bluuebunny/crossref_metadata_2025 huggingface dataset:
Localization of random copolymers at an interface: Numerical simulations
Authors: Chen Zheng Yu
Published: July 2002

The scaling behavior of the conformational properties of localized random copolymers at a sharp interface is systematically examined. The Garel–Huse–Leibler–Orland model is solved numerically for the localized monomer density at various temperatures, chain lengths, and disorder distributions. The average monomer distance from the interface, the mean free energy, and the localization transition temperatures are all explicitly evaluated and compared with scaling predictions from analytic approaches.
Coulomb energies of icosahedral h orbitals
Authors: Judd B. R. , Lo Edwin
Published: July 2002

Matrix elements of all two-electron and three-electron operators that are scalar with respect to the icosahedral group I have been tabulated for the icosahedral configurations hN. These operators represent the Coulomb interaction between electrons occupying h orbitals, and also the effects (to the lowest orders of perturbation theory) of configuration interaction on the levels of hN. States and operators are labelled by the irreducible representations (irreps) of the continuous groups SO(3) and SO(5) in addition to the irreps of I. An alternative scheme is introduced in which the irreps W of SO(5) are retained, but the orbital angular-momentum quantum numbers L associated with SO(3) are replaced by the irreps of the permutation groups S5 and S6, the latter corresponding to the interchanges (possibly nonfeasible) of the six fivefold axes of an icosahedron among themselves. The kaleidoscope operator 𝒦, which rotates the weight space of SO(5) by π/2, is an element of S5 and S6, and can be used to characterize the operators. The energy matrices in the second scheme are particularly simple, the scalar or pseudoscalar nature of the operators with respect to S5 leading to block forms either on the diagonal or off the diagonal, respectively. Operators of the former kind are invariant under the 𝒦 operation and, in the hypothetical absence of the pseudoscalars, would lead to every level of icosahedral type T1 being degenerate with a level of type T2.
Simulation of muonium formation in liquid hydrocarbons
Authors: Siebbeles Laurens D. A. , Pimblott Simon M. , Cox Stephen F. J.
Published: July 2002

Muonium formation in liquid hexane is examined by computer simulation. In track-end competition between muonium formation and cation–electron recombination, the muon is found to react with electrons from a significant part of the track end, corresponding to an energy attenuation of several tens of keV and a length of several microns. This muonium formation extends to microseconds following muon implantation. Delayed muonium formation leads to a much smaller amplitude of the muonium asymmetry than for prompt muonium formation during slowing down of the muon, and in this way may account for the missing polarization in transverse magnetic field experiments. If reaction of muons with electrons from their radiolysis tracks contributes to the experimentally observed muonium yield, the muon must thermalize between 60 and 150 nm from the last ionization of the track to reproduce the amplitudes of the muon and muonium asymmetries. For the smallest distance, 60 nm, the experimentally observed muonium asymmetry results from delayed muonium only. As the muon thermalization distance increases, prompt muonium formation also contributes, so that at 150 nm the observed asymmetry is almost entirely due to prompt muonium formation.
Phase separation in confined polymer blends
Authors: Cherrabi R. , Saout-Elhak A. , Benhamou M. , Daoud M.
Published: July 2002

We consider a binary blend of two polymers of different chemical nature, confined between two adsorptive parallel surfaces separated by a distance L. We assume that the two surfaces adsorb strongly one or both species at high temperature. This implies quenched compositions on surfaces. We assume that phase separation takes place at lower temperature. Two independent effects are present and must be taken into account, the quenched surface fluctuations and finite-size effect due to the finite thickness L. Using a systematic and analytical method, we first investigate the variation of the composition profile with the distance z from one surface taken as origin. The profile shape depends on the monomer fractions on the surfaces, the temperature, and the size L. We find that the profile may have three distinct behaviors depending on the value of the surface composition: it may (i) exhibit one extremum between the two plates, (ii) have a new, surprising, oscillatory character, or (iii) be strictly monotonous. We then evaluate the interaction forces between the walls due to density fluctuations. We show that these forces may be either repulsive or attractive, and we estimate in their dependence in the separation distance L for all cases. Such a system may play the role of a force sensor.
Diffusion of single long polymers in fixed and low density matrix of obstacles confined to two dimensions
Authors: Azuma Ryuzo , Takayama Hajime
Published: July 2002

Diffusion properties of a self-avoiding polymer embedded in regularly distributed obstacles with spacing a=20 and confined in two dimensions is studied numerically using the extended bond fluctuation method which we have developed recently. We have observed for the first time to our knowledge, that the mean square displacement of a center monomer φM/2(t) exhibits four dynamical regimes, i.e., φM/2(t)∼tνm with νm∼0.6, 38, 34, and 1 from the shortest to longest time regimes. The exponents in the second and third regimes are well described by segmental diffusion in the “self-avoiding tube.” In the fourth (free diffusion) regime, we have numerically confirmed the relation between the reptation time τd and the number of segments M, τd∝M3.
Absorption spectroscopy on single molecules in solids
Authors: Kador Lothar , Latychevskaia Tatiana , Renn Alois , Wild Urs P.
Published: July 2002

