bluuebunny/crossref_metadata_2025 huggingface dataset:
Semiclassical maps: A study of classically forbidden transitions, sub-h structure, and dynamical localization
Authors: Maitra N. T.
Published: July 2002

Representing the dynamics of a continuous time molecular system by a symplectic discrete time map can much reduce the computational time. The question then arises of whether semiclassical methods can be effectively applied to this reduced description: as in the classical case, the map should prove to be a much more computationally efficient description of the dynamics. Here we study the semiclassical propagation of the standard map, or kicked rotor, based on a Herman–Kluk propagator. This is a very interesting playground to test the feasibility of a semiclassical mapping approach, since it demonstrates a wealth of quantum and classical dynamical behavior: As the kick strength increases, the system goes from being very nearly integrable, through mixed phase space, to chaotic. The map displays phenomena that occur in generic molecular systems, so this study is also a test of how well semiclassics can describe such phenomena. In particular, we discuss (i) classically forbidden transport: the significance of branches of the semiclassical integrand in the complex phase plane must be understood in order for the semiclassics to be meaningful; (ii) sub-h structure: in the nearly integrable regime, the semiclassics can be poor due to the presence of islets of area less than Planck’s constant in phase space; (iii) dynamical localization: in the chaotic regime, the classical momentum diffuses, whereas the quantum localizes. Our results show that semiclassics also localizes, and we can confirm directly the theory that dynamical localization is due largely to phase interference.
Optical reflectivity changes induced by adsorption on metal surfaces: The origin and applications to monitoring adsorption kinetics
Authors: Dvorak Joseph , Dai Hai-Lung
Published: July 2002

It is observed that when a monolayer of CO and acetylene is chemisorbed on the Cu(100) surface, the reflectivity of the metal surface at the He–Ne laser wavelength of 632 nm is reduced on the order of 1%, while the physisorption of water, methanol, and acetone induces a reflectivity change on the order of 0.01%. The small reflectivity change induced by physisorption can be described by a three-layer model taking into account the molecular layer refractive index. The much bigger reflectivity change induced by the chemisorbed adsorbates, on the other hand, is a result of bonding perturbations to the electronic structure of the metal surface layer. The latter is supported by an electron scattering model description of the reflectivity change up to 1.96 eV on Cu. For both CO and acetylene, the optical reflectivity change is found to be linearly proportional to the submonolayer coverage. The phenomenon thus offers an excellent method to measure surface kinetics. It is found from the reflectivity change measurements that the initial sticking coefficient for both adsorbates is nearly unity at 110 K; 0.85 for CO and 1.0 for acetylene. The temperature and coverage dependence of the sticking coefficient shows that the adsorption behavior of both molecules is well described as direct adsorption mediated with an extrinsic precursor. For acetylene adsorption, the sticking coefficient shows little dependence on the substrate temperature suggesting that the “extrinsic precursor” is not a thermally equilibrated species. For CO, the transition into a compression phase beyond 0.5 ML results in a corresponding change in the sticking coefficient deduced from the reflectivity data.
Ionization and fragmentation of C60 with sub-50 fs laser pulses
Authors: Tchaplyguine M. , Hoffmann K. , Dühr O. , Hohmann H. , Korn G. , Rottke H. , Wittmann M. , Hertel I. V. , Campbell E. E. B.
Published: July 2002

Gas-phase C60 photoionization and photofragmentation experiments were performed using a sub-50 fs Ti Sapphire laser system and reflectron time-of-flight (RETOF) mass spectrometer. The dependence of the C60+ and C602+ signals on the laser intensity for the fundamental (795 nm) and second harmonic (ca. 400 nm) has been determined. For low laser intensities, before the onset of fragmentation, single ionization is a direct multiphoton process. Double ionization is a sequential process in which C602+ originates from already singly ionized fullerenes. At laser intensities beyond the onset of C602+ there is considerable metastable fragmentation indicating a strong coupling of electronic excitation energy into vibrational degrees of freedom that appears to be in competition with multiple ionization.
Adsorption of critical and supercritical fluids
Authors: Kiselev S. B. , Ely J. F. , Belyakov M. Yu.
Published: July 2002

We develop a crossover theory for critical adsorption of pure fluids in a semi-infinite system. In our previous publication [Phys. Lett. A 251, 212 (1999)] we applied the theory to the analysis of experimental data for adsorption of liquid SF6 on the critical isochore only. In this article we extend the theory on the noncritical isochores and present a comparison of the theoretical predictions for the surface excess (Gibbs) adsorption with experimental data for CO2/silica and SF6/graphite systems. Good representation of experimental data is achieved in the range of temperatures from the saturated temperature up to 1.15 Tc and densities 0.5ρc⩽ρ⩽1.5ρc. The optimization of the model to the excess isotherms in both systems indicates that they have surface critical behavior in the universality class of normal transition. However, in this case model does not reproduce the excess adsorption data for SF6/graphite system at temperatures τ=T/Tc−1⩽0.02 at ρ=ρc. Analysis of the excess adsorption data along the critical isochore in SF6/graphite system indicates that the surface field h1 vanishes linearly with τ as T→Tc, which corresponds to the ordinary transition.
An ab initio cluster study of the structure of the Si(001) surface
Authors: Shoemaker James , Burggraf Larry W. , Gordon Mark S.
Published: July 2002

