bluuebunny/crossref_metadata_2025 huggingface dataset:
Fluorescence excitation spectroscopic study of the jet-cooled acetyl cyanide
Authors: Yoon Min-Chul , Choi Young S. , Kim Sang Kyu
Published: July 2002

Fluorescence excitation spectrum of acetyl cyanide (CH3COCN) in a supersonic jet has been obtained for the (1n,π*) transition (S1–S0). A spectral origin band is located at 27 511 cm−1, and its fluorescence lifetime is measured to be 3.5±0.3 μs. The S1 state vibrational modes associated with CH3 torsion, CCO bend, CCN bend, and CO wag are found to be optically active. The fluorescence intensity decreases with increasing the energy from the origin up to ∼2000 cm−1, while the fluorescence lifetime changes little over the same energy region. Instead, a broad background signal appears in the high energy region, indicating that the intramolecular vibrational redistribution (IVR) process becomes important in the S1 state as the density of states increases.
Mechanism of wedge effect in splitting of chemical bond by impact of X2−(CO2)n onto silicon surface (X=Br, I)
Authors: Kalmbach Uwe , Yasumatsu Hisato , Koizumi Shin’ichi , Terasaki Akira , Kondow Tamotsu
Published: July 2002

Dissociation of Br2− (into Br and Br−) in a cluster anion, Br2−(CO2)n, by impact of Br2−(CO2)n on a silicon surface was investigated as a function of the number of CO2 molecules, n, at a collision energy per Br2− of 30–50 eV. The branching fraction of the Br2− dissociation used as a propensity of the Br2− dissociation rate showed a marked n-dependence similar to that observed in the collisional dissociation of I2−(CO2)n on a silicon surface. The result is explained in terms of wedge effect in which a CO2 molecule at a midpoint of Br2− splits the Br2− bond as a wedge vs. cage effect in which the bond splitting of Br2− in the CO2 solvent cage is suppressed. The agreement of the n-dependence between the Br2−(CO2)n and I2−(CO2)n collisions lends a further support for the validity of the bond splitting by the wedge action. A molecular dynamics simulation reproduces the wedge effect in the Br2−(CO2)n collision, as well. The cage effect appearing in the vicinity of n=12 corresponds to the completion of the first CO2 solvent shell as is the case of the I2−(CO2)n collision.
Soft symmetry selection rules in photoemission spectroscopy: The (1×2) phase of hydrogen adsorbed on Ni(110)
Authors: Birkenheuer Uwe
Published: July 2002

Based on the idea that systems may very well exhibit continuous changes in symmetry if one focuses on physical quantities such as transition matrix elements, the concept of soft symmetry selection rules for dipole transitions is developed. The high-coverage, low-temperature (1×2)-3H phase of H/Ni(110) is chosen to illustrate the new concept. Photoemission measurements on this adsorption system only reveal a single hydrogen-derived band in variance to the stoichiometry of the adlayer. A special procedure to quantitatively decompose the eigenstates of (1×2)-3H/Ni(110) according to their behavior under 2a/3 translation along [001] is derived. It is demonstrated that this symmetry transformation, though not a strict symmetry element of the adsorption system, can be drawn upon to rationalize the unexpected experimental observations in the spirit of soft symmetry selection.
Soft Coulomb hole method applied to theoretical equilibrium geometries of singlet diatomic molecules
Authors: Hernández-Laguna A. , Alfonso-Méndez L. , Otto P.
Published: July 2002

It has been demonstrated that the soft Coulomb hole method is a reliable and efficient approach to calculate the electron correlation energy for atoms and molecules. In this method the perturbation operator −e−ωr122/r12 is introduced, where ω determines the size of the Coulomb hole. The set of parameters for ω has been redetermined to calculate equilibrium bond distances. Calculations have been performed for 41 homo- and heteronuclear singlet diatomic molecules and ions (X 1Σ+), including atoms of the second and third periods of the periodic table. The soft Coulomb hole correlation energies are compared to the corresponding empirical correlation energies. In general, calculated equilibrium bond distances are in better agreement with the experimental values than Hartree-Fock and Mo/ller-Plesset-2 results. With respect to Mo/ller-Plesset-3, the soft Coulomb hole method gives slightly larger values for the average deviations, except for the homonuclear series.
Toward a universal extinction spectrum of self-affine silver colloid clusters: Experiment and simulation
Authors: Vlčková B. , Douketis C. , Moskovits M. , Shalaev V. M. , Markel V. A.
Published: July 2002

Polarized extinction spectra of large fractal aggregates of colloidal silver deposited gravitationally onto a quartz substrate were measured by transmission as a function of angle of incidence. The spectral components tangential and normal to the average plane of the clusters compacted along the direction of deposition were extracted from these and compared with spectra calculated from simulated fractal aggregates that were projected onto a plane. The two sets agree acceptably, suggesting that the normal and tangential spectral components represent “universal,” i.e., size-independent extinction spectra characterizing all (compacted) cluster–cluster aggregates of colloidal silver.
Low temperature relaxation of OH in the X 2Π and A 2Σ states in an argon free-jet
Authors: Ahern Michael M. , Smith Mark A.
Published: July 2002