Absorption signals of single terrylene molecules in n-hexadecane and naphthalene crystals were recorded at liquid-helium temperatures. The method is based upon rf Stark effect modulation in the megahertz range. The electric rf field strength was applied by means of interdigitating electrodes with 18 μm spacing. Signal-to-noise ratios better than 10 were obtained with approximately 300 ms integration time. The measured line shapes depend on the relative contributions of the linear and the quadratic Stark shift.
Response to “Comment on ‘Ab initio dynamic dipole polarizabilities for O2, its photoabsorption spectrum in the Schumann–Runge region, and long-range interaction coefficients for its dimer’ ” [J. Chem. Phys. 111, 11236 (1999)]
Authors: Spelsberg Dirk , Meyer Wilfried
Published: July 2002

The oscillator strengths of the discrete part of the Schumann–Runge band system is recalculated from single-state calculations using the adiabatic potential curve. Potential curves for three Πu3 states are computed. The integrated oscillator strength for the Πu3←Σu3 transition is recalculated from four-state coupled diabatic calculations.
State-to-state rotational excitation of CO by H2 near 1000 cm−1 collision energy
Authors: Antonova Stiliana , Tsakotellis Antonis P. , Lin Ao , McBane George C.
Published: July 2002

Relative state-to-state rotationally inelastic cross sections for excitation of carbon monoxide by hydrogen were measured in a crossed molecular beam experiment at collision energies 795, 860, and 991 cm−1. The results are compared to predictions of a recent ab initio potential energy surface [J. Chem. Phys. 108, 3554 (1998)]. The agreement is very good. A comparison with older data on thermally averaged total depopulation cross sections [Chem. Phys. 53, 165 (1980)] indicates that the absolute magnitudes of the cross sections predicted by the surface are too high. The CO excitation is dominated by collisions that are elastic in H2 rotation, and the collision dynamics are very similar for different rotational levels of hydrogen.
Structure of liquid caesium–bismuth alloys studied by neutron diffraction
Authors: van der Aart S. A. , Verhoeven V. W. J. , Verkerk P. , van der Lugt W.
Published: July 2002

Neutron diffraction experiments were carried out for two liquid alloys with compositions CsBi and Cs3Bi2. The results indicate that probably polyanions with an average number of about two Bi atoms per cluster are formed. This result contrasts with that for liquid Cs–Sb, which contains larger chains as polyanions.
A self-consistent integral equation study of the structure and thermodynamics of the penetrable sphere fluid
Authors: Fernaud Maria-Jose , Lomba Enrique , Lee Lloyd L.
Published: July 2002

The penetrable sphere fluid consists of a system of spherical particles interacting via a potential that remains finite and constant for distances smaller than the particle diameter and is zero otherwise. This system, which was proposed sometime ago as a model for micelles in a solvent, has represented so far a remarkable challenge for integral equation theories which proved unable to correctly model the behavior of the two-body correlations inside the particle overlap region. It is shown in this work that enforcing the fulfillment of zero separation theorems for the cavity distribution function y(r), and thermodynamic consistency conditions (fluctuation vs virial compressibility and Gibbs–Duhem relation), on a parametrized closure of the type proposed by Verlet, leads to an excellent agreement with simulation, both for the thermodynamics and the structure (inside and outside the particle core). Additionally, the behavior of the integral equation at high packing fractions is explored and the bridge functions extracted from simulation are compared with the predictions of the proposed integral equation.
Design of heteronuclear decoupling sequences for solids
Authors: Khitrin Anatoly , Fung B. M.
Published: July 2002

A strategy of designing new heteronuclear broadband decoupling sequences for solid state NMR is presented. From a semiquantitative analysis of the problem, it is concluded that the use of multifrequency excitation in the rotating frame would lead to an effective averaging of the heteronuclear dipolar interaction. The actual implementation involves a phase modulation of the decoupler as a function that is a sum of several cosine terms. The new decoupling sequences are abbreviated as CPM m-n for cosine phase modulation with m harmonics and having frequency intervals of ωrf/n, where m and n are integers. Experimental results show that their performances are considerably better than those of the existing decoupling methods, under conditions of moderate spinning rate and decoupling power.
Atomic integral driven second order polarization propagator calculations of the excitation spectra of naphthalene and anthracene
Authors: Bak Keld L. , Koch Henrik , Oddershede Jens , Christiansen Ove , Sauer Stephan P. A.
Published: July 2002

An atomic integral direct implementation of the second order polarization propagator approximation (SOPPA) for the calculation of electronic excitation energies and oscillator strengths is presented. The SOPPA equations are solved iteratively using an integral direct approach and, contrary to previous implementations, the new algorithm does not require two-electron integrals in the molecular orbital basis. The linear transformation of trial vectors are calculated directly from integrals in the atomic orbital basis. In addition, the eigenvalue solver is designed to work efficiently with only three trial vectors per eigenvalue. Both of these modifications dramatically reduce the amount of disk space required, thus, increasing the range of applicability of the SOPPA method. Calculations of the lowest singlet excitation energies and corresponding dipole oscillator strengths for naphthalene and anthracene employing basis sets of 238 and 329 atomic orbitals, respectively, are presented. The overall agreement of our results with experimental spectra is good. The differences between the vertical excitation energies calculated by SOPPA and the position of the maximum intensity peaks in the experimental spectra are within the range of ±0.35 eV with two exceptions, the 4 1Ag state of naphthalene and anthracene where a 0.85 eV and 0.41 eV deviation is found, respectively. The relatively large discrepancy for this transition is due to large contributions from two-electron excitations which cannot accurately be described in SOPPA. For naphthalene we find additional excitations to Rydberg states of 1Au and 1B2u symmetry as compared with previous calculations.
Charge recombination in contact ion pairs
Authors: Frantsuzov P. A. , Tachiya M.
Published: July 2002