Ab initio calculations, employing double zeta plus polarization (DZP) basis sets and generalized valence bond (GVB) wave functions, have been performed on clusters of varying size, to investigate the utility of such clusters as prototypes for the study of silicon surfaces, and to investigate the effect of the level of theory used on predicted results. This work builds on landmark papers by Goddard in 1982 and Paulus in 1998 that demonstrate that a single reference wave function description of the silicon dimer bond is incorrect, and that a multireference description results in a symmetric dimer in a silicon cluster containing one dimer. In this work, it is shown that the imposition of arbitrary geometrical constraints (fixing subsurface atoms at lattice positions) on cluster models of the Si(100) surface can also lead to nonphysical results. Calculations on the largest clusters, without geometrical constraints, reveal that surface rearrangement due to dimer bond formation is “felt” several layers into the bulk. The predicted subsurface displacements compare favorably to experiment. Thus, small clusters, such as Si9H12, cannot adequately represent bulk behavior. Vibrational analysis shows that dimer buckling modes require minimal excitation energy, so the experimental observation of buckled dimers on silicon surfaces may reflect the ease with which a symmetric dimer can be perturbed from its minimum energy structure. In the study of surface reconstruction and relaxation, and the associated issue of the buckling of dimer surfaces, it is critical to use adequate wave functions. As shown in this work and previously by Goddard and Paulus, this generally means that multireference treatments are needed to correctly treat the dangling bonds.
Xerographic study on a ladder-type poly(para-phenylene)
Authors: Pan Junyou , Scherf Ullrich , Schreiber Andreas , Haarer Dietrich
Published: July 2002

Photogeneration of charge carriers in a methyl-substituted ladder-poly(para-phenylene) (LPPP) has been investigated by xerographic experiments. The quantum efficiency of charge carrier generation was calculated by evaluating the photoinduced discharge curves (PIDCs) and found to be independent of both excitation wavelength and temperature. The results can be described by a modified Braun theory with a simple exponential distribution of radii of thermalized electrons. LPPP shows a very high primary quantum efficiency of 80%, a low residual potential, and a small dark decay. Thus, LPPP represents a promising material to build single component single-layer photoreceptors.
A new density functional approach to nonuniform Lennard-Jones fluids
Authors: Zhou Shiqi , Ruckenstein Eli
Published: July 2002

A density-functional methodology is presented for nonuniform Lennard-Jones fluids based on both a free energy density functional of nonuniform simple fluids recently proposed by the present authors and an approximate bridge function proposed in this note resulting from a combination of the hypernetted-chain closure and Verlet-modified closure. The predictions of present methodology compares well with corresponding simulation data.
Diffusion measurements with the pulsed gradient nonlinear spin echo method
Authors: Ardelean Ioan , Kimmich Rainer
Published: July 2002

Spin echo signal attenuation by diffusion is examined for coherence evolution in the course of ordinary pulsed gradient spin echoes and for nonlinear evolution in the presence of a spatially modulated demagnetizing field. It is shown, that, for given field gradient pulse widths (or equivalently for a given gradient strength), echo attenuation by diffusion is much more efficient for nonlinear echoes than for Hahn echoes. Remarkably, in the case of nonlinear echoes the refocusing process is spoiled by diffusion not only during the gradient intervals but also thereafter. The effect of displacements occurring in the gradient intervals is enhanced according to the order of the nonlinear echo the pulse sequence is adjusted for. A second attenuation mechanism takes place after the gradient pulses due to displacements in the presence of the spatially modulated demagnetizing field. This effect even occurs when the gradient intervals are too short to contribute. A complete formalism is presented describing all features of the test experiments. It is shown that nuclear magnetic resonance diffusometry based on nonlinear echo signals permits one to measure small diffusion coefficients with moderate field gradients. Nonlinear echo experiments demonstrate that the coherence pathway dominating by far is of a purely single-quantum nature.
Frenkel excitons beyond the Heitler–London approximation
Authors: Agranovich V. M. , Basko D. M.
Published: July 2002

