002

We analyze a model for CO oxidation on surfaces which incorporates both rapid diffusion of adsorbed CO, and superlattice ordering of adsorbed immobile oxygen on a square lattice of adsorption sites. The superlattice ordering derives from an “eight-site adsorption rule,” wherein diatomic oxygen adsorbs dissociatively on diagonally adjacent empty sites, provided that none of the six additional neighboring sites are occupied by oxygen. A “hybrid” formalism is applied to implement the model. Highly mobile adsorbed CO is assumed randomly distributed on sites not occupied by oxygen (which is justified if one neglects CO–CO and CO–O adspecies interactions), and is thus treated within a mean-field framework. In contrast, the distribution of immobile adsorbed oxygen is treated within a lattice–gas framework. Exact master equations are presented for the model, together with some exact relationships for the coverages and reaction rate. A precise description of steady-state bifurcation behavior is provided utilizing both conventional and “constant-coverage ensemble” Monte Carlo simulations. This behavior is compared with predictions of a suitable analytic pair approximation derived from the master equations. The model exhibits the expected bistability, i.e., coexistence of highly reactive and relatively inactive states, which disappears at a cusp bifurcation. In addition, we show that the oxygen superlattice ordering produces a symmetry-breaking transition, and associated coarsening phenomena, not present in conventional Ziff–Gulari–Barshad-type reaction models.
Experimental investigation of large nitrogen cluster scattering from graphite: Translational and rotational distributions of evaporated N2 molecules
Authors: De Martino A. , Châtelet M. , Pradère F. , Fort E. , Vach H.
Published: July 2002

We present experimental results on the translational and rotational energy transfers due to the collisions of large (N2)n clusters with a highly oriented pyrolytic graphite sample at 750 ms−1 incident velocity, for two surface temperatures Ts (440 and 580 K), for average cluster sizes n from 200 to 1000 monomers, and for incidence angles θi from 30° to 70°. Angular distributions of flux and angularly resolved time-of-flight profiles of scattered particles are measured with a quadrupole mass spectrometer while rotational state distributions are determined by resonantly enhanced multiphoton ionization. For all incidences but the largest (70°) the translational distributions of scattered molecules recorded at detection angles θd from 20° to 70° are compatible with a simple thermokinetic model assuming that monomer evaporation occurs at a well-defined temperature Tloc from the cluster gliding on the solid surface. Fits of the translational data yield Tloc values between 250 and 500 K, increasing with Ts and decreasing with n and θi. On the other hand, the rotational distributions are always non-Boltzmann. Actually, they are well described as sums of two contributions, at 75 and 375 K, respectively. The relative weight of the cold contribution is found to increase with θd, with a slope increasing with θi. Possible interpretations of the observed differences between translational and rotational degrees of freedom of evaporated molecules are discussed.
Structure of droplet microemulsions in the semi-dilute regime
Authors: Guerra C. , Somoza A. M. , Telo da Gama M. M.
Published: July 2002

We derive a functional of the microemulsion droplets size distribution function by adding the entropic free energy of a system of polydisperse hard spheres to the Helfrich interfacial free energy of the amphiphilic film. The latter is minimized by a monodisperse system of spherical (independent) aggregates, at the equilibrium radius, while the former is minimized by a random distribution of droplet sizes. As a result the equilibrium droplet size distribution yields a mean radius that is smaller than the equilibrium radius of isolated droplets. A link with molecular parameters is established by using our microscopic model for ternary amphiphilic mixtures and a (mean-field) free energy functional of the density profiles [J. Chem. Phys. 109, 1152 (1998)] to calculate the parameters of the Helfrich interfacial free energy for a single droplet. The theoretical results are compared with small-angle neutron scattering data reported by Gradzielski et al. [Phys. Rev. E 53, 3900 (1996)].
Boundary condition determined wave functions for the ground states of one- and two-electron homonuclear molecules
Authors: Patil S. H. , Tang K. T. , Toennies J. P.
Published: July 2002

Simple analytical wave functions satisfying appropriate boundary conditions are constructed for the ground states of one-and two-electron homonuclear molecules. Both the asymptotic condition when one electron is far away and the cusp condition when the electron coalesces with a nucleus are satisfied by the proposed wave function. For H2+, the resulting wave function is almost identical to the Guillemin–Zener wave function which is known to give very good energies. For the two electron systems H2 and He2++, the additional electron–electron cusp condition is rigorously accounted for by a simple analytic correlation function which has the correct behavior not only for r12→0 and r12→∞ but also for R→0 and R→∞, where r12 is the interelectronic distance and R, the internuclear distance. Energies obtained from these simple wave functions agree within 2×10−3 a.u. with the results of the most sophisticated variational calculations for all R and for all systems studied. This demonstrates that rather simple physical considerations can be used to derive very accurate wave functions for simple molecules thereby avoiding laborious numerical variational calculations.
Computational study of molecular hydrogen in zeolite Na-A. I. Potential energy surfaces and thermodynamic separation factors for ortho and para hydrogen
Authors: Anderson Cherry-Rose , Coker David F. , Eckert Juergen , Bug Amy L. R.
Published: July 2002

