bluuebunny/crossref_metadata_2025 huggingface dataset:
Soft-landed ion diffusion studies on vapor-deposited hydrocarbon films
Authors: Tsekouras A. A. , Iedema M. J. , Cowin J. P.
Published: July 2002

Cesium and hydronium ions were deposited with a “soft-landing” ion beam (1 eV) on n-hexane and 3-methyl-pentane vapor-deposited thin films on a Pt (111) surface at 27 K. Dielectric properties and ion migration were studied during the ion deposition and during a temperature ramp up to the desorption temperature of the molecular films. The ions were found to migrate through amorphous versions of these films as expected by simple viscosity models near 90 K with ion mobilities of about 10−18 m2 V−1 s−1. No, or very limited, diffusion was observed through crystalline films. The n-hexane films crystallize during the ion motion. Analysis of this permits the estimation that average diffusional motion for a neutral hexane during crystallization is about 1 molecular diameter.
Bond configurations in the Peierls–Hubbard model of small ring-shaped molecules
Authors: Liviotti E. , Ubertini F. , Erdös P.
Published: July 2002

The Peierls–Hubbard model applied to N-membered ring-shaped molecules is investigated numerically and analytically. The bond configurations minimizing the total energy at half-filling of the electronic states are determined by a self-consistent method for N⩽8 in a wide range of the electron–lattice and electron–electron coupling parameters. In the even-N case, only dimerized and homogeneous configurations have been found to be stable. Odd-N rings show three types of bond configurations depending on the coupling parameters. Two of these configurations have reflection symmetry whereas the third one is irregular.
Single-bubble sonoluminescence from hydrogen
Authors: Yasui Kyuichi
Published: July 2002

Single-bubble sonoluminescence (SBSL) from a hydrogen bubble is studied theoretically based on a quasiadiabatic compression model of a bubble collapse. It is clarified that the maximum temperature in a hydrogen bubble in 20 °C water under conditions of SBSL is always about 6000 K due to the effect of chemical reactions inside the bubble. It is suggested that the light emission at such temperature is by the transition from the lowest stable triplet state of the H2 molecule to the repulsive state resulting from two normal atoms (H2*→2H+hν). It is shown that the number of hydrogen molecules inside the bubble remains almost constant in spite of the high temperature and pressure inside the bubble at the collapse. It is also shown that the addition of argon to a hydrogen bubble results in the higher maximum temperature inside the bubble.
Response to “Comment on ‘A new algorithm for reverse Monte Carlo simulations’ ” [J. Chem. Phys. 111, 5620 (1999)]
Authors: da Silva Fernando Luı́s B. , Svensson Bo , Åkesson Torbjörn , Jönsson Bo
Published: July 2002

We present here results obtained from numerical calculations in order to respond to a misreading of our previous work. Sampling properties of our reverse Monte Carlo (RMC) algorithm are discussed and several tests are used to evaluate its properties. Important details are stressed, hopefully contributing to a better understanding of the technique.
The computer simulation of proton transport in water
Authors: Schmitt Udo W. , Voth Gregory A.
Published: July 2002

The dynamics and energetics of an excess proton in bulk phase water are examined computationally with a special emphasis on a quantum-dynamical treatment of the nuclear motion. The potential model used, the recently developed multistate empirical valence bond (MS-EVB) approach [U. W. Schmitt and G. A. Voth, J. Phys. Chem. B 102, 5547 (1998)], is also further refined and described in more detail. The MS-EVB model takes into account the interaction of an exchange charge distribution of the charge-transfer complex with the polar solvent, which qualitatively changes the nature of the solvated complex. Classical and quantum molecular dynamics simulations of the excess proton in bulk phase water reveal that quantization of the nuclear degrees of freedom results in an increased stabilization of the solvated H5O2+ (Zundel) cation relative to the H9O4+ (Eigen) cation, though the latter is still more stable, and that a species intermediate between the two also exists. The quantum proton transport rate, which is evaluated by the centroid molecular dynamics approach, is found to be on the order of two times faster compared to a purely classical treatment of the system and in good agreement with the experimental value. Calculation of the hydrogen-bonding lifetime beyond the first solvation shell of the excess proton reveals a similar quantum enhancement factor compared to the classical regime.
On the origin of the dip in the KrF laser gain spectrum. II. The short-pulse gain saturation experiment
Authors: Datsyuk V. V. , Hooker C. J. , Divall E. J. , Hirst G. J. , Ross I. N. , Lister J. M. D. , Osvay K.
Published: July 2002

The wavelength resolved spectra recorded during subnanosecond depletion of the gain in a KrF laser amplifier have been used to specify the state responsible for the dip in the KrF(B→X) emission spectra. Self-absorption of the KrF laser emission at 248.9 nm has been found to be due to the phototransition from the KrF(C) state to a 2Π Rydberg state.
Relaxation of vibrationally excited HCN+ and DCN+ ions in collisions with He
Authors: Wisthaler A. , Hansel A. , Schwarzmann M. , Scheiring Ch. , Lindinger W. , Ferguson E. E.
Published: July 2002