Low temperature (translational temperatures below 10 K) relaxation of OH in the X 2Π and A 2Σ states has been studied in an argon free jet. We determine upper limits on v=1 relaxation in the X 2Π manifold from laser induced fluorescence (LIF). We measure absolute relaxation rate coefficients for v=2(N), v=1(N), and v=0(N) levels in the A 2Σ state manifold. In addition, from comparison of the dispersed LIF we obtain state-to-state rate coefficients for v=1, N=0 and N=1 going to v′=0,N′ levels in the A 2Σ manifold. Bimolecular rate coefficients are reported which are all much greater than similar measurements at room temperature. Rates for vibrational relaxation at these low temperatures are 5.7(±0.7)×10−10 cm3/s for v(2−1) relaxation, 3.2(±1)×10−10 cm3/s for v(1−0) relaxation, and we report rotational relaxation rates for N=1 and 2 of v=0, 1 and 2 excited states, all near the collision limited values.
Derivative state analysis of intramolecular vibrational energy redistribution of acetylene
Authors: Hasegawa Hirokazu , Someda Kiyohiko
Published: July 2002

The intramolecular vibrational energy redistribution (IVR) of acetylene in the electronically ground state is analyzed by a novel method called derivative state analysis [K. Someda, Bull. Chem. Soc. Jpn. 69, 3037 (1996)]. The derivative state analysis clarifies how the Hilbert space of quantum states are explored in IVR, and we are thereby able to classify the quantum states and to know their genealogy. The Hamiltonian presented by Temsamani and Herman [M. A. Temsamani and M. Herman, J. Chem. Phys. 102, 6371 (1995)] is adopted in the analysis. The IVR from three different types of initial vibrational states are analyzed: (1) The initial states excited in the trans-bending (ν4) mode undergo a rapid and instantaneous IVR when v4⩾10. (2) The IVR from the states with the CH antisymmetric stretch (ν3) excitation has an onset at v3=6 and is sequential. The vibrational energy is transmitted from the ν3 mode to the CC stretch (ν2) in the first stage and then to the trans- and cis-bending. (3) Simultaneous excitation in ν2 and ν4 modes also gives rise to sequential IVR, in which the energy flows via cis-bending (ν5) to symmetric CH stretch (ν1) and ν2.
The dynamics of proton transfer in a water chain
Authors: Sadeghi Raymond R. , Cheng Hai-Ping
Published: July 2002

We perform quantum molecular dynamics simulations to study proton transfer along small water aggregates, such as a chain of hydrogen-bonded water molecules (proton wire) which is an important mechanism for charge species permeation. The electronic structure of the system is calculated concurrently with the nuclear motion using Born–Oppenheimer molecular dynamics within the framework of density functional theory. The simulations are performed on protonated linear chains of six water molecules, a linear water chain containing the water molecules, and an ammonia molecule. We discover that proton transfer along the chain is an extremely fast process, occurring in subpicosecond time scales. The translocation mechanism of the proton is neither a concerted mechanism in which the donor-acceptor pattern would occur over the entire chain in a single step, nor a result of a single proton hopping along the chain. The process takes place through a series of semicollective motion during which rapid fluctuations of the hydrogen-bond lengths along with reorganizations of water molecules are observed. The proton is translocated after a series of successive protonation-dissociation steps along the chain where hydrogen ions hop from oxygen to oxygen. We also discover that H3O+ and H5O2+ are the dominant species found during the course of the process. These simulations allow the study of dynamical properties of the systems at finite temperatures.
Universal correlation between energy gap and foldability for the random energy model and lattice proteins
Authors: Buchler Nicolas E. G. , Goldstein Richard A.
Published: July 2002

The random energy model, originally used to analyze the physics of spin glasses, has been employed to explore what makes a protein a good folder versus a bad folder. In earlier work, the ratio of the folding temperature over the glass–transition temperature was related to a statistical measure of protein energy landscapes denoted as the foldability ℱ. It was posited and subsequently established by simulation that good folders had larger foldabilities, on average, than bad folders. An alternative hypothesis, equally verified by protein folding simulations, was that it is the energy gap Δ between the native state and the next highest energy that distinguishes good folders from bad folders. This duality of measures has led to some controversy and confusion with little done to reconcile the two. In this paper, we revisit the random energy model to derive the statistical distributions of the various energy gaps and foldability. The resulting joint distribution allows us to explicitly demonstrate the positive correlation between foldability and energy gap. In addition, we compare the results of this analytical theory with a variety of lattice models. Our simulations indicate that both the individual distributions and the joint distribution of foldability and energy gap agree qualitatively well with the random energy model. It is argued that the universal distribution of and the positive correlation between foldability and energy gap, both in lattice proteins and the random energy model, is simply a stochastic consequence of the “thermodynamic hypothesis.”
Trapping dynamics of ethane on Si(100)-(2×1): Molecular beam experiments and molecular dynamics simulations
Authors: Reeves C. T. , Ferguson B. A. , Mullins C. B. , Sitz G. O. , Helmer B. A. , Graves D. B.
Published: July 2002