We simulate H2 adsorbed within zeolite Na-A. We use a block Lanczos procedure to generate the first several (9) rotational eigenstates of the molecule, which is modeled as a rigid, quantum rotor with an anisotropic polarizability and quadrupole moment. The rotor interacts with Na cations and O anions; interaction parameters are chosen semiempirically and the truncation of electrostatic fields is handled with a switching function. A Monte Carlo proceedure is used to sample a set of states based on the canonical distribution. Potential energy surfaces, favorable adsorbtion sites, and distributions of barriers to rotation are analyzed. Separation factors for ortho–parahydrogen are calculated; at low temperatures, these are controlled by the ease of rotational tunneling through barriers.
The electric-field-gradient-induced birefringence of Helium, Neon, Argon, and SF6
Authors: Coriani Sonia , Hättig Christof , Rizzo Antonio
Published: July 2002

The results of an investigation of the electric-field-gradient-induced birefringence of the noble gases He, Ne, Ar and of the octahedral system SF6 are presented. For all these systems the induced anisotropy of the refractive index is related to the sole temperature-independent contribution b(ω), a combination of quadratic response functions. These hyperpolarizabilities, as well as their dispersion coefficients to seventh order, are calculated at the optical experimental frequency by the CCSD response approach. The dispersion coefficients are used to determine the curve of b(ω) in the normal dispersion region. We show that for atoms the dipole–dipole–quadrupole and the dipole–dipole–magnetic dipole contributions to the dispersion coefficients of b(ω) have intimate relations to the Cauchy moments and to the dispersion coefficients for the Verdet and the Cotton–Mouton constants.
Comment on “Reaction cross sections for the H+D2 (v=0,1) system for collision energies up to 2.5 eV: A multiconfiguration time-dependent Hartree wave-packet propagation study” [J. Chem. Phys. 110, 241 (1999)]
Authors: Aoiz F. J. , Bañares L. , Castillo J. F. , Herrero V. J.
Published: July 2002

Exact quantum mechanical (QM) scattering calculations for the H+D2 (v=0, j=0−2) reaction at 0.54 eV collision energy on the LSTH potential energy surface show that the reactivity increases with increasing initial j, in agreement with previous quasiclassical trajectory data, and in contrast with the time-dependent QM calculations by Jäckle et al. using the coupled states approximation.
Response to “Comment on ‘Surface diffusion near the points corresponding to continuous phase transitions’ ” [J. Chem. Phys. 111, 11232 (1999)]
Authors: Uebing C. , Zhdanov V. P.
Published: July 2002

We show that (i) the comment on our paper by I. Vattulainen, S. C. Ying, T. Ala-Nissila, and J. Merikoski [J. Chem. Phys. (submitted)] does not contain any new physics compared to that discussed earlier in our and their publications, and (ii) their attempts to criticize our choice of the dynamics for describing oxygen diffusion on the W(110) surface are senseless.
Dipole–dipole interactions among CH3Cl molecules on Ru(001): Correlation between work function change and thermal desorption studies
Authors: Livneh T. , Lilach Y. , Asscher M.
Published: July 2002

Work function change measurements (ΔΦ) combined with temperature programmed desorption (TPD) were employed to study layer growth mechanism and the CH3Cl dipole–dipole interactions on Ru(001), over the temperature range of 97 K–230 K. The activation energy for desorption (Ea) and the molecular dipole moment (μ) both decrease from 55.9 kJ/mol and 2.44 D, at the zero coverage limit, to 38.6 kJ/mol and 1.27 D, at one monolayer. This coverage dependence originates from strong dipolar lateral repulsion among neighbor CH3Cl molecules. Using a model introduced by Maschhoff and Cowin (MC) [J. Chem. Phys. 101, 8138 (1994)], the isolated adsorbed molecule’s dipole moment, μ0 (2.35 D) and polarizability α(8.1×10−24 cm3), were extracted from TPD data. These values agree very well with μ0 (2.12 D) and α(9.2×10−24 cm3) obtained from work function change measurements by employing the same MC model. The ability to simulate both TPD and work function change data over a wide coverage range within the framework of a single electrostatic model has been demonstrated. It enabled better understanding of fine details of surface dipolar interactions.
Chemiluminescent reactions of excited calcium atoms with HCl and HBr: Selective charge-transfer “harpooning” and synchronized intermediate complex rearrangement
Authors: De Castro Miguel , Candori Roberto , Pirani Fernando , Aquilanti Vincenzo , Garay Macarena , González Ureña Angel
Published: July 2002