A theoretical explanation of the recently observed non-Marcus free energy gap dependence of the charge recombination rate in contact ion pairs is presented. The electron transfer event is described as a nonadiabatic depopulation of the initially excited adiabatic state. This model explains the absence of the normal region. Quantitative predictions based on the perturbation theory in the nonadiabatic interaction show good agreement with experimental results.
Negative ion photoelectron spectroscopy of OH−(NH3)
Authors: Schwartz Rebecca L. , Davico Gustavo E. , Kim Joseph B. , Carl Lineberger W.
Published: July 2002

The 351 nm photoelectron spectra of OH−(NH3)n n=1,2 and the deuterated analogs exhibit two broad peaks. Ab initio calculations of the anion and neutral potential-energy surfaces have been carried out using an MP2 (second-order Mo/ller–Plesset)/6-31++G** basis set. The geometries, frequencies, and energetics from these calculations aid in the interpretation of the experimental results. An estimate of the OH(NH3) electron affinity is 2.35±0.07 eV based on experimental and theoretical results. Calculations of the anion vibrational wave functions indicate that following electron photodetachment, the neutral potential-energy surface is accessed from the reactant entrance channel through the transition state region.
Production of fullerenes and single-wall carbon nanotubes by high-temperature pulsed arc discharge
Authors: Sugai Toshiki , Omote Hideki , Bandow Shunji , Tanaka Nobuo , Shinohara Hisanori
Published: July 2002

Fullerenes and single-wall carbon nanotubes (SWNTs) have been produced for the first time by the high-temperature pulsed arc-discharge technique, which has developed in this laboratory. Fullerenes are identified quantitatively by high-performance liquid chromatography (HPLC), and scanning electron microscopy (SEM) and transmission electron microscopy (TEM) observations reveal a significant amount of production of bundles of SWNTs in soot. The pulse arc production of fullerenes and SWNTs favors the high-temperature (⩾1000 °C), long pulses (⩾1 ms) and a heavy rare gas such as Ar or Kr as a buffer gas. We have found that fullerenes and SWNTs have complementary relationships in their early stage of production. The details of the pulsed arc discharge have been obtained by observing the transition from the pulsed arc discharge to the steady arc discharge while increasing the pulse width.
Mechanism and cross sections for HD and CH4−xDx (x=1–4) formation in D(g)+CH3/Cu(111) reaction at 100 K
Authors: Kim Jae-Young , Lee Jihwa
Published: July 2002

We have investigated the kinetics of the gas-phase D atom reaction with methyl (CH3) adsorbed on Cu(111) at 100 K, in which the product molecules desorbing from the surface were directly monitored with a mass spectrometer. While adsorbed D atom combines with CH3(ad) to form CH3D at temperatures ⩾ 300 K, the incident D(g) atom readily abstracts CH3(ad) to form CH3D at 100 K. In addition, the D(g) atom also abstracts a H atom from CH3(ad) to form HD and CH2(ad) which is subsequently converted to CH2D(ad) by addition of an incident D(g) atom. CH2D(ad) thus formed in turn undergoes the same reaction sequence to lead to desorption of CH2D2, CHD3, and CD4. A kinetic analysis was made to extract the reaction cross sections for the elementary reactions involved: σCH3=2.9±0.2, σH=0.5±0.05, and σa⩾22 Å2 for the CH3(ad) abstraction, H abstraction, and D atom addition reactions, respectively. These are essentially barrierless reactions, showing almost no temperature dependence. σCH3 varied with the beam incidence angle θi as cos0.63 θi and σH as cos0.85 θi. The mechanism of each elementary reaction was discussed in terms of a direct Eley–Rideal (ER) and primary hot atom (p-HA)—trapped but not accommodated incident atom—mechanisms by considering the cross section, energetics, and reaction dynamics. Finally, we concluded that (1) the H abstraction from CH3(ad) occurs exclusively by an ER mechanism, (2) the CH3(ad) abstraction predominantly occurs by an ER mechanism with some contribution by a p-HA mechanism, and (3) the D(g)-addition to CH2(ad) exclusively by a p-HA mechanism.
Diffusion of reactive species tuned by modulated external fields: Application to high performance chromatography
Authors: Jullien L. , Lemarchand A. , Lemarchand H.
Published: July 2002

In order to improve the separation of any given chemical species from a mixture of compounds with close thermodynamic and kinetic properties, we propose a new chromatography procedure in the presence of a uniform time-periodic field. In the framework of a macroscopic reaction–diffusion model in an external field, we prove that the apparent motion of the chemical species is of diffusion type and determine an approximate analytical expression for the effective diffusion coefficient. Considering this coefficient as a function of the rate constants and maximizing it leads to specific relations between rate constants and field properties interpreted as stochastic resonances. In the case of an electric field, we show that these constraints are compatible with typical experimental values.
Study of the dissociation of neutral intermediates using charge inversion mass spectrometry
Authors: Hayakawa Shigeo , Harada Kengo , Arakawa Kazuo , Morishita Norio
Published: July 2002