A selected ion flow drift tube (SIFDT) has been used to measure vibrational quenching rate constants of HCN+ and DCN+ in collisions with He from 0.05 to 0.35 eV mean relative kinetic energy. The measured quenching rate constants fit linear Landau–Teller (L-T) plots in the 0.20 to 0.35 eV energy range, equivalent to 1540 to 2700 K effective temperature range. These are the first L-T plots for polyatomic ion vibrational quenching. The L-T plots imply large vibrational excitation in the CH (CD) fundamental stretching mode by electron impact ionization of HCN in the threshold to ∼40 eV energy range. The L-T plots also imply that vibrational quenching of the CH (CD) fundamental stretching mode by He is either directly to the ground vibrational state, or possibly to the low-frequency bending mode, but not via the CN stretching mode. There is a large HNC+ ion (45%±5%) production by electron impact ionization of HCN. This is in contrast with HCN photoionization, which yields only HCN+.
Construction of a grazing incidence x-ray reflection system for liquid-vapor interfaces by use of an imaging plate
Authors: Yano Yohko F. , Iijima Takao
Published: July 2002

We have constructed a grazing incidence x-ray reflection system for liquid-vapor interfaces by use of an imaging plate as an area detector. The reflectivity data were obtained with high resolution even by use of a conventional x-ray tube. The surface reflectivity measurements for pure water, ethanol and 2-butoxyethanol were performed and the values of the surface roughness were obtained as 4.1±0.1, 7.1±0.3 and 6.2±0.2 Å, respectively. For water, slight broadening of reflection peaks was observed. This was caused by the surface curvature due to the large surface tension. By fitting the reflection profiles, the radius of curvature was found to be nearly 100 m for water and ten times larger for ethanol and 2-butoxyethanol.
Time-dependent Hartree approaches for the study of intramolecular dynamics in dimer systems
Authors: Roy Pierre-Nicholas , Light John C.
Published: July 2002

We apply and the time-dependent Hartree (TDH) method to the study of intramolecular dynamics in dimer systems. The HCl dimer is chosen as test case. Model calculations are performed on reduced dimensional representation of this system namely two-, three-, and four-dimensional ones. We assess the validity of different implementations of the TDH method including the account of direct correlations between coordinate pairs, and mixed quantum-classical and quantum-Gaussian wave packets treatments. The latter yields very good results compared to the fully quantal treatment.
Identical collision partners in the coherent control of bimolecular reactions
Authors: Brumer Paul , Bergmann Klaas , Shapiro Moshe
Published: July 2002

The coherent control of bimolecular processes typically requires that the system be initiated in a superposition of correlated translational and internal reactant states. We show that by colliding identical molecules one bypasses many of these complexities, allowing for direct studies of coherently controlled collision phenomena.
Adsorbate phase transformations and the coverage-dependent oscillation of electron transfer probabilities
Authors: Staicu-Casagrande E. M. , Guillemot L. , Lacombe S. , Esaulov V. A. , Canepa M. , Mattera L. , Pasquali L. , Nannarone S.
Published: July 2002

We report a study of the effects of chlorine adsorption on the interaction of positive ions (H+, Ne+, Ar+ with a Ag(111) surface from the submonolayer Cl chemisorption to initial stages of AgCl formation. Cl adsorption on Ag(111) proceeds through different phases and we observed that the neutralization probabilities oscillate in this range, attaining an intermediate minimum at about 2/3 coverage and reach a maximum at full coverage. The subsequent appearance of AgCl phase again leads to a reduction in neutralization. These results are described in terms of changes in Auger neutralization rates due to modifications in the adsorbate density of states.
Efficient viscosity estimation from molecular dynamics simulation via momentum impulse relaxation
Authors: Arya Gaurav , Maginn Edward J. , Chang Hsueh-Chia
Published: July 2002

A new momentum impulse relaxation method for obtaining the shear viscosity of Newtonian fluids using molecular dynamics simulations is introduced. The method involves the resolution of a decaying coarse-grain Gaussian velocity profile in a properly thermostated simulation box. This localized velocity profile, along with a modification of the periodic boundary conditions, allows computations in a periodic box with minimal phonon feedback due to periodicity. The short-time decay of the small-amplitude velocity profile yields shear viscosities for atomic and molecular species that are in quantitative agreement with those obtained using conventional techniques, but with more than an order of magnitude reduction in computational effort.
Solvation in binary mixtures of dipolar hard sphere solvents: Theory and simulations
Authors: Morillo M. , Denk Claus , Sánchez-Burgos Francisco , Sánchez Antonio
Published: July 2002

The structure of mixtures of dipolar hard sphere fluids with components of equal size but different dipole moments around a single ion is studied. The solvation energy and the polarization around the ion is obtained in the framework of the mean spherical approximation (MSA). Our theoretical results and the results of other workers are compared with simulation data obtained from Monte Carlo simulations. An interpretation of the meaning of preferential solvation is given in terms of the contrasting behaviors of partial polarization in the bulk and near the ion.
Chemical structure of dihydride phase on saturated H-chemisorbed Si surfaces
Authors: Watanabe Satoru
Published: July 2002