The trapping probability, or physical adsorption probability, of ethane on a clean Si(100)-(2×1) surface has been measured as a function of the incident translational energy and incident polar angle of the molecule at a surface temperature of 65 K. At all incident angles the trapping probability decreases as the translational energy of the incoming ethane molecule is increased from 0.05 to 1.3 eV. As the incident polar angle, with respect to the surface normal, is increased, the trapping probability decreases. This decrease in trapping probability with increasing polar angle contradicts the idea of normal energy scaling and has been seen in very few cases. Classical molecular dynamics calculations have been employed to study the cause of this unusual angular dependence. This simulation predicts trapping probabilities in good agreement with the experimental data. Analysis of the computed trajectories indicates that the initial site of impact within the unit cell, as well as energy exchange on initial impact with the surface, is important in determining the fate of an incident molecule. Normal momentum of the incident molecule is dissipated during the first impact much more efficiently than is parallel momentum. The simulations also indicate that the observed angular dependence can be explained in terms of parallel momentum accommodation. Large amounts of parallel momentum remaining after initial impact may be converted to normal momentum on subsequent impacts, causing molecules to scatter from the surface. Therefore, molecules that impact the surface at glancing angles and high translational kinetic energies are more likely to scatter from the surface than those at normal incidence or with lower translational kinetic energy.
Moderately dense gas transport coefficients via time correlation functions. I. General formalism
Authors: Snider R. F. , Alavi Saman
Published: July 2002

A new method is developed for deriving first order density corrections to gas transport coefficients using the time correlation function formalism. In a moderately dense gas, both kinetic and potential contributions to the flux are significant. This article extends the projection operator technique developed in our previous work for purely kinetic flux operators [J. Chem. Phys. 109, 3452 (1998)] to include the effects of the potential contribution to the flux. The method introduces two projection operators, one for each of the kinetic and potential flux contributions, with the consequence that the calculation of a transport coefficient involves a matrix associated with the two flux contributions, and the inversion of this matrix. The binary collision expansion of the resolvent in each of the matrix elements allows a transport coefficient at moderate gas densities to be expressed in terms of integrals over functions of the intermolecular potential. In the following article, it is shown that these results are consistent (that is, within a similar level of approximation of the integrals) with the known density corrections for the coefficients of viscosity and thermal conductivity.
Surface temperature dependence of rotational excitation of H2 scattered from Pd(111)
Authors: Watts Elizabeth , Sitz Greg O.
Published: July 2002

We have measured rotational excitation into rotational states J=3, 4, and 5 for H2 scattered from Pd(111) as a function of surface temperature and incident translational energy. Excitation is found to occur even when the incident H2 translational energy is less than the energy level spacing between the initial and final rotational states. Thus, part of the excitation energy is coming from the surface, not from solely translational–rotational energy coupling. There is a strong surface temperature dependence to the rotational excitation that is well described by an Arrhenius-type expression. When fit to the Arrhenius equation, the apparent activation energy is less than the rotational energy level spacing and decreases as the translational energy of the incident molecules is increased. Based on inspection of the calculated H2/Pd(111) potential energy surface, we attribute this lowered activation energy to an extension of the bond length when the molecule interacts with the surface. The stretching of the molecular bond increases the moment of inertia of the molecule, which then decreases the spacing between the rotational energy levels. We suggest that the final states of molecules which do not dissociate reflect features of the potential energy surface associated with open, dissociative pathways.
Vibrational spectrum, elastic moduli and mechanical stability in ice VIII
Authors: Tse John S. , Shpakov Vladimir P. , Belosludov Vladimir R.
Published: July 2002

The elastic moduli of ice VIII at different temperatures and pressures have been calculated from the quasiharmonic lattice dynamics method employing the TIP4P potential for water. It was found that under decompression, one of the Born’s stability conditions for solids was violated and ice VIII became mechanically unstable which led to a phase transformation. The transition pressure was found to decrease with temperature. This phenomenon is a symmetric equivalent of the pressure-induced crystal→amorphous transformation in ice Ih. Based on the theoretical results, it is proposed that the observed transformation of ice VIII to high density amorphous ice at low temperature is probably due to a mechanical instability in the crystal.
Toluene internal-rotation: Measurement and simulation of the high-resolution S1–S fluorescence excitation spectrum at 0.5 K
Authors: East Allan L. L. , Liu Haisheng , Lim Edward C. , Jensen Per , Déchène Isabelle , Zgierski Marek Z. , Siebrand Willem , Bunker P. R.
Published: July 2002

Rotational structure in the origin band of the S1–S0 fluorescence excitation spectrum of toluene has been measured at 0.012 cm−1 resolution with a rotational temperature of 0.5 K using a pulsed beam apparatus. Such spectra have been obtained for the parent isotopomer and for the isotopomers with mono- and di-deuterated methyl groups. These, and previously known forbidden bands in which the internal-rotation quantum number Ki changes, are simulated here using ab initio internal-rotation-angle-dependent geometries, potential functions, and electronic transition moment function. An adjustment of some of the ab initio parameters allows a close fitting of the spectra to be made, and this can only be achieved if bond lengths and angles are allowed to vary with internal rotation. The resulting geometries for ground and excited-state toluene are the most accurate to date.
Ab initio investigations on the HOSO2+O2→SO3+HO2 reaction
Authors: Majumdar D. , Kim Gap-Sue , Kim Jongseob , Oh Kyung Seok , Lee Jin Yong , Kim Kwang S. , Choi Won Yong , Lee Sung-Hoon , Kang Myung-Ho , Mhin Byung Jin
Published: July 2002