In charge inversion experiments using a tandem mass spectrometer, mass-selected positive ions are made to collide with an alkali metal target, and the resulting negative ions formed upon two-electron transfer are mass-analyzed. The internal energy depositions are measured for the so-called thermometer molecule W(CO)6. The difference between the centered value of the internal energy of W(CO)6 and the energy level of the precursor ion is in good agreement with the ionization energy of the Cs target. This correlation indicates that dissociation occurs from energy-selected neutrals formed via near-resonant neutralization.
The effect of force-field parameters on properties of liquids: Parametrization of a simple three-site model for methanol
Authors: Walser Regula , Mark Alan E. , van Gunsteren Wilfred F. , Lauterbach Monika , Wipff Georges
Published: July 2002

A simple rigid three-site model for methanol compatible with the simple point charge (SPC) water and the GROMOS96 force field is parametrized and tested. The influence of different force-field parameters, such as the methanol geometry and the charge distribution on several properties calculated by molecular dynamics is investigated. In particular an attempt was made to obtain good agreement with experimental data for the static dielectric constant and the mixing enthalpy with water. The model is compared to other methanol models from the literature in terms of the ability to reproduce a range of experimental properties.
Zero-field signal in the electron paramagnetic resonance spectrum of Mn+2 in silicate glasses
Authors: Rakhimov Rakhim R. , Jones David E.
Published: July 2002

A 9.4–9.8 GHz electron paramagnetic resonance (EPR) study of Mn+2-doped Na2O–CaO–MgO–SiO2 glasses has revealed a nonresonant microwave magneto-absorption near zero magnetic field in addition to normal paramagnetic absorption due to Mn+2 ions, electron spin S=5/2. The low-field response has an opposite phase relative to paramagnetic signal and is independent of the mutual orientation of the magnetic field of the microwave H1 and static magnetic field H. In contrast, the paramagnetic signal is different for perpendicular H1⊥H and parallel H1∥H polarization of the microwave field, which is attributed to enhancement of forbidden magnetic dipolar transitions and suppression of the allowed transitions for parallel polarization. The low-field response is described in terms of microwave dielectric losses that derive from the magneto-induced charge migration in the first coordination sphere of Mn+2. As opposed to the spin-polarized tunneling that was described in ferromagnets between different valence forms of Mn, the observed effect is due to spin-dependent tunneling that occurs in the vicinity of Mn+2 in a diluted paramagnetic system.
The electronic structure and properties of group 7 oxychlorides, MO3Cl, where M=Tc, Re, and element 107, Bh
Authors: Pershina V. , Bastug T.
Published: July 2002

Fully relativistic density-functional calculations have been performed for group 7 oxychlorides MO3Cl, where M=Tc, Re, and element 107, Bh. The results have shown the Bh compound to be thermochemically stable and the most stable towards reduction. Due to increasing dipole moments and electric dipole polarizabilities in the group, volatility of the MO3Cl compounds proved to change as TcO3Cl>ReO3Cl>BhO3Cl. For gas-phase chromatography experiments, the adsorption enthalpy of the molecules on the surface of a chromatography column has been predicted as −78±5 kJ/mol.
Collisional dependence of polarization spectroscopy with a picosecond laser
Authors: Reichardt Thomas A. , Di Teodoro Fabio , Farrow Roger L. , Roy Sukesh , Lucht Robert P.
Published: July 2002

The collisional dependence of polarization spectroscopy (PS) with a picosecond-pulse laser is investigated theoretically with a perturbative treatment and experimentally by probing hydroxyl (OH) in a flow cell with a buffer gas of argon. Using a frequency-doubled distributed-feedback dye laser (DFDL), the PS signal strength is monitored as a function of pressure using a nonsaturating pump beam and a saturating pump beam. The collisional dependence of the PS signal is found to decrease significantly with a saturating pump beam. Increasing the flow-cell pressure by a factor of 50 (from 10 torr to 500 torr), the PS signal strength produced with a nonsaturating pump beam decreases by a factor of 18 while that produced with a saturating pump decreases by only a factor of 3. A third-order perturbative (weak-field) approach is used to develop an analytical expression for the PS signal generated by single-mode, exponentially decaying laser pulses. This expression correctly predicts the experimental results acquired with the nonsaturating pump beam. The analytical solution is used to examine the effects of pulse length on the collisional dependence of the weak-field PS signal strength. Results are also presented for a numerical simulation of the time-dependent density matrix equations for the high intensity case.
Conformal symmetry and constants of motion
Authors: Hussin V. , Sinzinkayo S.
Published: July 2002

Conformal space-time symmetries of electromagnetic fields and potentials are studied in order to determine whole sets of constants of motion when spin- 1/2 charged particles interact with such external electromagnetic fields. The relativistic and nonrelativistic contexts are discussed through the Hamiltonian formalism. In particular, the interesting example of the magnetic monopole field is recovered and related to the recent works of Jackiw and D’Hoker–Vinet.
Lie–Bäcklund transformations for the massive Thirring model
Authors: Kersten Paul H. M. , Martini Ruud
Published: July 2002