By observing infrared absorption features including dynamic polarizations due to Si–H stretching vibrations, chemical structures were determined on H-chemisorbed single-crystal Si surfaces that were formed in solution. A technique using polarized infrared multiple internal reflections was applied. The absorption features were obtained as a function of surface H density by systematically tilting the orientation of the surfaces from (111) through (113) up to (001). For surface orientations from (111) to (113), narrow absorption peaks, which had been assigned due to the strained vertical dihydride, and (111)-terrace monohydride species were predominantly observed. But, as the surface orientation moved away from (111), narrow peaks with dynamic polarizations in the (1̄10) plane were observed for the first time. Meanwhile, the broad feature with several peaks in the whole Si–H stretching region was detected in the surface-parallel component of dynamic polarization. Because the absorption area for the surface parallel component increased monotonically with the angle, the features were concluded to be localized at the vertical-dihydride step edges along 〈1̄10〉. A complex composed of a strained horizontal dihydride and a strained monohydride provided a temporary explanation. On (001), the peaks caused by the strained vertical dihydride disappeared completely, and the predominant peaks were those observed for the first time on the other surfaces. A major part of the (001) surface was composed of the complex. The microscopic origin for the appearance of such a disordered structure is described.
Ladder and cross terms in second-order distorted Born approximation
Authors: Jin Y. Q. , Kong J. A.
Published: July 2002

In the strong fluctuation theory for a bounded layer of random discrete scatterers, the second moments of the fields in the second-order distorted Born approximation are obtained for copolarized and cross-polarized fields. The backscattering cross sections per unit area are calculated by including the mutual coherence of the fields due to the coincidental ray paths, and that due to the opposite ray paths, corresponding to the ladder and cross terms in the Feynman diagramatic representation. It is proved that the contributions from ladder and cross terms for the copolarized backscattering cross sections are the same, while the contributions for the cross-polarized backscattering cross sections are of the same order. The bistatic scattering coefficients in the second-order approximation for both the ladder and cross terms are also obtained. The contributions from the cross terms explain the enhancement in the backscattering direction.
Lagrangian dynamics on higher-dimensional spaces with applications to Kaluza–Klein theories
Authors: Chiang C-C. , Lee S-C. , Marmo G.
Published: July 2002

We review and apply the method of Lagrangian dynamics to particle motion in higher-dimensional spaces. We discuss in detail the case of a Kaluza–Klein theory with coset spaces as fiber. While the total metric we use in general need not allow for Killing vectors, we require that the restriction to the fiber does. We find that for general Jordan–Thiry scalar fields, the geodesic motion in total space is not describable in terms of particle motion in the base manifold with the usual internal charges. The cases when this is possible are discussed. We also consider the geodesic motion in the Sorkin–Gross–Perry Kaluza–Klein monopoles. We find all the conserved quantities and the equations can be integrated by quadrature.
A simple derivation of the addition theorems of the irregular solid harmonics, the Helmholtz harmonics, and the modified Helmholtz harmonics
Authors: Weniger E. Joachim , Steinborn E. Otto
Published: July 2002

In this article a simple derivation of the addition theorems of the irregular solid harmonics, the Helmholtz harmonics, and the modified Helmholtz harmonics is presented. Our derivation is based upon properties of the differential operator 𝒴ml(∇), which is obtained from the regular solid harmonic 𝒴ml(r) by replacing the Cartesian components of r by the Cartesian components of ∇. With the help of this differential operator 𝒴ml(∇), which is an irreducible spherical tensor of rank l, the addition theorems of the anisotropic functions are obtained by differentiating the addition theorems of the isotropic functions. The performance of the necessary differentiations is greatly facilitated by a systematic exploitation of the tensorial nature of the differential operator 𝒴ml(∇).
Branching index sum rules for simple Lie algebras
Authors: Okubo Susumu
Published: July 2002

Let L and L0 be a simple Lie algebra and its sub-Lie algebra, respectively. Then, a given irreducible representation ω of L decomposes into a direct sum of irreducible components of L0, which is called the branching rule. The general Dynkin indices introduced earlier satisfy many sum rules for the branching rule. These are found to be strong enough to uniquely determine the branching rule for many cases we have studied. The sum rules are especially useful for cases of exceptional Lie algebras.
The resonant thermonuclear reaction rate
Authors: Haubold H. J. , Mathai A. M.
Published: July 2002

Basic physical principles for the resonant and nonresonant thermonuclear reaction rates are applied to find their standard representations for nuclear astrophysics. Closed-form representations for the resonant reaction rate are derived in terms of Meijer’s G-function. Analytic representations of the resonant and nonresonant nuclear reaction rates are compared and the appearance of Meijer’s G-function is discussed in physical terms.
Special solutions of the Sparling equation
Authors: Hsieh S. H. , Kent Steven L. , Newman E. T.
Published: July 2002

The Sparling equation, a first-order, matrix-valued linear differential equation that is equivalent to the self-dual Yang–Mills equations for any group, has recently been solved by quadratures for the case of SL(2,C) or its subgroup. It is the purpose of this paper to show how for a series of special cases, rather than integrating the quadratures, the Sparling equation can be reduced to an algebraic equation and then solved, yielding the single- and multi-instanton fields parallel to isospace.
A new method of constructing the symmetry-adapted linear combinations based on the correspondence theorem and induced representations
Authors: Kim Shoon K.
Published: July 2002

The theory of induced representations is incorporated into the method of constructing symmetry-adapted linear combinations for a symmetry group based on the correspondence theorem developed previously. The theory is effective for a highly symmetric molecule with a set of equivalent radicals, each of which again consists of a number of equivalent atoms. An illustrative example is given to construct the internal symmetry coordinates of molecular vibrations of C(CH3)4 with the frozen configuration belonging to the point group Td.
An algebraic approach to the exponential cosine screened Coulomb potential
Authors: Roychoudhury R. K. , Roy Barnana
Published: July 2002