HOSO 2 radical is the key intermediate for the oxidation SO2 to SO3 by OH radical in the atmosphere. The structural aspects and the energetics of the reaction HOSO2+O2→SO3+HO2 have been studied using Mo/ller–Plesset (MP2) and density functional (DFT) techniques with 6-31G** and triple-ζ, quadruple-ζ, and quintuple-ζ quality basis sets including diffuse basis functions. The detailed theoretical analyses have further revealed that this reaction could proceed through the formation of intermediate complexes and an intramolecular proton transfer like transition state. The energetics of these intermediate reactions has been studied in detail. The use of MP2 methods to study such radical mechanisms had some characteristic symmetry-breaking problem with larger basis sets. This unphysical situation with larger basis set MP2 calculations in this hypervalent system has been explained through the interpretation of the relevant energy surface.
Theoretical study of the potential energy surfaces and bound states of HCP
Authors: Nanbu Shinkoh , Gray Stephen K. , Kinoshita Tomoko , Aoyagi Mutsumi
Published: July 2002

Global, ab initio potential energy surfaces for HCP in its ground 1 1Σ+ (1 1A′) and low-lying excited 1 1A″, 2 1A′, and 1 1Δ(2 1A″) electronic states are determined. The multireference configuration interaction method at the double zeta with polarization basis set level is used, although some calculations augmented with diffuse functions are also discussed. Numerous quantum mechanical rovibrational states are then obtained for these surfaces, with emphasis on those corresponding to excited electronic state levels which have not been studied theoretically before. The results agree reasonably well with available experimental data for the 1 1A″ state. Furthermore, the presence of certain local minima on the 1 1A″ and 2 1A′ surfaces leads to one new series of levels on the 1 1A″ surface, and two new series on the 2 1A′ surface.
Microscopic calculations of linear and quadratic optical response in model Langmuir–Blodgett multilayers
Authors: in het Panhuis M. , Munn R. W.
Published: July 2002

Microscopic calculations are reported of linear and quadratic nonlinear optical response in Langmuir–Blodgett films. The films are modeled as ordered layers of molecules that can tilt from the vertical and have a higher polarizability and first hyperpolarizability in the head than in the tail. The local electric field varies little after the first layer and negligibly after the second, which simplifies the analysis. Tilted two-layer Y-type films can have quadratic susceptibility components as large as X- or Z-type ones. Overall the results provide a systematic account of the linear and nonlinear optical properties as a function of molecular and film structure that should assist interpretation of experimental results.
Effective interaction between monolayers of block copolymer compatiblizer in a polymer blend
Authors: Thompson R. B. , Matsen M. W.
Published: July 2002

The stability of ternary blends of two immiscible homopolymers and a block copolymer compatiblizer depends crucially on the effective interaction between the copolymer monolayers that form between the unlike homopolymer domains. Here, the interaction is calculated for blends involving A and B homopolymers of equal size with AB diblock copolymers of symmetric composition using both self-consistent field theory (SCFT) and strong-segregation theory (SST). If the homopolymers are larger than the copolymer molecules, an attractive interaction is predicted which would destroy the blend. This conclusion coupled with considerations regarding the elastic properties of the monolayer suggests that the optimum size of the homopolymer molecules is about 80% that of the copolymer molecule. A detailed examination of the theory demonstrates that the attraction results from the configurational entropy loss of the homopolymer molecules trapped between the copolymer monolayers. We conclude by suggesting how the monolayers can be altered in order to suppress this attraction and thus improve compatiblization.
Potential-energy surfaces related to the thermal decomposition of ethyl azide: The role of intersystem crossings
Authors: Arenas Juan F. , Marcos Juan I. , López-Tocón Isabel , Otero Juan C. , Soto Juan
Published: July 2002

The potential-energy surfaces of ethyl azide relevant to its thermal decomposition have been studied theoretically. The geometries of minima and transition states on the S0 surfaces, as well as the lowest energy points in the seam of crossing of the triplet and singlet surfaces, have been optimized with the complete active space self-consistent field (CAS-SCF) method, and their energies, re-calculated with second-order multireference perturbation (CAS/MP2) theory and corrected by the zero-point energy (ZPE). The reaction mechanism is described by the following steps: (1) CH3CH2N3→CH3CH2N+N2, (2a) CH3CH2N→H2+CH3CN; (2b) CH3CH2N→CH3CHNH. The CN–N2 fission of ethyl azide is the rate limiting step (1), leading to ethylnitrene either along a spin-allowed path (1a) or along an alternative spin-forbidden one (1b). Both 1a and 1b channels show barriers of similar heights for CN–N2 bond fission, ΔE=42 kcal/mol, ΔE being the energy difference between the minimum of the ground singlet state potential-energy surface of ethyl azide and either the singlet transition state (TS1) or the lowest energy point of the intersystem crossing (ISC1), respectively. The decomposition of ethanimine formed in step (2b) has been studied as well and high energetic transition states have been identified for its decomposition.
Parallel-propagated frame along the geodesics of the metrics admitting a Killing–Yano tensor
Authors: Kamran Niky , Marck Jean-Alain
Published: July 2002