A “harpooning” mechanism is investigated for the chemiluminescent reactions of Ca*(1D2) atoms with HCl (leading to CaCl* in the A state) and with HBr (leading to CaBr* in both the A and B states). A model of the interactions in the entrance channels, which involves an electron jump and leads to a charge-transfer intermediate complex, accounts for the selective dependence of reactivity on the relative orientation between the molecule and the outer electronic orbital of the atom. The dynamical treatment incorporates in the Landau–Zener approach the synchronization between times for nonadiabatic transitions and for triggering the rearrangement of the intermediate collision complex. The treatment accounts for the observed features of the translational energy dependence of the cross sections: The steep initial increase with a pronounced maximum, the sharp decline and also fine details, such as a stairlike behavior.
Comment on “Calculation of ab initio dynamic hyperpolarizabilities of polymers” [J. Chem. Phys. 110, 2717 (1999)]
Authors: Jacquemin Denis , Champagne Benoı̂t
Published: July 2002

We evaluate the static and dynamic electronic longitudinal polarizability and first hyperpolarizability of infinite poly-water by using the same geometry, the same orientation and the same basis set as Otto et al. but by applying the finite oligomer technique. We show that for the first hyperpolarizability, the polymeric values per unit cell calculated by Otto et al. are inconsistent by several orders of magnitude with respect to the infinite oligomer limit.
New generalized gradient approximation functionals
Authors: Boese A. Daniel , Doltsinis Nikos L. , Handy Nicholas C. , Sprik Michiel
Published: July 2002

New generalized gradient approximation (GGA) functionals are reported, using the expansion form of A. D. Becke, J. Chem. Phys. 107, 8554 (1997), with 15 linear parameters. Our original such GGA functional, called HCTH, was determined through a least squares refinement to data of 93 systems. Here, the data are extended to 120 systems and 147 systems, introducing electron and proton affinities, and weakly bound dimers to give the new functionals HCTH/120 and HCTH/147. HCTH/120 has already been shown to give high quality predictions for weakly bound systems. The functionals are applied in a comparative study of the addition reaction of water to formaldehyde and sulfur trioxide, respectively. Furthermore, the performance of the HCTH/120 functional in Car–Parrinello molecular dynamics simulations of liquid water is encouraging.
A quantum model Hamiltonian to treat reactions of the type X+YCZ3→XY+CZ3: Application to O(3P)+CH4→OH+CH3
Authors: Palma Juliana , Clary David C.
Published: July 2002

In this paper we present a model Hamiltonian to treat the dynamics of reactions of the general type X+YCZ3→XY+CZ3, where the CZ3 group has C3v symmetry. The main assumption of the model is that CZ3 maintains its symmetry during the reaction. The Hamiltonian we derive can be used as the starting point for more simplified models. We present here one of these simpler models and use it to study the role of the umbrella vibrational motion in the reaction O(3P)+CH4→OH+CH3. Finally, we compare our results with previous theoretical and experimental results.
Rotational spectra and dynamics of the van der Waals adducts of neon and argon with 1,1-difluoroethylene
Authors: Dell’Erba Adele , Melandri Sonia , Millemaggi Aldo , Caminati Walther , Favero Paolo G.
Published: July 2002

The free jet millimeter wave spectra of the complexes of Ne and Ar with 1,1-difluoroethylene are reported. Information on the equilibrium configurations, dynamics, and dissociation energies of these weakly bonded complexes are obtained from their nonrigidity. The vibrational doubling (0.78 MHz) of the rotational transitions of 1,1-difluoroethylene–Ne has been useful in scaling the ab initio potential energy function calculated for the tunneling of Ne above and below the plane of 1,1-difluoroethylene. This motion is hindered by a barrier of about 36 cm−1 at the planar C2v configuration.
Calculation of the vibrational wave function of polyatomic molecules
Authors: Åstrand Per-Olof , Ruud Kenneth , Taylor Peter R.
Published: July 2002

A modified perturbation approach for the calculation of the vibrational wave function of polyatomic molecules is discussed. It is demonstrated that if the expansion point of the potential is determined variationally, the leading first-order term in the perturbation expansion of the vibrational wave function vanishes. Furthermore, the new expansion point is a very good approximation to the vibrationally averaged molecular geometry. The required third derivatives of the potential energy with respect to geometrical distortions have been calculated by numerical differentiation. Two approaches are discussed, one based on the differentiation of the molecular Hessian and the other on the molecular gradient. Results are presented for the averaged molecular geometry of a large set of molecules, including studies of electronically excited states and effects of electron correlation. The largest molecule included is butane with a total of 14 atoms.
Phase transitions in an associating, network-forming, Lennard-Jones fluid in slit-like pores. II. Extension of the density functional method
Authors: Huerta Adrian , Pizio Orest , Sokołowski Stefan
Published: July 2002