An analytical formula is obtained for the energy eigenvalues of the exponential cosine screened Coulomb potential by a method that is a combination of algebraic perturbation theory based on the Lie algebra of the SO(2,1) group and the scaling variational method. The results are found to be in excellent agreement with Padé approximation calculations.
Eigenvalue problem for Schrödinger’s equation with repulsive potential
Authors: Matsumoto S. , Kakazu K. , Nagamine T.
Published: July 2002

Schrödinger’s operator −(ℏ2/2m){d2/dr2+(2/r)d/dr}+V(r) is studied, and what happens when V(r) approaches −∞ rapidly as r→∞ is shown. The cases in which V(r)∼−βrδ (β>0, δ>2) as r→∞ are covered. If V(r) approaches −∞ rapidly, then the above operator is not self-adjoint and in order to get a self-adjoint operator a boundary condition must be imposed. For such a self-adjoint operator there are states that belong to the discrete energy spectrum. To obtain the discrete energy spectrum, a quantization rule that corresponds to the quantization rule of Bohr and Sommerfeld in old quantum mechanics is considered.
Fluid spheres of uniform density in general relativity
Authors: Ponce de León J.
Published: July 2002

A number of exact solutions for spherically symmetric nonstatic fluids of uniform density, surrounded by empty space, are derived and investigated. Solutions that represent expanding and contracting spheres, which tend asymptotically to static configurations described by the Schwarzschild interior solution ( ρ=const), are obtained In some cases the motion of contraction or expansion is reversed, while in other cases there is no bouncing at all. Oscillating solutions are presented.
Total energy momentum in general relativity
Authors: Ó Murchadha Niall
Published: July 2002

The energy momentum of any asymptotically flat vacuum solution to the Einstein equations is a well-defined, conserved, Lorentz-covariant, timelike, future-pointing vector. The only requirement is that one be given asymptotically flat initial data that satisfy very weak continuity and falloff conditions; the three-metric must go flat faster than r−1/2. A large class of such data exists, consistent with the constraints, and the constraints play a key role in guaranteeing that the energy momentum is well behaved.
Integrability of restricted multiple three-wave interactions
Authors: Verheest Frank
Published: July 2002

Using a Hamiltonian framework with complex canonical variables allows for the determination of irreducible forms, which serve as building blocks for polynomial invariants. All the independent invariants in involution are thus obtained for the restricted multiple three-wave interactions, where all triads are coupled through a common pump (or daughter) wave, in the case of equal coupling strengths in all triads. The mixed, common pump/daughter wave case is not integrable.
Curvature structure in general relativity
Authors: Hall G. S. , Kay W.
Published: July 2002

This paper investigates the extent to which the curvature structure of space-time determines the metric stucture. It continues the work of earlier papers by prescribing the curvature structure and the curvature covariant derivatives up to certain orders. It is shown that, with the exception of the so-called generalized pp waves, the curvature and its first and second covariant derivatives essentially determine the metric up to coordinate transformations.
Neutrino spectrum of Einstein universes
Authors: Holm Christian
Published: July 2002

The study of higher-dimensional Kaluza–Klein universes constructed from the unitary groups UN is continued. They form Bergmann manifolds of dimension N2 with Finslerian geometry induced by their hyperspin structure. In this paper Lagrangians for relativistic wave equations, which are generalizations of the Klein–Gordan, Dirac, and Weyl neutrino equations, are formulated. The wave equations are in general of differential order N. The hyperneutrino equation is examined in detail as the simplest example and its discrete symmetries are discussed. It is found that for N=3 and N>4 TCP and all its constituent symmetries are violated. The boson calculus is used to solve the linear neutrino equation exactly on UN and the energy spectra of the neutrino and antineutrino are presented. It is found that the density ratio of negative to positive energy states is unity only for N=2, producing asymmetry for all higher-dimensional UN. The neutrino acquires a negligible rest mass of O(10−31 eV) due to the global curvature of our manifold.
The Hamiltonian structure of the modified and fifth-order Korteweg–de Vries equation
Authors: Kentwell G. W.
Published: July 2002

Dirac’s theory of constraints is used to derive the Hamiltonian structure of the modified and fifth-order Korteweg–de Vries equations. A transformation to ‘‘physical’’ variables is performed on the canonical structure and is shown to be equivalent to the Dirac bracket.
Integrability of restricted multiple three-wave interactions. II. Coupling constants with ratios 1 and 2
Authors: Verheest Frank
Published: July 2002

The system of ordinary differential equations describing the multiple three-wave interactions with a common pump (daughter) wave is proved to be completely integrable by obtaining the necessary 2N+1 independent first integrals in involution for the case when the coupling constants and the frequency mismatches have ratio 1 and/or 2. This case was deemed integrable on the basis of a Painlevé analysis, but a direct proof has been lacking for some time. The first integrals are the N+1 quadratic Manley–Rowe relations, the cubic Hamiltonian, N−1 quartic integrals (analogous to the ones needed for complete integrability in the case of equal coupling constants and detunings in all wave triads), and a new sixth-order integral involving all wave quantities. The form of this last invariant was deduced from the recent result for the analogous interaction between five waves (N=2), and essentially made possible by the proper use of irreducible forms, elementary building blocks for polynomial first integrals in involution with the Manley–Rowe invariants.
Inverse scattering for the mixed spectrum of δ potentials
Authors: Jian-cheng Lin
Published: July 2002