It is shown that the equations for a parallel-propagated frame along geodesics can be solved explicitly by separation of variables assuming the existence of a valence-2 Killing–Yano tensor that is indecomposable and such that the associated Killing tensor has no constant eigenvalue.
On an expression for the average resolvent using Grassmann integration
Authors: Ullah Nazakat
Published: July 2002

The integral representation of the inverse of a determinant and the Grassmann representation of a determinant are used to derive an expression for the average resolvent for a Gaussian orthogonal ensemble. The expression is compared with the one obtained using Lagrangian formalism.
Relativistic plasma dispersion functions
Authors: Robinson P. A.
Published: July 2002

The known properties of plasma dispersion functions (PDF’s) for waves in weakly relativistic, magnetized, thermal plasmas are reviewed and a large number of new results are presented. The PDF’s required for the description of waves with small wave number perpendicular to the magnetic field (Dnestrovskii and Shkarofsky functions) are considered in detail; these functions also arise in certain quantum electrodynamical calculations involving strongly magnetized plasmas. Series, asymptotic series, recursion relations, integral forms, derivatives, differential equations, and approximations for these functions are discussed as are their analytic properties and connections with standard transcendental functions. In addition a more general class of PDF’s relevant to waves of arbitrary perpendicular wave number is introduced and a range of properties of these functions are derived.
Painless nonorthogonal expansions
Authors: Daubechies Ingrid , Grossmann A. , Meyer Y.
Published: July 2002

In a Hilbert space ℋ, discrete families of vectors {hj} with the property that f=∑j〈hj‖ f〉hj for every f in ℋ are considered. This expansion formula is obviously true if the family is an orthonormal basis of ℋ, but also can hold in situations where the hj are not mutually orthogonal and are ‘‘overcomplete.’’ The two classes of examples studied here are (i) appropriate sets of Weyl–Heisenberg coherent states, based on certain (non-Gaussian) fiducial vectors, and (ii) analogous families of affine coherent states. It is believed, that such ‘‘quasiorthogonal expansions’’ will be a useful tool in many areas of theoretical physics and applied mathematics.
Unitary implementability of gauge transformations for the Dirac operator and the Schwinger term
Authors: Falkensteiner P. , Grosse H.
Published: July 2002

Recent interest in external field problems led to the determination of the classes of unitarily implementable gauge, axial gauge, and chiral transformations for the Dirac operator on a finite interval. Various charge quantization conditions are obtained. The algebra of charge operators is worked out and the well-known Schwinger term is identified.
Supersymmetric extension of the Korteweg–de Vries equation
Authors: Mathieu Pierre
Published: July 2002

It is shown that among a one-parameter family of supersymmetric extensions of the Korteweg–de Vries equation, there is a special system that has an infinite number of conservation laws, which can be formulated in the second Hamiltonian structure, and which has a nontrivial Lax representation. Its modified version is also discussed.
String wave equations in Polyakov’s path integral framework
Authors: Botelho Luiz C. L.
Published: July 2002

String wave equations in Polyakov’s path integral framework for string quantization are studied. This analysis is applied to formally solve the quantum chromodynamic [SU(∞)] (bosonic) contour wave equation by means of a self-avoiding string theory possessing intrinsic fermionic degrees of freedom.
Higher-dimensional unification by isometry
Authors: Cho Y. M. , Kimm D. S.
Published: July 2002

A unified theory based on a homogeneous fiber bundle Q(M,G/H) is discussed in detail. In spite of the fact that the theory retains the full G-gauge invariance, the physical gauge group K is shown to be K=H*/(H∩H*), where H* is the centralizer of H in G. A principal fiber bundle P(M,G,H) is also constructed by introducing an additional left action H on P(M,G) that commutes with the right action G, and a unified theory based on P(M,G,H) is discussed. It is shown that the theory based on Q(M,G/H) is, in fact, the H projection of the Einstein–Hilbert action from P(M,G,H), with the identification Q(M,G/H)=P(M,G,H)/H.
Linear kinetic theory in stochastic media
Authors: Sanchez Richard
Published: July 2002

Linear kinetic particle transport in stochastic heterogeneous media is discussed. The analysis includes scattering in a three-dimensional setting and deals with arbitrary time-dependent statistics. Ensemble-average operators are used to derive two independent complete descriptions for the ensemble-averaged angular flux. The first description consists of an infinite system of integral, renewal-like equations for averaged flux values over spatially dependent, increasingly smaller sets. The second approach results in an infinite system of kinetic, balancelike equations for locally averaged flux values. Both types of equations include averagings over transitional sets of states that change locally of physical properties. Previous results are recovered from the limit form of these equations for no-memory statistics and purely absorbing media. Also, the Levermore–Pomraning–Wong proposed models are shown to correspond to truncated forms of these equations.
Topological aspects of a fermion and the chiral anomaly
Authors: Roy Ashim , Bandyopadhyay Pratul
Published: July 2002

It is here shown that the chiral anomaly is related to the topological properties of a fermion. The quantization procedure of a relativistic particle requires that the particle be an extended one, and to quantize a Fermi field, it is necessary to introduce an anisotropic feature in the internal space of the particle so that it gives rise to two internal helicities corresponding to a particle and an antiparticle. This specific quantum geometry of a Dirac particle gives rise to the solitonic feature as envisaged by Skyrme and the Skyrme term appears as an effect of quantization. When in the Lagrangian formulation the effect of this topological property is taken into account, it is found that the anomaly vanishes.
Killing spinors and separability of Maxwell’s equations
Authors: Torres del Castillo G. F.
Published: July 2002