We study adsorption of hydrogen-bonded fluids in slit-like pores with strongly attractive walls, in the framework of the four-site associating Lennard-Jones model. The density profiles, as well as the phase behavior, are obtained by using a density functional method. We have found that, at temperatures lower than the critical temperature of the bulk fluid, the confined fluid undergoes one or more layering transitions dependent on the pore width, followed by capillary condensation. Each of the transitions is localized by analyzing the grand thermodynamic potential. The density profiles of nonbonded and differently bonded particles demonstrating changes of the structure of the fluid in the pore along the coexistence are discussed briefly. The critical temperature for capillary condensation is lower for confined fluid, compared with that for the bulk liquid–vapor transition, as expected. However, an increase of the energy of association between fluid species increases the critical temperatures for layering transitions and for capillary condensation. The envelope of the capillary condensation is narrower than the bulk liquid–vapor phase diagram. The ratio between the critical temperatures for layering transitions and capillary condensation depends on the pore width. The critical temperature for the second layering is always lower than for the first one. The triple point temperature between either the second layering transition and the capillary condensation (in wider pores) or the first layering transition and the capillary condensation (in narrower pores) increases with decreasing pore width. The triple point temperature between the layering transitions is much lower than the relevant temperature between the second layering transition and the capillary condensation. The triple point temperatures also depend on the association energy. We have shown that highly bonded fluid species prevail at triple point temperatures.
Ammonia adsorption by hydrogen bond on ice and its solvation
Authors: Ogasawara Hirohito , Horimoto Noriko , Kawai Maki
Published: July 2002

Regarding the solvation of molecules to water, the adsorption of molecules on the water surface has mostly been considered. Here we provide spectroscopic evidence for the adsorption and solvation behavior of ammonia on the ultra thin ice film surface formed on Ru(001) by the use of infrared reflection absorption and thermal desorption spectroscopies. Here we prove that the solvation of ammonia involves two steps. They are the hydrogen bond adsorption and the transfer into bulk. The hydrogen bonding adsorbed ammonia on ultra thin ice film in a NH3 form is evidenced for the first time. Upon heating, bulk transfer upon a conversion to a NH4+ form is observed for this hydrogen bonded species, however it is not for bilayer and multilayer species. © 2000 American Institute of Physics.
Ground and excited Hubbard states for buckminsterfullerene with uniform and alternating bond strengths
Authors: Flocke N. , Schmalz T. G. , Klein D. J.
Published: July 2002

A detailed investigation on the π-electronic ground and lowest excited g- and u-symmetrical singlet and triplet states of icosahedral C60 is performed in the framework of the semiempirical Hubbard model using single and double excited configuration interaction (SDCI) upon an appropriately chosen reference space constructed out of Hartree–Fock-type molecular orbitals. We present SDCI results for energies, wave-function symmetries, bond orders and spin–spin correlations for these states. For the ground state, second order Mo/ller–Plesset (MP2) and size-consistency corrected energies are presented and compared with Monte Carlo results. We also examine the influence of bond length alternation on the calculated properties. It is shown that within the Hubbard model the lowest excited g and u singlet and triplet states of C60 give very similar overall bond orders and spin–spin correlations.
Orientational averaging in the intense field tunnel ionization of molecules
Authors: DeWitt Merrick J. , Prall Bradley S. , Levis Robert J.
Published: July 2002

The effect of molecular structure and orientation on the rate of tunnel ionization in intense laser fields is considered for linear molecules. The nonspherical nature of the molecular electrostatic potential near the classical electron turning point results in a nonisotropic distribution of tunneling rates. This must be considered when determining the overall ionization rate of a randomly oriented ensemble. Calculations are performed for two atom:molecule test pairs with similar ionization potential, Ar:N2 and Xe:O2, and the results are compared to experiments [Talebpour, Chien, and Chin, J. Phys. B 29, L677 (1996); Guo et al., Phys. Rev. A 58, R4271 (1998)].
Morphisms of crystallographic groups: Kernels and images
Authors: Senechal Marjorie
Published: July 2002

The crystallographic groups play an important role in solid state physics, where their representations are of particular interest. In this paper we classify the kernels of all possible representations by deriving necessary and sufficient conditions for a subgroup H of a crystallographic group G to be invariant. The structure of G/H is also discussed. A list of the one- and two-dimensional invariant subgroups of the two-dimensional crystallographic groups is appended as Table I; it includes the structural features of these subgroups needed for determining their settings, relative to the parent groups, and identifies the corresponding images. Table II is a list of the commutator subgroups of the two-dimensional groups.
Solution of the Cauchy problem for a generalized sine–Gordon equation
Authors: Boiti Marco , Leon Jérôme J. P. , Pempinelli Flora
Published: July 2002

We consider a spectral problem generating a hierarchy of nonlinear evolution equations including the sine-Gordon equation and a physically interesting generalization in the laboratory coordinates. The direct and inverse problems are treated. The time evolution of the spectral data is explicitly given and, therefore, the Cauchy problem for the related equations is solved.
Nonlocal Lie–Bäcklund transformations of the massive Thirring model
Authors: Kersten Paul H. M. , Martini Ruud
Published: July 2002

Previously we obtained second- and third-order Lie–Bäcklund transformations of the massive Thirring model. Now by introduction of nonlocal variables we obtain two (x,t)-dependent Lie–Bäcklund transformations. These nonlocal Lie–Bäcklund transformations act as generating operators on first- and second-order Lie–Bäcklund transformations, and we conjecture that they lead to two infinite hierarchies of commuting Lie–Bäcklund transformations.
Characteristic functional structure of infinitesimal symmetry mappings of classical dynamical systems. III. Systems with cyclic variables
Authors: Katzin Gerald H. , Levine Jack
Published: July 2002