The inverse problem is studied in a system of mixed spectrum of which the continuous part coincides with that of a repulsive δ potential and the discrete part coincides with that of an attractive δ potential.
The absence of small solutions of nonlinear field equations
Authors: Malec Edward
Published: July 2002

A simple criterion for the absence of small solutions of nonlinear field equations is proved. The key step in the proof consists of the use of energy Sobolev inequalities. Field-theoretic implications are shown.
Wave splitting and the reflection operator for the wave equation in R3
Authors: Weston Vaughan H.
Published: July 2002

The problem of wave splitting in a nonhomogeneous medium in R3 is considered. Previous results for wave splitting in a planar stratified medium can be generalized to a general nonhomogeneous medium (with sufficiently smooth velocity). The wave equation is factorized into an up- and down-going wave system using certain integral and integral-differential operators. The equation for the reflection operator (which relates the up-going wave to a down-going wave) is then obtained, and certain properties of the reflection operator are deduced.
Bounds on the number of bound states for potentials with critical decay at infinity
Authors: Stubbe Joachim
Published: July 2002

Let V be a potential whose negative part V− decays like c‖x‖−2 at infinity. If c is not too large, then the Schrödinger operator HV=−Δ+V on Rn, n≥3, has only a finite number of bound states although the associated classical phase space volume is infinite. Optimal conditions are derived for the absence of bound states and a family of bounds on the total number of bound states for the operator HV of the form N0(V)≤ cγ,n ∫Rn (V+c/‖x‖2)γ− ‖x−x0‖2γ−n dn x. The basic tool used to obtain results is a family of sharp Sobolev inequalities for the operator A(c)=−Δ−c/‖x‖2.
A path integral for a nonrelativistic spinor particle
Authors: Miura Takashi
Published: July 2002

By formulating a path integral in the SU(2) fiber bundle space, a nonrelativistic spinor particle moving in external electromagnetic fields is studied. This formulation is a direct extension of Schulman’s [Phys. Rev. 176, 1588 (1968)] continuous treatment for spin; it unifies all spin states to a spherical top model. This theory enjoys a definite classical theory with spin–orbital interactions and the corresponding semiclassical approximation for the path integral. This method is also applicable to a particle moving in a more general Yang–Mills field.
Amplitudes and the universal influence function
Authors: Gudder Stanley
Published: July 2002

Following ideas of Hemion, a method for deriving the complex amplitudes of quantum mechanics from physically motivated principles is presented. First, a generalized action and a universal influence function is introduced. It is postulated that the probability of a measurement outcome is given in terms of the sum of influences between alternatives that result in that outcome.
A probabilistic approach to Euclidean Dirac fields
Authors: Lehmann Detlef
Published: July 2002

Using a simple isomorphism between the symmetric and antisymmetric Fock space over L2(Rd) and the Wiener isomorphism, a unitary mapping U(s)𝒜ℬ:𝒜(ℋs)→L2R(𝒮′R(Rd), dφsR) is constructed, yielding an isomorphism Ws,l■𝒜(ℋsl)⊗𝒜(ℋsl)→L2R (𝒮C(Rd)l,dlμsR), where ℋs Sobolev space of order s, dφs Gaussian measure on the real Schwartz distributions with covariance operator (−Δ+1)s, dμs=dφs⊗dφs. Using W−1/2,4, the fields are constructed on L2(𝒮′C(R4)4,d4μ−1/2R), yielding a functional integral representation for the two point function of the Euclidean Dirac field with a true Gaussian measure.
Higgs potentials from multidimensional Yang-Mills theories
Authors: Kubyshin Yu. A.
Published: July 2002

Properties of four-dimensional theories on M(4), obtained from multidimensional pure Yang–Mills theories on E=M(4)×S/R via coset space-dimensional reduction, are discussed. Scalar potentials of the reduced theory for the case where S/R is a symmetric space are studied in detail. An explicit relation between extrema of these potentials and solutions of the multidimensional equations of motion (spontaneous compactification solutions) are established. Some quantum properties of the dimensionally reduced theory are also discussed.
Solitons and isometric immersions
Authors: Gerold A. , Buchner K.
Published: July 2002

Let u be any one-soliton solution of class C3 of a single differential equation with two independent variables. Then u satisfies the immersion equations of a Dini surface. In this way, it is possible to generate all C3 one-soliton solutions of differential equations in two variables. In the discussion of a two-soliton solution, a new surface of Gaussian curvature −1 (a Joachimsthal surface of Enneper’s type) has been found.
A note on the symmetry group and perturbation algebra of a parabolic partial differential equation
Authors: Cohen de Lara M.
Published: July 2002