Second- and third-order Lie–Bäcklund transformations of the massive Thirring model are computed by symbolic integration.
N-dimensional spinors: Their properties in terms of finite groups
Authors: Braden H. W.
Published: July 2002

A classification scheme is presented for the finite multiplicative group generated by the gamma matrices associated with a given Clifford algebra. This group reflects the periodicities observed in n-dimensional spinors, and its representations and other properties are studied, thus highlighting the dependence on the number of spacelike and timelike vectors. The reality of the representations is examined and tabulated; application is made to the imposition of Majorana and Weyl conditions.
The Gel’fand realization and the exceptional representations of SL(2,R)
Authors: Basu Debabrata , Bhattacharya T.
Published: July 2002

It is shown that the canonical representation space of Gel’fand and co-workers is particularly appropriate for problems requiring explicit reduction under the noncompact SO(1,1) and E(1) bases for both the principal and exceptional series of representations of SL(2,R). We use this realization to set up complete orthonormal sets of eigendistributions corresponding to the three subgroup reductions, namely, SL(2,R)⊇SO(1,1), SL(2,R)⊇E(1), and SL(2,R)⊇SO(2), and evaluate the unitary transformations connecting these reductions. These overlap matrix elements appear as the applications of these distributions to a set of well-defined test functions. Using the rigorous theory of analytic continuation we show that the results for the exceptional representations have the same analytic forms as the corresponding results for the principal series. Some of these results are essential prerequisites for the solution of the Clebsch–Gordan problem (series and coefficients) of SL(2,R) in the SO(1,1) basis.
Noether-type conservation laws for perfect fluid motions
Authors: Caviglia G. , Morro A.
Published: July 2002

A general approach is developed for the derivation of conservation laws in continuum physics. A Noether-type theorem is applied in connection with transformations which leave the action functional invariant to within the integral of a divergence. Specific results are derived in the case of fluid dynamics: the pertinent equations are considered within the Lagrangian (material) description and are associated with a genuine variation formulation. The physical meaning of the conservation laws is emphasized and the greater generality of the approach is commented upon.
The equivariant inverse problem and the Maxwell equations
Authors: Noriega R. J. , Schifini C. G.
Published: July 2002

In affirmative, the equivariant inverse problem for Maxwell-type Euler–Lagrange expressions is solved. This allows the proof of the uniqueness of the Maxwell equations.
Coexistence of periodic points in reversible dynamical systems on a surface
Authors: Tanikawa Kiyotaka , Yamaguchi Yoshihiro
Published: July 2002

Coexistence of periodic points is investigated in area-preserving reversible dynamical systems on a plane which are not necessarily close to an integrable one. It is shown that on the symmetry axis a higher cycle implies a lower cycle and any cycle implies an infinite number of higher cycles. The standard map is investigated as an example. It is shown that k-cycles for any k≥2 densely fill the phase plane of the map as the parameter goes to infinity. In addition, the number of these cycles are estimated.
Generalized coupling coefficients for O(6)⊇O(5) and O(5)⊇O(3) in Bose–Fermi symmetries for odd–odd nuclei
Authors: Van Isacker P.
Published: July 2002

Generalized coupling coefficients associated with the reductions O(6)⊇O(5) and O(5)⊇O(3) are derived in cases of interest for the UBν(6)×UBπ(6) ×UFν(12)×UFπ(4) scheme for odd–odd nuclei.
An angular momentum analysis of symmetric products of paired nucleon states
Authors: Sheikh J. A. , Sita J. , Sarma C. R.
Published: July 2002

Pair correlated angular momentum projected standard Weyl tableau states spanning an m-dimensional paired shell-model space have been obtained for a system of 2N identical nucleons. A simple procedure has been developed for carrying out the restriction of the unitary group U(m) to the rotation group O(3) for configurations of both single and multilevel distributions of the single particle states. The mapping of the correlated pair configuration space onto the antisymmetric states allowed by Pauli principle is achieved using the particle antisymmetrizer. The procedure for determining the shell-model Hamiltonian matrix using the above basis is outlined.
An example of ∂̄ problem arising in a finite difference context: Direct and inverse problem for the discrete analog of the equation ψx
x+uψ=σψy
Authors: Ragnisco O. , Santini P. M. , Chitlaru-Briggs S. , Ablowitz M. J.
Published: July 2002

The direct and inverse spectral problem for the discrete analog of the equation ψxx+uψ=σψy is solved in the framework of ‘‘∂̄’’ theory. The time evolution of the spectral data for the simplest nonlinear differential-difference equations associated to this linear problem is derived.
Superspace formulation of N=2 pseudomechanics and superpotentials
Authors: Bouquiaux L. , Dauby P. , Hussin V.
Published: July 2002

The general formalism of N=2 pseudomechanics in the superspace is presented for one spatial dimension. Taking into account the (super) symmetries of the Lagrangian, an exhaustive classification of superpotentials into three categories is obtained. The first class contains the harmonic oscillator potential, the free particle constant potential, and the superposition of both with a linear potential. The second one contains the λ2/q2 potential and its superposition with the harmonic oscillator potential and a constant one. The third class contains all other potentials. Through Noether’s theorem, conserved quantities are associated with (super)symmetry properties, and, for each class, we, respectively, get the following superalgebras: osp(2,2) ⧠ sh(1), osp(2,2), and spl(1,1) ⧠ so(2).
The Green’s function of a slab of a diatomic Montroll–Potts crystal
Authors: Mazur Paul , Barron Robert H.
Published: July 2002