It is shown that the separation constant not related to the space-time symmetries, which appears in the solution of the source-free Maxwell equations on a type-D vacuum background with cosmological constant, can be defined in an invariant way as the eigenvalue of a differential operator made out of a two-index Killing spinor, with the eigenfunctions being the separable solutions of the Maxwell equations.
Regular double Riemann–Hilbert problems and double Kac–Moody algebraic structures for two-dimensional reduced gravity
Authors: Zhong Zai-Zhe
Published: July 2002

By using the double-complex function method, two regular double Riemann–Hilbert problems are established; therefore two double Kac–Moody algebras are given. These structures show that in two-dimensional reduced gravity, in fact, there is more exquisite hidden symmetry than common nonlinear systems.
Factorizations of the S matrix
Authors: Newton Roger G.
Published: July 2002

The S matrix of the Schrödinger equation, regarded as a function on the real axis with values in the group of unitary operators L2(S2)]L2(S2), where S2 is the unit sphere in R3, is factorized in two different ways. One of these is a standard Wiener–Hopf factorization with respect to the real line. The other is the kind of factorization that defines the Jost function and which has been found to be a useful tool for the solution of the inverse scattering problem. A number of results are given that relate the two factorizations, their existence as well as the indices they give rise to. Some known theorems on the standard factorization lead to new results for the three-dimensional inverse scattering problem for the Schrödinger equation with a noncentral potential; in particular, a characterization of admissible S matrices is obtained.
Chern–Simons terms in metric-affine space-time: Bianchi identities as Euler–Lagrange equations
Authors: Hehl Friedrich W. , Kopczyński Wojciech , McCrea J. Dermott , Mielke Eckehard W.
Published: July 2002

The metric-affine gauge theory of gravity encompasses a space-time with the following geometrical fields: coframe ϑα, metric g, and an independent linear connection Γαβ. Within this geometrical framework, all four-forms B=dC are constructed which qualify as boundary terms for a gauge Lagrangian, that is, they are GL(4,R)-scalars as well as exact forms derived from Chern–Simons type three-forms C. The result of our search is summarized in Eq. (4.20). The translational piece dCTT is new. The boundary terms effectively serve as Lagrangians for the Bianchi identities of nonmetricity, torsion, and curvature. In the canonical formalism, the normal parts of the Chern–Simons three-forms represent generating functions that are capable of generating new Ashtekar type variables. Eventually, the Bach–Lanczos identity is generalized to the metric-affine space-time.
On the gravitational interaction of plane symmetric clouds of null dust
Authors: Tsoubelis Dimitri , Wang Anzhong
Published: July 2002

Plane symmetric solutions of the Einstein field equations are considered, solutions that represent the collision of oppositely moving clouds of initially unidentified massless particles—clouds of ‘‘null dust.’’ In terms of specific examples it is shown that the corresponding Cauchy problem remains ambiguous even when the Riemann tensor is free of any kind of discontinuity. By solving the corresponding Einstein–Klein–Gordon and Einstein–Maxwell–Weyl field equations the ambiguity is resolved and space-time models are constructed representing, among others, various types of collisions between a pair of scalar wave pulses as well as of a pulse of electromagnetic waves with a cloud of neutrinos.
Ergodicity and invariant measures of some randomly perturbed classical fields
Authors: Haba Z.
Published: July 2002

Time evolution, ergodic properties, and invariant measures of some classical fields described by second-order differential equations are discussed. The classical system is not ergodic. A class of Markovian random perturbations is considered. It is shown that the stochastic system with a fixed stochastic perturbation is uniquely ergodic. We discuss in detail the Euler equation in two dimensions and the wave equation in one dimension. In our models an arbitrarily small stochastic perturbation selects one of the invariant measures for the deterministic system.
Steady currents in composite conductors, eigenfunction expansions, and exactly solvable linear integral equations
Authors: Inayat-Hussain A. A.
Published: July 2002

A novel connection is uncovered between the simple physics of steady current flow in a composite conductor and the theory of integral equations. With a judicious choice of eigenfunction expansions, exploitation of the physical continuity of current flow across a chosen interface in a composite conductor is shown to yield an infinite class of integral equations with exact closed-form solutions. The mathematical derivation of this class is based on the elementary (but also new) notion of formally equating two different eigenfunction expansions of a given arbitrary function. The new class contains as special cases the celebrated Abel integral equation of classical mechanics and the Kramers–Kronig relations of electromagnetic scattering. But it also contains new integral equations (with exact solutions), some with the Cauchy-singularity 1/(x−y) in their kernels, and a new summation equation. These new equations are in themselves intriguing and their exact solutions do not appear to be derivable by the known methods for solving integral equations. An application of the new class of integral equations is given in the context of a particular composite conductor, which consists of a semi-infinite strip imbedded in an otherwise homogeneous whole space conductor (containing a uniform current flow parallel to the strip).