This paper is a continuation of previous papers I and II with similar titles [J. Math. Phys. 26, 3080, 3100 (1985)]. In those papers a theory was developed that described the characteristic functional structures of infinitesimal symmetry mappings of systems of first- or second-order dynamical equations. Now an investigation is made of how cyclic variables of the dynamical equations affect the symmetry equations and thereby propagate through the theory to influence the form of the characteristic functional structure of the symmetries. These special symmetries, which have a particularly simple form, are characterized by infinitesimal point mappings in which only cyclic coordinates are varied, with the variation essentially determined by constants of motion of the dynamical system. For Lagrangian systems with cyclic coordinates these special symmetry mappings include the well-known Noether symmetries characterized by constant variation of the cyclic coordinates.
On exomorphic types of phase transitions
Authors: Litvin D. B. , Fuksa J. , Kopsky V.
Published: July 2002

An algorithmic method is presented to determine the irreducible representations that engender the irreducible representations associated with phase transitions involving a change of symmetry to a subgroup of index n. This method is based on the work of Ascher and Kobayashi [E. Ascher and J. Kobayashi, J. Phys. C 10, 1349 (1977)] and the derivation of faithful irreducible representations contained in the permutation representation of transitive subgroups of permutation groups Sn. Character tables of all such irreducible representations, and their epikernels, associated with a change in symmetry to a subgroup of index n=2, 3, 4, 5, and 6 are given explicitly. The relationship to exomorphic types of phase transitions is then discussed. The irreducible representations associated with the phase transitions O1h to C14v in BaTiO3 and D46h to D162h in β-K2SO4 are derived and it is shown that these two phase transitions belong to the same exomorphic type.
Newman–Penrose constants for zero-rest-mass fields on Minkowskian space-time
Authors: Hogan P. A.
Published: July 2002

It is proved that the Newman–Penrose constants associated with zero-rest-mass spin-1 fields on Minkowskian space-time are inherited from the Newman–Penrose constants associated with the complex wave function from which these fields are constructed. This latter construction is also given and a possible extension of these results to spin-s (=0,1,2,...) fields is indicated.
Clebsch–Gordan coefficients for SU(5) unification models
Authors: del Olmo M. A. , Patera J. , Rodriquez M. A. , Rousseau C.
Published: July 2002

The Clebsch–Gordan coefficients for the product (1001)⊗(1001), where (1001) is the adjoint representation of SU(5), with respect to the group basis and the subgroup basis in the reduction SU(5)⊇SU(3)×SU(2)×U(1) are computed. One of the basic tools in this computation is the exhaustive use of the Verma algorithm to find bases for the weight subspaces of dimension higher than 1. It allows for the construction of bases in a systematic way by using the so-called Verma inequalities. Only the coefficients for the dominant weights are calculated. The other ones can be obtained by using the elements of finite order (charge conjugation operators) of SU(5).
Comment on ‘‘On a property of a classical solution of the nonlinear mass transport equation u
t=u
x
x/1+u
x 2. II’’ [J. Math. Phys. 2
8, 536 (1987)]
Authors: Kitada Akihiko
Published: July 2002

A mechanism of smoothing due to evaporation condensation of the roughly perturbed surface of a solid is formulated as a Cauchy problem in the real line R1 for the equation ut =uxx/1 +ux2, which describes the evolution of the profile u(x,t) of the surface. In the preceding paper [A. Kitada and H. Umehara, J. Math. Phys. 28, 536 (1987)], it was demonstrated that, if the solution u(x,t) of the Cauchy problem is obtained in the classical sense with an additional restriction u∈C3(R1×(0,∞)), each peak in the surface decreases in height with time in the strict sense. In the present paper, by modifying the proof, it is shown that the additional restriction to the classical solution is excessive.
Totally vicious space-times and reflectivity
Authors: Matori Yoshihiro
Published: July 2002

A reflecting space-time with a closed timelike curve is proved to be totally vicious. In contrast with this, it is shown that there exists a compact space-time that is not totally vicious.
Yang–Mills equations and solvable groups. II
Authors: Cahen M. , Gutt S. , Kozameh C. , Newman E. T.
Published: July 2002

It is shown that the necessary and sufficient condition for the Yang–Mills equations (associated with an arbitrary group G) to be derivable from a Lagrangian (which is polynonial in the derivatives of the connection) is that the Lie algebra ℊ of G possesses an invariant nondegenerate quadratic form γ. It is well known that for semisimple groups such a γ exists, namely the Killing form. What is not so well known is that such a γ exists for many other groups and in particular for many solvable and nilpotent groups. Several examples in this class are discussed.
N=2 supersymmetric Ward identities on the harmonic superspace
Authors: Lhallabi T.
Published: July 2002

The quantization of N=2 supersymmetric Yang–Mills theory coupled to a matter hypermultiplet has been done in the harmonic superspace by requiring BRS and anti-BRS invariances. The corresponding Ward identities have also been derived.
On the Gribov ambiguity in the Polyakov string
Authors: Jaskolski Z.
Published: July 2002