Using the Dyson equation repeatedly, starting with the Green’s function for the infinite medium, the Green’s function for the semi-infinite medium and finally the Green’s function for a slab of a diatomic NaCl-type crystal using the Montroll–Potts model of nearest-neighbor central and noncentral forces are obtained.
Reflection of waves in nonlinear integrable systems
Authors: Mel’nikov V. K.
Published: July 2002

Solutions of the boomeron type are found in two nonlinear integrable systems describing the interaction of a long wave with a short wave packet. These solutions follow from two-soliton solutions if certain additional conditions are imposed on their parameters. The results are relevant to some problems of plasma physics, solid-state physics, hydrodynamics, etc.
On spherically symmetric shear-free perfect fluid configurations (neutral and charged). III. Global view
Authors: Sussman Roberto A.
Published: July 2002

The topology of the solutions derived in Part I [J. Math. Phys. 28, 1118 (1987)] is discussed in detail using suitable topological embeddings. It is found that these solutions are homeomorphic to S3×R, R4, or S2×R2. Singularities and boundaries in these manifolds are examined within a global framework. One of these boundaries (mentioned but not examined in Part II) is regular (though unphysical), and is associated with an ‘‘asymptotically de Sitter’’ behavior characterized by an exponential form of the Hubble scale factor. Solutions with S2×R2 topology lack a center of symmetry [fixed point of SO(3)] and present a null boundary at an infinite affine parameter distance along hypersurfaces orthogonal to the four-velocity. This boundary, which in most cases is singular, can be identified as a null ℐ surface arising as an asymptotical null limit of timelike hypersurfaces. Solutions with this topology, matched to a Schwarzschild or Reissner–Nordstro/m region, describe collapsing fluid spheres whose ‘‘surface’’ (as seen by observers in the vacuum region) has finite proper radius, but whose ‘‘interior’’ is a fluid region of cosmological proportions. In the case when the null boundary of the fluid region is singular, it behaves as a sort of ‘‘white hole.’’ Uniform density solutions which are not conformally flat are all homeomorphic to S2×R2. Conformally flat solutions are also examined in detail. Their global structure has common features with those of FRW and de Sitter solutions. The static limits of all nonstatic solutions are discussed. In particular, under suitable parameter restrictions, some of these static solutions, together with the nonstatic conformally flat subclass, are the less physically objectionable of all solutions. Hence, it is suggested that kinetic theory models could be applied to them. Possible cosmological applications are discussed. The global structure of Wyman’s and McVittie’s solutions is examined in the Appendices.
Multiplications of distributions in elasticity and hydrodynamics
Authors: Colombeau J. F. , Le Roux A. Y.
Published: July 2002

It is shown how a mathematical theory of generalized functions, in which the multiplications of distributions appearing in nonlinear equations of physics make sense, gives new formulas and new numerical results. The new methods shown here are quite general but since each particular problem requires its own study, this paper is limited to elasticity and hydrodynamics. In elasticity Hooke’s law gives systems in a nonconservative form; the study of shock waves for these systems gives nonclassical multiplications of distributions of the form Y⋅δ (Y=Heaviside function, δ=Dirac mass at the origin). Using this new mathematical tool new formulas are obtained (more generally new numerical schemes): in a first step ‘‘ambiguous’’ results are obtained; then the ambiguity is removed. In hydrodynamics a formulation is obtained that has a nonconservative form and is at the basis of efficient new numerical schemes. Strictly speaking the reader is not assumed to know anything either on distributions or on elasticity and hydrodynamics, since the basic equations are recalled. All computations done in this paper are rigorous from the mathematical viewpoint.
Two-sided conformally recurrent four-dimensional Riemannian manifolds
Authors: Plebański J. F. , Przanowski M.
Published: July 2002

Two-sided conformally recurrent four-dimensional Riemannian manifolds are defined and analyzed from the point of view of the Petrov–Penrose classification. All two-sided conformally recurrent four-dimensional Riemannian manifolds of types D⊗D, N⊗N, and N⊗[−] are given.
SU(1,1) and the vector model for continuous bases
Authors: de Prunelé E.
Published: July 2002

The vector model is formulated in a general form that allows its application for calculating square moduli of matrix elements involving continuous bases. The model is applied to positive discrete unitary irreducible representations of SU(1,1) and the classical estimates are compared with the exact results.
Additive decomposition for the product of two θ3 functions and modular equations
Authors: Montaldi Emilio , Zucchelli Giuseppe
Published: July 2002

By using a general additive decomposition for the product of two θ3 functions, a simple and unified derivation of the modular equations of degree 3, 5, and 7 is given.
On the entropic formulation of uncertainty for quantum measurements
Authors: Schroeck Franklin E.
Published: July 2002

The formulation of the uncertainty principle based on entropy is given with the (noncommuting) observables described via positive operator-valued measures.
A static cylindrically symmetric solution for perfect fluid in general relativity
Authors: Davidson W.
Published: July 2002