The coefficient in the eigenfunction expansion of the potential in the strip satisfies a one-dimensional singular integral equation with a Cauchy-singularity. This singularity is regularized by the application of an integral equation and its exact solution from the new class, resulting in an integral equation with a smooth kernel. This equation together with the eigenfunction expansion provides an elegant representation for the potential in the strip. (The only known exact solutions are for the cases of elliptic-cylinder and ellipsoid geometries in two and three dimensions, respectively.) The new class of integral equations yields the first examples of singular kernels which possess a bilinear expansion in terms of two different complete sets of eigenfunctions, with only the diagonal terms (i.e., those terms in which the summation indices or integration variables are equal) in the expansion being nonzero. Such an expansion for square-integrable kernels (as opposed to singular kernels) is well known in the Hilbert–Schmidt theory of Hermitian operators and in Schmidt’s extension to the non-Hermitian case, and it forms the basis for a method of solving Fredholm integral equations. None of these theories, however, yields the bilinear expansions for the singular kernels of our new class.
Error bounds for maximum entropy approximate solutions to Fredholm integral equations
Authors: Kopeć S.
Published: July 2002

A new method of calculating a posteriori error bounds for maximum entropy approximate solutions to Fredholm integral equations is introduced. A numerical example confirming the efficacy of the method is also presented.
Head-on collision of gravitational plane waves with noncollinear polarization: A new class of analytic models
Authors: Tsoubelis Dimitri , Wang Anzhong
Published: July 2002

A new four-parameter class of exact solutions of Einstein’s field equations is obtained, using the inverse scattering method of Belinsky and Zakharov. Its members represent the head-on collision of a variably polarized gravitational plane wave with one having constant polarization and, in general, different profile, or with an infinitely thin shell of null dust. In some of these models no curvature singularity develops along the future boundary of the region of interaction. In certain cases the singularity avoidance is the direct result of the noncollinear polarization of the waves involved in the collision.
The pattern calculus for tensor operators in quantum groups
Authors: Gould Mark , Biedenharn L. C.
Published: July 2002

An explicit algebraic evaluation is given for all q-tensor operators (with unit norm) belonging to the quantum group Uq(u(n)) and having extremal operator shift patterns acting on arbitrary Uq(u(n)) irreps. These rather complicated results are shown to be easily comprehensible in terms of a diagrammatic calculus of patterns. A more conceptual derivation of these results is discussed using fundamental properties of the q−6j coefficients.
General results for massive N-point Feynman diagrams with different masses
Authors: Davydychev A. I.
Published: July 2002

General expressions are obtained for scalar one-loop massive Feynman diagrams with any number of external lines and with arbitrary momenta of these lines, with arbitrary values of masses and powers of denominators of internal lines, the space-time dimension n also being arbitrary. Special cases are considered when two (or more) masses are equal to 0. The results are represented in terms of hypergeometric functions.
On the Kadomtsev–Petviashvili hierarchy, Ŵ∞ algebra, and conformal SL(2,R)/U(1) model. I. The classical case
Authors: Yu Feng , Wu Yong-Shi
Published: July 2002

In this article the interrelationship between the integrable Kadomtsev–Petviashvili (KP) hierarchy, nonlinear Ŵ∞ algebra, and the conformal noncompact SL(2,R)/U(1) coset model at the classical level is studied. The Poisson brackets of the second Hamiltonian structure of the KP hierarchy is derived first explicitly, then the Ŵ1+∞ algebra and its reduction Ŵ∞ are defined. Then it is shown that the latter is realized in the SL(2,R)/U(1) coset model as a hidden current algebra, through a free field realization of Ŵ∞, in closed form for all higher-spin currents, in terms of two bosons. An immediate consequence is the existence of an infinite number of KP flows in the coset model, which preserve the Ŵ∞-current algebra.
Convergence of unitary and complex decompositions of exponential operators
Authors: Suzuki Masuo , Yamauchi Takashi
Published: July 2002

The convergence of the fractal unitary and complex decompositions of exponential operators is proved for Hermitian operators in a Banach space.
Two-dimensional integrable systems and self-dual Yang–Mills equations
Authors: Guil F. , Mañas M.
Published: July 2002

The relation between two-dimensional integrable systems and four-dimensional self-dual Yang–Mills equations is considered. Within the twistor description and the zero-curvature representation a method is given to associate self-dual Yang–Mills connections with integrable systems of the Korteweg–de Vries and nonlinear Schrödinger type or principal chiral models. Examples of self-dual connections are constructed that as points in the moduli do not have two independent conformal symmetries.
Quantum aspects of 2+1 gravity
Authors: Loll R.
Published: July 2002

We review and systematize several recent attempts to canonically quantize general relativity in 2+1 dimensions, defined on space–times R×Σg, where Σg is a compact Riemann surface of genus g. The emphasis is on quantizations of the classical connection formulation, which use Wilson loops as their basic observables, but results from the ADM formulation are also summarized. We evaluate the progress and discuss the possible quantum (in)equivalence of the various approaches.
General properties between the canonical correlation and the independent-oscillator model on a partial *-algebra
Authors: Hirokawa Masao
Published: July 2002