The global aspects of the gauge fixing in the Polyakov path integral for the bosonic string are considered within the Ebin–Fischer–Mareden approach to the geometry of spaces of Riemannian metrics and conformal structures. It is shown that for surfaces of higher genus, the existence of local conformal gauges is sufficient to derive the globally defined integral over the Teichmüller space. The generalized Faddeev–Popov procedure for incomplete gauges is formulated and used to derive the global expression for the Polyakov path integral in the cases of torus and sphere. The Gribov ambiguity in the functional integral over surfaces without boundary can be successfully overcome for arbitrary genus.
Bounds for the C*-algebraic transition probability yield best lower and upper bounds to the overlap
Authors: Alberti Peter M. , Heinemann Volker
Published: July 2002

Bounds are proved for the C*-algebraic transition probability PA(ω,ν) between the abstract ground state ν with respect to a symmetric subspace N of a unital C* algebra A and a state ω with the restriction ω‖N=σ‖N to N for an arbitrarily given, but fixed state σ. A is assumed to be the unital C*-algebra generated by N. The results are specified in the case where A is a subalgebra of a vN algebra in standard form and N is dimensionally finite. Under these assumptions, the relationships of the algebraic transition probability to the notion of the (square of the) overlap integral known in quantum physics are clearly established. The general results are used to treat the standard problem of finding upper and lower bounds to the overlap in a quantum mechanical context. The best bounds are found and their properties discussed.
The delta expansion in zero dimensions
Authors: Cho Hing Tong , Milton Kimball A. , Pinsky Stephen S. , Simmons L. M.
Published: July 2002

The recently introduced δ-expansion (or logarithmic-expansion) technique for obtaining nonperturbative information about quantum field theories is reviewed in the zero-dimensional context. There, it is easy to study questions of analytic continuation that arise in the construction of the Feynman rules that generate the δ series. It is found that for six- and higher-point Green’s functions, a cancellation occurs among the most divergent terms, and that divergences that arise from summing over an infinite number of internal lines are illusory. The numerical accuracy is studied in some detail: The δ series converges inside a circle of radius one for positive bare mass squared, and diverges if the bare mass squared is negative, but in all cases, low-order Padé approximants are extremely accurate. These general features are expected to hold in higher dimensions, such as four.
Wigner’s little group and decomposition of Lorentz transformations
Authors: Vassiliadis Dimitris V.
Published: July 2002

It is shown how an arbitrary Lorentz transformation can be expressed in terms of elements of Wigner’s little group and its cosets. This yields a natural parametrization for the little group, while its coset members turn out to be helicity-preserving transformations. The associated Wigner angle and its relation to the actual change in helicity are discussed. Finally, the extension to zero-mass particles shows how the little group becomes a gauge transformation in that limit.
The Helmholtz conditions in terms of constants of motion in classical mechanics
Authors: Pardo Francisco
Published: July 2002

The Helmholtz conditions are the necessary and sufficient conditions for a set of second-order differential equations to be equivalent to a variational principle. In this work an alternative approach to the inverse problem in classical mechanics is described. It is proven that the Helmholtz conditions can be transformed into a set of conditions for a nonsingular antisymmetric matrix whose entries are constants of motion of the problem in question.
Fokker–Wheeler–Feynman interactions without integrals
Authors: Stephas Paul
Published: July 2002

The conserved quantities associated with Fokker–Wheeler–Feynman interactions between two particles are usually presented in terms of arbitrary times t1 and t2 for particles one and two, respectively; these conserved quantities involve integrals over the world lines of the particles. These integrals are evaluated so as to yield integral-free conserved quantities, with a resulting shift in focus to one particle at arbitrary time t1 and the second particle at the t1-related times of t2 (retarded) and t2 (advanced).
Relativistic fluids and metric symmetries
Authors: Duggal K. L.
Published: July 2002

This paper deals with fluid space-times within the framework of general relativity and subject to a metric symmetry (self-similarity and conformal or conformal collineation). Via the investigation of the kinematic properties of such fluids, it is shown that the conformal collineation symmetry plays the important role of smooth transition at the boundary of a change in the fluid pattern (such as shear-free and isotropic to distorted fluids). As applications, it is shown that the study is relevant to the radiationlike viscous fluid Friedman–Robertson–Walker model, with the conformal collineation symmetry vector parallel to its tilted velocity vector. Also, the results lead to physically significant material curves (a curve that moves with the fluid as the fluid evolves) in the fluid.
Affine structure and isotropy imply Minkowski space-time and the orthochronous Poincaré group
Authors: Schutz John W.
Published: July 2002

Minkowski space-time is characterized in terms of affine structure and a property of isotropy with respect to the path of a single freely moving observer. It can then be shown that the property of isotropy applies for all freely moving observers, and that the associated isotropy mappings generate the orthochronous Poincaré group.
Affine fields and operator representations for the nonlinear σ model
Authors: Isham Christopher J. , Klauder John R.
Published: July 2002