A solution of Einstein’s equations for a stationary cylindrically symmetric perfect fluid is presented. The extent of the fluid is radially infinite but the proper density μ and pressure p are physically well behaved everywhere. On the axis μ and p are finite and positive. As the radial coordinate ρ increases μ and p decrease monotonically to zero at infinity. The ratio p/μ(<1) also steadily decreases. It is shown that the regularity condition at the axis is satisfied. The solution is algebraically general of Petrov type I.
A possible generalization of the concept of symmetry in analytical mechanics
Authors: Grigore D. R.
Published: July 2002

A theorem of Chung [Proc. R. Soc. Edinbburgh, Sec. A LXII, 237 (1947)] suggests a possible generalization of the symmetry concepts in classical mechanics. It is shown that the theory of Kostant–Souriau–Kirillov can be adapted easily to this more general case. The theory is illustrated with a number of examples.
The uniqueness of the energy momentum tensor in non-Abelian gauge field theories
Authors: Noriega R. J. , Schifini C. G.
Published: July 2002

The uniqueness of the energy momentum tensor in non-Abelian gauge field theories is established under minimal hypothesis.
Topology of parametrized systems
Authors: Hajicek Peter
Published: July 2002

The discussion is limited to finite-dimensional parametrized systems with one constraint—the so-called super-Hamiltonian. The topology of the corresponding Hamiltonian vector field on the constraint hypersurface, in particular the question of the existence of cross sections, is studied. This has some bearing on the applicability of the reduction method, as well as on unitarity within the Dirac method, of canonical quantization [see the previous paper, Phys. Rev. D 34, 1040 (1986)]. The main theorem of the present paper states that a cross section will exist if and only if the following conditions are both satisfied: (i) no dynamical trajectory is closed or almost closed; and (ii) the quotient set topology of the set of all dynamical trajectories is Hausdorff. Examples of systems that separately violate each of these conditions are given.
Inverse scattering problem for the 3-D Schrödinger equation and Wiener–Hopf factorization of the scattering operator
Authors: Aktosun Tuncay , van der Mee Cornelis
Published: July 2002

Sufficient conditions are given for the existence of a Wiener–Hopf factorization of the scattering operator for the 3-D Schrödinger equation with a potential having no spherical symmetry. A consequence of this factorization is the solution of a related Riemann–Hilbert problem, thus providing a solution of the 3-D inverse scattering problem.
Corepresentations of superalgebras and an antilinear Dirac operator
Authors: Hannabuss K. C. , Weiss W. R.
Published: July 2002

The reasons that lead to the use of only linear representations of Lie algebras in quantum theory seem to permit antilinear representations of superalgebras. Such corepresentations of Clifford algebras are investigated and shown to lead to a two-component Dirac equation. It is shown that there exists a one-component corepresentation of the supertranslation algebra, but that this cannot be induced to a corepresentation of the super-Poincaré algebra.
Taylor series expansion of the dominating eigenvalue of the Ruelle–Araki transfer operator
Authors: Thron Christopher P.
Published: July 2002

The mean free energy for a one-dimensional spin system with exponential interaction and the large-deviation probability for a one-dimensional ergodic dynamical system are found in exact Taylor expansion by computing the largest eigenvalue of the corresponding Ruelle–Araki transfer operator.
Nonassociative superconformal algebras
Authors: Hasiewicz Z. , Defever F. , Troost W.
Published: July 2002

A study of conventional superconformal not-necessarily Lie superalgebras is performed. A uniform prescription is given, leading to the definition of a family of structures with N=1,...,8 supersymmetries. For N≤4, Lie superalgebras are recovered, for N≥5 the algebras are nonassociative. The not-Lie superconformal algebras with N=5,6,7,8 share interesting common properties, relating them to the Cayley numbers, covariant derivation of spinors on the seven-sphere S7 and torsions on supercoset manifolds. The N=8 case is related to the (soft) constraint algebra of a recent reformulation of the Green’s–Schwarz superstring.
Grassmann algebra and fermions in the lattice: A simple example
Authors: de Souza S. M. , Thomaz M. T.
Published: July 2002

Using the exact results for integrals of exponentials of polynomials of Grassmann variables and the Feynman construction of path integrals, an approximate method is presented to calculate the thermodynamic quantities of a fermionic system in equilibrium with a reservoir at temperature T and chemical potential μ. To exemplify, the quantum anharmonic fermionic oscillator is considered in a lattice with N points, where N=2, 3, and 4.
Renormalization of gauge coset models
Authors: Bandelloni Giuseppe
Published: July 2002

The renormalization of a four-dimensional pure Yang–Mills model built on a compact homogeneous coset space is studied. The possible anomalies are explicitly derived.
On the quantization of the planar N-point vortex problem
Authors: Wu Yihren
Published: July 2002

In this paper the velocity field of a planar fluid with point vortices is recognized as induced by a connection on a principal bundle. Various geometric/topological invariants, including braiding of the trajectories of the vortices and the Berry’s phase, are discussed in this bundle context. These invariants give rise to quantization schemes for the system.
Classical and quantum dispersion in Robertson–Walker cosmologies
Authors: Tomaschitz Roman
Published: July 2002