In this paper, the symmetry group of the parabolic partial differential equation ∂tf=Af is focused on (A is an analytic second-order elliptic linear differential operator on Rn). Following Olver [Applications of Lie Groups to Differential Equations (Springer, New York, 1986)], Ovsjannikov [Group Analysis of Differential Equations (Academic, New York, 1982)], and Rosencrans [J. Math. Anal. Appl. 56, 317 (1976); 61, 537 (1977)], the Lie algebra of infinitesimal symmetries is studied. It will be proven that it is finite dimensional (putting apart the trivial symmetries due to the linearity of the partial differential equation) by relating it to the Lie algebra of infinitesimal homothetic transformations of a Riemannian manifold (Rn,a), thus generalizing results of Ovsjannikov on elliptic equations and making use of the same Riemannian geometric techniques. Thanks to these techniques, the perturbation algebra of A, introduced by Rosencrans, is also shown to be related to geometric characteristics of (Rn,a).
The space of leaves of a shear-free congruence, multipole expansions, and Robinson’s theorem
Authors: Bailey T. N.
Published: July 2002

What it means for (relative) sheaf cohomology classes to have a pole of a given order on a surface S in twistor space will be defined and that they can be described in terms of some formal neighborhood sheaves will be shown. In space-time, S corresponds to a foliation by α-surfaces and the filtration of cohomology gives a filtration on the fields that extends the idea of being algebraically special along the foliation. We use this idea also for the case of the ‘‘double-valued’’ congruence associated with a world line, in which case the filtration applied to sourced fields is essentially a multipole expansion. In the case of curved space-times, it will be shown that if a certain curvature condition holds, then the space of leaves of a foliation by α surfaces has an ambient twistor space defined to first order, and we relate this to an extended version of Robinson’s theorem.
A rapid proof for a flattening property of a classical solution of the Mullins equation
Authors: Kitada Akihiko , Umehara Hiroyuki
Published: July 2002

Modifying previous proof based on the maximum principles [J. Math. Phys. 27, 1391 (1986); 28, 536, 2982 (1987)], a rapid proof is proposed for a flattening property of a classical solution of the Cauchy problem associated with the Mullins equation ut=uxx/(1+ux2), (x,t)∈R1×(0,∞), u(x,0)=α(x), x∈R1 which describes the development of material surface due to evaporation condensation.
Time-dependent normal form theory and Schrödinger initial value problems
Authors: Gompa Raghu R.
Published: July 2002

Time-dependent normal form theory is introduced and studied in the context of Schrödinger initial value problems associated with Hamiltonians having time-dependent perturbations to arrive at approximations that deviate in norm from the exact solution by a term of order εm+1(1+t) provided the initial vector is restricted to an appropriate dense subspace. In addition to the abstract theory within a rigorous Hilbert space formalism, it is applied to the quantum mechanical Hamiltonians of the form n harmonic oscillators coupled via an interaction of the form ε times sum of products of bounded continuous functions with polynomials in the position and momenta variables satisfying a nonresonance condition. In particular, first-order approximation is explicitly constructed for time evolution of a system describing anharmonic oscillator which changes trigonometrically with time.
Geodesic motion and scattering in the field of a Kaluza–Klein dyon
Authors: Moussa Karim Ait , Clément Gérard
Published: July 2002

The Kaluza–Klein dyon is the only stationary solution of the sourceless Jordan–Thiry field equations with a constant scalar field. The geodesic motion of photons and charged test particles in this five-dimensional space-time is discussed, and the classical cross section for forward scattering of a charged particle is computed.
Dynamics of field fluctuations in the Schwinger model
Authors: Verbeure A.
Published: July 2002

The Schwinger model is formulated as a dynamical system. The β-KMS states and ground state are explicitly given. The dynamics of the field fluctuations is explicity computed, explaining the mechanism for the occurrence of oscillations with frequency ω≠0 at momentum k=0.
Palatini variation of curvature-squared action and gravitational collapse
Authors: Shahid-Saless Bahman
Published: July 2002

It is shown that Palatini variation of a class of gravitational actions based on a quadratic generalization of the Einstein–Hilbert action results in a metric-incompatible theory of gravity but one that satisfies Birkhoff’s theorem. The usual fourth-order field equations are replaced by two second-order equations. Application of the field equations to a model of freely falling dust are discussed.
Spherically symmetric density perturbation in relativistic cosmology
Authors: Liu Hongya
Published: July 2002

Einstein’s field equations for spherically symmetric perfect fluids are reduced to two equations plus three definitions, and from these the spherical density perturbation equation is derived. It is found that this perturbation equation can be separated into two equations by the method of separation of variables and can be solved explicitly in some special cases. An interesting result is that for matter-dominated era the perturbation equation is found to be of the Bonnor form of Newtonian theory. Another interesting result is that for zero-curvature universe and radiation-dominated era the density perturbation has two growing modes: one is something like a power of the proper time, and the other is of the exponential law of the conformal time, each corresponds to a different limit of approximation.
Supergroups factorizations through matrix realization
Authors: Hussin V. , Nieto L. M.
Published: July 2002

Using a matrix realization, generic elements of the supergroups U(m/n) and OSP(m/2n) are obtained through the exponentiation of the corresponding super Lie algebra elements. The emphasis is put on the contribution of the odd part. The application to the factorization problem is given, and the relationship with nonlinear differential superequations is clarified.
Density matrix for the damped harmonic oscillator within the Lindblad theory
Authors: Isar Aurelian , Sandulescu Aurel , Scheid Werner
Published: July 2002