The problem of operator representations and associated Hamiltonians for quantum fields and their conjugates appropriate to the nonlinear σ model is discussed. To respect the target-space constraints, canonical field momenta are rejected in favor of alternative affine conjugate fields that serve to generate constraint-preserving group transformations in the target space. Various operator representations are discussed at length, some of which do not admit canonically conjugate fields. After establishing certain general properties for Hamiltonians, there is an analysis of how operator field representations and Hamiltonians can be linked.
Rough surfaces and the renormalization group
Authors: Dashen Roger , Orris Gregory J.
Published: July 2002

Perturbative techniques are used to derive a renormalization group equation for a free scalar field in a domain with rough boundaries and mixed boundary conditions. It is found that to second order in the surface height the boundary conditions scale not only as the perturbed area, but also with a nonlinear term that arises from matching orders of surface height in the perturbation series for the field amplitude.
On the mixing-enhancing structure of a class of quantum dynamical semigroups
Authors: Benatti Fabio
Published: July 2002

A sufficient condition for a dissipative evolution to give rise to an ever more chaotic state is obtained and the structure of the corresponding density matrix is studied. As a byproduct, the equation of motion in the Schrödinger picture is, in some cases, explicitly solved.
Initial value formulation for the spherically symmetric dust solution
Authors: Liu Hongya
Published: July 2002

An initial value formulation for the dust solution with spherical symmetry is given explicitly in which the initial distributions of dust and its velocity on an initial surface are chosen to be the initial data. As special cases, the Friedmann universe, the Schwarzschild solution in comoving coordinates, and a spherically symmetric and radially inhomogeneous cosmological model are derived.
Semiclassical Jaynes–Cummings model, Painlevé test, and exact solutions
Authors: Steeb W.-H. , Euler N. , Mulser P.
Published: July 2002

The semiclassical model equations for a quantum system of N two-level atoms interacting with a single-mode field in a resonant cavity are discussed. For this system of ordinary differential equations the Painlevé test is performed and first integrals are found. It is also shown that exact solutions can be found with the help of the Painlevé test.
Commutative differential operator and a class of solutions for the BKP equation on the singular rational curve
Authors: Chowdhury A. Roy , Gupta N. Das
Published: July 2002

The technique of Krichever and Novikov was used to construct a new class of solutions for the BKP equation. This class contains the solitary waves as a special case, and also a class of rational solutions. The present methodology overcomes the difficulty associated with the Gelfand–Levitan equation of the BKP system, as pointed out by Hirota [J. Phys. Soc. Japan 58, 2705 (1989)]. An added advantage of the Krichever–Novikov approach is that it also gives a straightforward derivation of the BKP equation.
On the non-Lie reduction of the nonlinear Dirac equation
Authors: Fushchich W. I. , Zhdanov R. Z.
Published: July 2002

The method of construction of exact solutions of nonlinear spinor equations based on their conditional (non-Lie) symmetry is suggested. With the help of this method new ansätze that reduce the nonlinear Poincaré-invariant Dirac equation to ordinary differential equations are constructed. The new family of exact solutions of the nonlinear Dirac equation with scalar self-interaction is found.
Local symplectic operators and structures related to them
Authors: Dorfman I. Ya , Mokhov O. I.
Published: July 2002

Matrices with entries being differential operators, that endow the phase space of an evolution system with a (pre)symplectic structure are considered. Special types of such structures are explicitly described. Links with integrability, geometry of loop spaces, and Bäcklund transformations are traces.
Proper special conformal Killing vectors and the quadratic theory of gravity
Authors: Sharma Ramesh
Published: July 2002

If a space-time admits a proper (nonhomothetic) special conformal Killing vector (SCKV) and the space-time solution in the quadratic theory of gravity inherits the conformal symmetry due to SCKV then, besides other results, it is shown that the only perfect fluid solution of such a space-time is either the stiff matter or a curvature fluid.
Helicity-supersymmetry of dyons
Authors: Bloore F. , Horváthy P. A.
Published: July 2002

The ‘‘dyon’’ system of D’Hoker and Vinet, consisting of a spin 1/2-particle with anomalous gyromagnetic ratio 4 in the combined field of a Dirac monopole plus a Coulomb plus a suitable 1/r2 potential (which arises in the long-range limit of a self-dual monopole), is studied following Biedenharn’s approach to the Dirac–Coulomb problem: the explicit solution is obtained using the ‘‘Biedenham–Temple operator,’’ Γ, and the extra twofold degeneracy is explained by the subtle supersymmetry generated by the ‘‘monopole helicity’’ or generalized ‘‘Johnson–Johnson–Lippmann’’ operator ℛ. The new supersymmetry anticommutes with the chiral one discussed in previous papers.
Lagrangians for differential equations of any order
Authors: Hojman Sergio , Pardo Francisco , Aulestia Luis , de Lisa Francisco
Published: July 2002