The instability of world lines in Robertson–Walker universes of negative spatial curvature is investigated. A probabilistic description of this instability, similar to the Liouville equation, is developed, but in a manifestly covariant, non-Hamiltonian form. To achieve this the concept of a horospherical geodesic flow of expanding bundles of parallel world lines is introduced. An invariant measure and a covariant evolution equation for the probability density on which this flow acts is constructed. The orthogonal surfaces to these bundles of trajectories are horospheres, closed surfaces in three-space, touching the boundary at infinity of hyperbolic space, where the flow lines emerge. These horospheres are just the wave fronts of spherical waves, which constitute a complete set of eigenfunctions of the Klein–Gordon equation. This fact suggests that the evolution of the quantum mechanical density with the classical one be compared, and asymptotic identity in the asymptotically flat region is found. This leads, furthermore, to the study of the time behavior of the dispersion of the energy and the coordinates and the energy-time uncertainty relation, and identity in the late stage of the cosmic evolution is again found. In an example it is finally demonstrated that this identity can persist in the early phase of the expansion with a rapidly varying scale factor, provided the fields are conformally coupled to the curvature.
Scaling limit of a model of quantum electrodynamics
Authors: Hiroshima Fumio
Published: July 2002

This article gives a solution to an open problem in the paper by Arai [J. Math. Phys. 31, 2653 (1990)]. In it is presented an abstract asymptotic theory of families of unitary operators {𝒰(κ)}κ≳0 and self-adjoint operators {Hκ}κ≳0 acting in the tensor product of two Hilbert spaces. It is proven that Hεren(V,κ), which represents a scaled total Hamiltonian of a coupled system of a one electron atom and a quantized radiation field, with parameters 0≤ε≤1, κ≳0, and the electron mass renormalized, is unitarily equivalent to an operator H̃εren(V,κ), which can be regarded as a decoupled Hamiltonian. Applying the abstract asymptotic theory and the unitary equivalence, it is proven that the resolvent of Hεren(V,κ) strongly converges as κ→∞ to an operator which defines an effective potential of the electron. The effective potential is compared with that obtained in the paper mentioned above.
A soluble model for scattering and decay in quaternionic quantum mechanics. I. Decay
Authors: Horwitz L. P.
Published: July 2002

The Lee–Friedrichs model has been very useful in the study of decay-scattering systems in the framework of complex quantum mechanics. Since it is exactly soluble, the analytic structure of the amplitudes can be explicitly studied. It is shown in this article that a similar model, which is also exactly soluble, can be constructed in quaternionic quantum mechanics. The problem of the decay of an unstable system is treated here. The use of the Laplace transform, involving quaternion-valued analytic functions of a variable with values in a complex subalgebra of the quaternion algebra, makes the analytic properties of the solution apparent; some analysis is given of the dominating structure in the analytic continuation to the lower half plane. A study of the corresponding scattering system will be given in a succeeding article.
Fluctuations of a rotating impulsive wave
Authors: Hortaçsu M. , Kaya R.
Published: July 2002

The vacuum fluctuations for an impulsive spherical gravitational wave due to the snapping of a ‘‘rotating’’ cosmic string are calculated herein. This is complementary to the previous calculation due to a snapping string, which had the null result. Although the mathematical expressions are different at the intermediate steps, the same null result is found.
Spatial theory of *-automorphisms of partial O*-algebras
Authors: Antoine J.-P. , Inoue A. , Trapani C.
Published: July 2002

The spatial theory of *-automorphisms is well known for C*- or W*-algebras and for algebras for unbounded operators on Hilbert spaces (O*-algebras). In this article, the theory is extended to partial *-algebras of closable operators (partial O*-algebras), with many similar results.
Curvature of gravitationally bound mechanical systems
Authors: Szydlowski Marek
Published: July 2002

In the present work mathematical aspects of determining the local instability parameters are focused on by using invariant characteristics of the internal Riemannian geometry with the Jacobi metric (in principle, for Hamiltonian dynamical systems with the natural Lagrangian). First, it is shown that the Ricci scalar indeed measures the sectional curvature averaged upon all two-directions. Second, necessary and sufficient criteria for non-negativity and of nonpositivity of the sectional curvature for any system with the natural Lagrangian are given. Third, analytical formulas allowing us to compute the separation rate of nearby trajectories are given. Fourth, it is shown that for any collisionless problem of n gravitationally bounded bodies, the sectional curvature in every direction is negative if n tends to infinity.
Quantum scattering on a Cantor bar
Authors: Makarov Konstantin A. , Pavlov Boris S.
Published: July 2002

A solvable model of the scattering of a one-dimensional particle by the familiar ‘‘middle-third’’ Cantor set is considered. It is shown that the presence of positive energy levels in such a model is typical. From the high-energy behavior of the scattering, data computation of the Hausdorff dimension of the scatterer is suggested.
Cosmological CP violation
Authors: Tomaschitz Roman
Published: July 2002

Spinor fields are studied in infinite, topologically multiply connected Robertson–Walker cosmologies. Unitary spinor representations for the discrete covering groups of the spacelike slices are constructed. The spectral resolution of Dirac’s equation is given in terms of horospherical elementary waves, on which the treatment of spin and energy is based in these cosmologies. The meaning of the energy and the particle–antiparticle concept is explained in the context of this varying cosmic background. Discrete symmetries, in particular inversions of the multiply connected spacelike slices, are studied. The violation of the unitarity of the parity operator, due to self-interference of P-reflected wave packets, is discussed. The violation of the CP and CPT invariance—already on the level of the free Dirac equation on this cosmological background—is pointed out.