The time evolution of the density matrix of the damped harmonic oscillator is studied within the Lindblad theory for open quantum systems. The density matrix is represented via a generating function, which is obtained by solving a time-dependent linear partial differential equation derived from the master equation of the damped harmonic oscillator. Illustrative examples for specific initial conditions of the density matrix are provided. It is also shown that various master equations for the damped quantum oscillator, for damped collective modes in deep inelastic collisions of heavy ions and in different models of quantum optics are particular cases of the Lindblad equation and that only some of these equations satisfy the quantum mechanical constraints on the diffusion coefficients.
Invariants and Lie algebraic solutions of Schrödinger equation
Authors: Salmistraro Franco , Rosso Riccardo
Published: July 2002

A representation of invariants in quantum mechanics for a general time-dependent Hamiltonian is provided. The main properties of these operators and their relevance for solving the Schrödinger equation are discussed in light of this representation. In particular, the well-known Lewis and Riesenfeld’s method is shown to be recovered quite directly by the present approach. A detailed analysis is concerned with Hamiltonians which at each instant are elements of a finite dimensional Lie algebra. Exploiting the Wei and Norman’s theory for such Hamiltonians, it is found that the evolution of a quantum system is always determined, in part or fully, by an invariant which belongs to the same algebra.
Fourier–Bessel analysis for ordinary and graded 2×2 Hermitian matrices
Authors: Guhr Thomas
Published: July 2002

Chainlike integrals in matrix spaces play an important part in high-energy and solid-state physics and in general random matrix theory. In the special case of ordinary and graded 2×2 Hermitian matrices, a method is proposed to integrate out all angular variables. The essence of this method is a Fourier–Bessel analysis in these matrix spaces which is formulated in this paper. Close formal similarities are found between the ordinary and the graded case. The main differences arise from the fact that the ordinary case can be reduced to the study of a vector space whereas no analogous feature is present in the graded case.
Gauge invariance of systems with first-class constraints
Authors: Cabo Alejandro , Chaichian Masud , Louis Martinez Domingo
Published: July 2002

The infinitesimal canonical transformations which map solutions of the total Hamiltonian equations of motion into each other are investigated. For that, the generating function Ψ of such transformations should satisfy certain conditions. In general, Ψ is a function which depends on the coordinates, the momenta, and the Lagrange multipliers λ. However, it is shown that the requirement of independence of the function Ψ on the Lagrange multipliers is sufficient for the existence of gauge invariant transformations in the Lagrange formalism. It is shown that the condition that the Poisson brackets between Ψ and all the primary first-class constraints are a linear combination of the latter ones provides the λ independence of the function Ψ. The existence of such a λ-independent function Ψ is proven for some systems. In particular, this is proven for the relevant case of systems having primary and secondary first-class constraints. The authors suggest the possibility that for some specific systems a λ-independent generating function Ψ cannot be constructed. This conclusion concerns the systems with more than primary and secondary constraints.
Some asymptotically flat generalizations of the Curzon metric
Authors: Hernández-Pastora J. L. , Manko V. S. , Martín J.
Published: July 2002

Four exact asymptotically flat solutions of the Einstein–Maxwell equations generalizing the well-known Curzon metric are presented in explicit form. A new generalization of the Dietz–Hoenselaers metric for two rotating isolated sources is obtained.
Exact, composite ternary nearest-neighbor degeneracies
Authors: Hock J. L. , McQuistan R. B.
Published: July 2002

Closed-form expressions are developed that describe exactly the composite ternary nearest-neighbor degeneracies that arise when three different types of simple, indistinguishable particles are distributed on a one-dimensional lattice space to form prescribed numbers of the six possible kinds of nearest-neighbor pairs: (1–1), (1–2), (1–3), (2–2), (2–3), and (3–3).
Quantization of dynamical systems subject to second class constraints
Authors: Nakamura M. , Minowa H.
Published: July 2002

It is shown that the operator formulation of the quantization of dynamical systems subject to second class constraints by Batalin and Fradkin (BF method) is equivalent to the projection-operator method (POM), which is the alternative method of the quantization of such systems, at the commutator level. It is also shown that the commutators in the BF method as well as those in the POM contain a quantum effect, which is completely missed in the usual quantization scheme with the Dirac brackets.
Probabilistic representation formulas for the time evolution of quantum systemsa)
Authors: Pereyra P. , Quezada R.
Published: July 2002

By using a new procedure representation formulas are obtained for the solution of the Cauchy problem for hyperbolic systems generalizing Schrödinger and Dirac equations. This procedure makes explicit the relation of the underlying Poisson jump process with the perturbation series. It allows one to find out a path integral representation formula for the two-dimensional Dirac equation. Further, it can be applied in the four-dimensional case with a Coulombian potential. This approach is also used to describe the time evolution of dissipative two-level systems and estimate transition probabilities.
Supersymmetry and the Atiyah–Singer index theorem. II. The scalar curvature factor in the Schrödinger equation
Authors: Mostafazadeh Ali
Published: July 2002

The quantization of the superclassical system used in the proof of the index theorem results in a factor of (ℏ2/8)R in the Hamiltonian. The path integral expression for the kernel is analyzed up to and including the two-loop order. The existence of the scalar curvature term is confirmed by comparing the linear term in the heat kernel expansion with the two-loop order terms in the loop expansion. In the operator formalism this term arises from the fermionic sector whereas in the path integral formulation it comes from the bosonic sector.
A class of graded Lie algebras of vector fields and first order differential operators
Authors: Post Gerhard
Published: July 2002