In this work the inverse problem of the variational calculus for systems of differential equations of any order is analyzed. It is shown that, if a Lagrangian exists for a given regular system of differential equations, then it can be written as a linear combination of the equations of motion. The conditions that these coefficients must satisfy for the existence of an S-equivalent Lagrangian are also exhibited. A generalization is also made of the concept of Lagrangian symmetries and they are related with constants of motion.
Energy levels of two-dimensional anharmonic oscillators with sextic and octic perturbations
Authors: Witwit M. R. M.
Published: July 2002

Two renormalized versions of inner product and hypervirial techniques are presented together with the Hill determinant approach for performing accurate calculations of the energy levels of two-dimensional oscillators characterized by the potentials VN=6(x, y)=(x2+y2) +λ(axxx6+ayyy6+3axyx4 y2+3ayxx2y4) and VN=8(x,y)= (x2+y2)+λ(axxx8+ayyy8+6b xyx4y4 +4axyx6y2+4ayxx2y6). The methods have been used effectively to calculate the energy eigenvalues for many eigenstates over a wide range values of perturbation parameter λ and various values of coefficients aIJ. The results produced by various techniques are compared with each other.
Representations of Kac–Moody and Virasoro algebras on modules of Greenberg–Mohapatra algebras
Authors: Cougo-Pinto M. V.
Published: July 2002

The theory of Greenberg–Mohapatra algebras is developed in continuation to a previous paper. Standard cyclic modules are constructed for the algebras, and on them Kac–Moody and Virasoro algebras are represented through a basic procedure. The representations of Kac–Moody and Virasoro algebras help to understand the structure of Greenberg–Mohapatra algebras and the question of possible violation of the Pauli exclusion principle.
Generalized expression of the perfect matching number for 2×3×n lattices
Authors: Narumi Hideyuki , Hosoya Haruo
Published: July 2002

A closed form of the perfect matching number for the cubic lattice of 2×3×n was obtained in terms of the linear combination of determinants, which was derived from its recursive expression. This is the first analytic solution for dimer statistics on three-dimensional, cubic-cell lattices. It is potentially applicable to the analytic solution of the Ising model for the general l×m×n lattice.
The role of the internal metric in generalized Kaluza–Klein theories
Authors: Drechsler W. , Hartley D.
Published: July 2002

The dimensional reduction of a Weyl space WN of N=4+n dimensions to a principal fiber bundle P̃(W4,G̃n) over a four-dimensional space–time W4 with structural group G̃n of dimension n arising from the existence of n conformal Killing vector fields of the original N-metric is studied. The framework of a Weyl geometry is adopted in order to investigate conformal rescalings of the metric on the bundle P̃(W4,G̃n) obtained. The Weyl symmetry is then, finally, broken again by choosing a particular Weyl gauge in which the internal, i.e., fiber metric, is of constant Cartan–Killing form. This choice of gauge, yielding a Riemannian theory, forces the internal metric to play no dynamical role in the theory, as is usually assumed to be the case in non-Abelian gauge theories. However, this gauge induces a conformal transformation of the metric in the space–time base of P̃ compared to the space–time metric obtained by the ordinary Kaluza–Klein reduction of a Riemannian space VN. The role of vector torsion in this dimensional reduction by isometries and scale transformations is also investigated.
Characterization of Riemann tensors using Ricci-type equations
Authors: Haddow Barry M.
Published: July 2002

The extent to which Ricci-type equations characterize the Riemann curvature tensor of a metric connection is investigated and a geometric approach is followed to generalize the results of Edgar [J. Geom. Phys. 7, 191 (1990); Int. J. Theor. Phys. 32, 121 (1993)] to arbitrary dimension and signature. The difference between a Riemann (curvature) candidate satisfying Ricci-type equations and the actual Riemann tensor is related to the isotropy of the candidate. Some new examples are presented and the results are applied to conformally recurrent space–times.
Thermodynamics of ideal boson and fermion gases in the static Taub universe
Authors: Huang Wung-Hong
Published: July 2002

Some thermodynamic quantities of nonrelativistic ideal boson and fermion gases in the static Taub universe are derived to first order in a small anisotropy parameter d measuring the deformation from the spherical Einstein universe. They are used to investigate the problem of how the curvature anisotropy affects the thermodynamic behaviors of an ideal gas. It is found that, when the universe is in the oblate configuration (i.e., d≳0), the effect of curvature anisotropy is to increase the number of the fraction in the Bose–Einstein condensation and to decrease the fermion distribution function at low temperature. When the universe is in the prolate configuration (i.e., d<0), the effects of curvature anisotropy on the thermodynamic quantities is contrary to that in the oblate configuration. The density matrix of a two particle system is evaluated and it is used to define the ‘‘statistical interparticle potential’’ as an attempt to give a ‘‘statistical interpretation’’ about the found thermodynamic behaviors. It is found that when the universe is in the oblate (prolate) configuration the curvature anisotropy will enhance (reduce) both the ‘‘statistic attraction’’ among the bosons and ‘‘statistical repulsion’’ among the fermions. It is expected that such a behavior will also be shown in the relativistic system.