We consider a quantum particle in thermal equilibrium with any quantum system in a finite volume under some conditions. For the Heisenberg operator of the momentum operator of the quantum particle, we show that, on a partial *-algebra, the Heisenberg operator satisfies a quantum Langevin equation, which is similar to the work of Ford et al. [ G. W. Ford, J. T. Lewis, and R. F. O’Connell, Phys. Rev. A 37, 4419 (1988)]. Through the Langevin equation, we show general and mathematical properties between the canonical correlation and the independent-oscillator model.
Solution to three-magnon problem for S=1/2 periodic quantum spin chains with elliptic exchange
Authors: Inozemtsev V. I.
Published: July 2002

The method of solving the three-particle quantum elliptic Calogero–Moser problem is applied to the description of three-magnon wave functions for the S=1/2 quantum Heisenberg chains with the exchange interaction given by the Weierstrass d function. The Bethe-like algebraic equations for the three-magnon case are presented in the explicit form.
On the quantum deformations of Hamiltonian systems
Authors: Lledó M. A. , García-Sucre M.
Published: July 2002

In this paper we analyze the relationship between operatorial quantization and deformation quantization for Hamiltonian systems on R2n. We define heuristically generalized symbols for the operators, which make this connection. We construct explicitly deformations which are not equivalent to the Moyal one and show that an infinitesimal, classical canonical transformation does not change the equivalence class of the deformation. The results are applied to the quantum integrability of some two dimensional Hamiltonian systems.
New solution of the wave equation with a uniformly moving point source
Authors: Borghardt Alexander A. , Karpenko Darya Ya.
Published: July 2002

A new solution of the inhomogeneous d’Alembert equation with the point uniformly moving charge is found. The comparison of the new solution with the Kirchhoff formula solution is performed.
The initial singularity in solutions of the Einstein–Vlasov system of Bianchi type I
Authors: Rendall Alan D.
Published: July 2002

The dynamics of solutions of the Einstein–Vlasov system with Bianchi I symmetry is discussed in the case of massive or massless particles. It is shown that in the case of massive particles the solutions are asymptotic to isotropic dust solutions at late times. The initial singularity is more difficult to analyze. It is shown that the asymptotic behavior there must be one of a small set of possibilities, but it is not clear whether all of these possibilities are realized. One solution is exhibited in the case of massless particles, which behaves quite differently near the singularity from any Bianchi I solution with perfect fluid as a matter model. In particular, the matter is not dynamically negligible near the singularity for this solution.
Majorana parafermions
Authors: Dunne Robert S.
Published: July 2002

A Majorana analog to the parafermion algebra is constructed and shown to be isomorphic to so(n). Ansatz realizations of this algebra are constructed and used to establish the properties of particular representations. The construction of specific so(n) representations is discussed for odd and even n, and for even n the procedure is illustrated explicitly in the case of so(4). By contracting the Majorana parafermion algebra, the para-Grassman algebra and its representation theory are obtained.
Diffuse tomography modulo Grassmann and Laplace
Authors: Patch S. K.
Published: July 2002

Complicated and unphysical families of modified transition probabilities for the 4×4 diffuse tomographic problem are presented. Grassmann–Plücker identities and Laplace expansions of determinants are used to simplify the initial transition probabilities. Besides restoring self-consistency to the system, enforcing range conditions eliminates one-half of the parameters.
Prolongation approach to Bäcklund transformation of Zhiber–Mikhailov–Shabat equation
Authors: Yang Huan-Xiong , Li You-Quan
Published: July 2002

The prolongation structure of Zhiber–Mikhailov–Shabat (ZMS) equation is studied by using Wahlquist–Estabrook’s method. The Lax pair for ZMS and Riccati equations for pseudopotentials are formulated respectively from linear and nonlinear realizations of the prolongation structure. Based on nonlinear realization of the prolongation structure, an auto-Bäcklund transformation of ZMS equation is obtained.
A noncommutative Hopf structure on 𝒞 ∞[SL(2,C)] as a quantum Lorentz group
Authors: Martin Christiane , Zouagui Mohamed
Published: July 2002

We introduce a ‘‘classical’’ Fréchet Hopf algebra 𝒜 containing the quantum deformation of the enveloping Lorentz algebra of Ogievestky and Wess et al. (as a dense Hopf subalgebra). We also show that 𝒜 is isomorphic to a quasitriangular twisted topological tensor product Hopf algebra. By duality, we recover on the topological dual space of 𝒜, the non-commutative algebra structure introduced by Podles and Woronowicz. Finally, this non-commutative product can be extended to 𝒞∞(SL(2,C)) which then becomes a topological Hopf algebra for its natural Fréchet topology.
Relativistic classical theory of a free particle
Authors: Bosanac S. Danko
Published: July 2002

By shifting the emphasis from the concept of trajectory to the concept of probability density it is possible to incorporate the uncertainty principle into classical mechanics. This amendment in the nonrelativistic classical theory is sufficient to derive the Schrödinger equation for a general potential. In order to show that the approach has general validity it is necessary to show that it can be generalized to the classical relativistic dynamics. In this paper it is shown how this generalization is achieved for a free particle, and as a result the Dirac instead of the Klein–Gordon equation is obtained. It is shown that the spin and the magnetic moment of charged particles are classical in character because their correct values are calculated as the averages over the classical (relativistic) phase space density, subject to the constraint imposed by the uncertainty principle. Since the Dirac equation has direct connection to the classical (relativistic) dynamics the problem of the positive and negative energy states is discussed.