Finite-dimensional Lie algebras of polynomial vector fields on Rn, that contain the elements ∂/∂xi and xi(∂/∂xi) for i=1...n were studied. To any Lie algebra 𝔏 of this class, an N-valued n×n matrix A and a set of special elements 𝒮⊆{1,...,n} are associated. It is proven that the pair (A,𝒮) necessarily satisfies two properties. Conversely, to any pair (A,𝒮) satisfying those two properties is associated a Lie algebra 𝔏(A,𝒮), such that 𝔏(A,𝒮) is maximal in the class of all 𝔏 with matrix A and special elements 𝒮. For the Lie algebras 𝔏(A,𝒮) the possible extensions to first order differential operators, and its modules of C∞ functions are discussed. © 1994 American Institute of Physics.
Modular algebras in geometric quantization
Authors: Ali S. Twareque , El Gradechi Amine M. , Emch Gérard G.
Published: July 2002

Presented here is a discussion on the connection between geometric quantization and algebraic quantization. The former procedure relies on a construction of unitary irreducible representations that starts from co-adjoint orbits and uses polarizations, while the latter depends on the purely algebraic characterization of unitary irreducible representations, which is based on central decompositions of von Neumann algebras in involutive duality, and their decompositions in terms of maximal Abelian subalgebras. Intermediate stages of these two quantization methods turn out to be complementary, leading thus to a new characterization of the so-called discrete series representations.
Bifurcation solutions of the Schwinger–Dyson equation
Authors: Cheng G. , Kuo T. K.
Published: July 2002

As a function of the coupling constant, it is shown that the Schwinger–Dyson equation has many bifurcation solutions that branch off from the trivial solution. Three of these solutions are obtained explicitly, using the parameter imbedding method and the Liaponov–Schmidt method. Application of these methods to other nonlinear problems is discussed.
Event structures in nonstandard quantum mechanics
Authors: Gudder Stanley
Published: July 2002

Event structures in nonstandard quantum mechanics are represented by closed subspaces of a nonstandard Hilbert space. There are four natural types of closed subspaces of a nonstandard Hilbert space and these different types coalesce in the standard theory. These types are the closed internal subspaces, the splitting subspaces, the ⊥-closed subspaces, and the norm-closed subspaces. The algebraic properties of these four types are studied and compared. Moreover, the resulting structures are compared to others that have recently appeared in the literature.
A new approach for the Jeffreys–Wentzel–Kramers–Brillouin theory
Authors: Monaco R. L. , Capelas de Oliveira E.
Published: July 2002

A new approximation to obtain solutions for the time-independent Schrödinger equation, similar to the classical Jeffreys–Wentzel–Kramers–Brilloin theory, is obtained by means of the theory of continued fractions. A particular case is discussed in detail.
Fully relativistic plasma dispersion function
Authors: Kamp Léon P. J.
Published: July 2002

Properties of a relativistic plasma dispersion function (PDF) that is required for the description of waves propagating perpendicular to a magnetic field in a fully relativistic, magnetized, Maxwellian plasma, are presented. Series, asymptotic series, recurrence relations, integral representations, derivatives, generating functions, approximations, differential equations, and connections with standard transcendental functions are discussed, as are the PDF’s analytic properties.
Padé-like approximation and maximum entropy formalism applied to chaotic systems
Authors: Steeb W.-H. , Stoop R.
Published: July 2002

It is shown how the Padé-like approximation and the maximum entropy formalism can be applied in nonlinear chaotic systems. In particular, it is shown how one can use a few moments of the time evolution of a dynamical variable to infer the probability density and hence the Ljapunov exponent.
Bäcklund transformations of linear Weingarten surfaces in Minkowski three-space
Authors: Buyske Steven G.
Published: July 2002

The classical Bäcklund transformation, which transforms surfaces of constant negative curvature, has been extended to surfaces in Minkowski three-space. In this article the tangency requirement of the Bäcklund transformation is relaxed to obtain a transformation of surfaces of Minkowski three-space with mean and Gaussian curvatures satisfying a linear relationship.
An inequality for Legendre polynomials
Authors: Elbert Árpád , Laforgia Andrea
Published: July 2002

The following inequality is established: ‖Pn(cos ϑ)‖< [√1+(π4/16)(n+1/2)4 sin4 ϑ]−1, 0<ϑ<π, n=1,2,..., where Pn(x) denotes the Legendre polynomial of degree n. The relation P2n(cos ϑ) + (4/π2)× Q2n(cos ϑ) < [√1+(π4/16)(n+1/2)4 sin4 ϑ]−1, n=1,2,..., on [θn1,θn,n+1], is proven where Qn(x) denotes the Legendre function of second kind, cos θn1 the largest zero of Qn(x), and cos θn,n+1=−cos θn1. Similarly we obtain the inequalities ‖J0(x)‖ < [√1+(π4/16)x4]−1, x≠0, and J20(x) + Y20(x)< [√1+(π4/16)x4]−1, x≥y1, where y1=0.893577... is the first positive zero of Y0(x), and J0(x), Y0(x) denote the Bessel functions of the first and second kind, respectively. The results of the present paper arise out of some problems of nuclear and particle physics.
Algebraic spinor solution to the Kähler equation
Authors: Talebaoui Wathek
Published: July 2002

The Kähler equation for an inhomogeneous differential form is analyzed in some detail. Algebraic spinorial solution to the Kähler equation lying in a minimal left ideal characterized by a certain idempotent projector has been examined.