We consider Frenkel excitons in molecular crystals beyond the Heitler–London approximation (HLA). Beyond the HLA the wave function of the molecular crystal with one exciton contains states with several excited molecules. In this case the statistics of the molecular excitations becomes important. Thus, the boson approximation, frequently used to go beyond the HLA, needs to be corrected. We calculate the corrections to the HLA for Frenkel exciton energy and oscillator strength taking into account the exact statistics of molecular excitations. In these calculations we consider the crystals of general structure and beyond the two-level model, thus taking into account also the mixing of molecular configurations. For the model of a one-dimensional chain of two-level molecules and in the nearest-neighbor approximation our results coincide with the results found earlier by Bakalis and Knoester who used the Jordan–Wigner transformation from paulions to fermions. We show that for multilevel molecules the crystal Hamiltonian contains additional terms that give important contributions to the corrections for the Frenkel exciton energy.
On the diffusion-influenced reversible trapping problem in one dimension
Authors: Kim Hyojoon , Joe Shin Kook
Published: July 2002

The exact Green function for a particle moving between two static reversible traps in one dimension is obtained for the continuous diffusion model. From this function, we derive the exact expressions of various survival probabilities, which are the key elements in devising the efficient Brownian dynamics algorithm. An exact expression of the mean survival probability is also obtained for the periodic distribution of reversible traps both for the crossing-allowed and crossing-forbidden cases. For the random distribution of reversible traps, the exact mean survival probability is obtained only for the crossing-forbidden case and its long time behavior is compared with that of the crossing-allowed case. We find, in this case, that not only the long time asymptotic relaxation behavior but also the equilibrium concentration itself can be changed from the classical results due to the fluctuation effect of the trap density.
Direct determination of second-order density matrix using density equation: Open-shell system and excited state
Authors: Nakata Maho , Ehara Masahiro , Yasuda Koji , Nakatsuji Hiroshi
Published: July 2002

We formulated the density equation theory (DET) using the spin-dependent density matrix (SDM) as a basic variable and calculated the density matrices of the open-shell systems and excited states, as well as those of the closed-shell systems, without any use of the wave function. We calculated the open-shell systems, Be(3S), Be−(2S), B+(3S), B(2S), C2+(3S), C+(2S), N3+(3S), and N2+(2S), and the closed-shell systems, Be, Be2−, B+, B−, C2+, N3+, H2O, and HF. The new properties calculated are the transition energies and the spin densities at the nuclei. Generally speaking, the accuracy of the present results is slightly worse than that of the previous one using the spin-independent density matrix.
Absolute partial cross sections for electron-impact ionization of NO and NO2 from threshold to 1000 eV
Authors: Lindsay B. G. , Mangan M. A. , Straub H. C. , Stebbings R. F.
Published: July 2002

Absolute partial cross sections for electron-impact ionization of nitric oxide and nitrogen dioxide are reported for electron energies from threshold to 1000 eV. The product ions are mass analyzed using a time-of-flight mass spectrometer and detected with a position-sensitive detector whose output demonstrates that all product ions are collected irrespective of their initial kinetic energy. Data are presented for the production of NO+, N+, O+, and NO2+ ions from NO; and for the production of NO2+, NO+, N+, O+, and (N2++O2+) ions from NO2. The overall uncertainty in the absolute cross section values is ±5% for singly charged parent ions, while that for the fragment ions may be as large as ±20%. For NO, the previously published data are generally in reasonable agreement with those presented here, although there remain some significant discrepancies with even the most recent work. No previous comprehensive study of NO2 has apparently been reported but the experimental NO2+ cross section data that are available disagree substantially with the present measurements. The present total NO2 cross section is, however, in excellent agreement with recent theoretical work.
A mesoscopic model of nucleation and Ostwald ripening/stepping: Application to the silica polymorph system
Authors: Ozkan G. , Ortoleva P.
Published: July 2002

Precipitation is modeled using a particle size distribution (PSD) approach for the single or multiple polymorph system. A chemical kinetic-type model for the construction of the molecular clusters of each polymorph is formulated that accounts for adsorption at a heterogeneous site, nucleation, growth, and Ostwald ripening. When multiple polymorphs are accounted for, Ostwald stepping is also predicted. The challenge of simulating the 23 order of magnitude in cluster size (monomer, dimer, …, 1023-mer) is met by a new formalism that accounts for the macroscopic behavior of large clusters as well as the structure of small ones. The theory is set forth for the surface kinetic controlled growth systems and it involves corrections to the Lifshitz–Slyozov, Wagner (LSW) equation and preserves the monomer addition kinetics for small clusters. A time independent, scaled PSD behavior is achieved both analytically and numerically, and the average radius grows with Rave∝t1/2 law for smooth particles. Applications are presented for the silica system that involves five polymorphs. Effects of the adsorption energetics and the smooth or fractal nature of clusters on the nucleation, ripening, and stepping behavior are analyzed. The Ostwald stepping scenario is found to be highly sensitive to adsorption energetics. Long time scaling behavior of the PSD reveals time exponents greater than those for the classical theory when particles are fractal. Exact scaling solutions for the PSD are compared with numerical results to assess the accuracy and convergence of our numerical technique.
Harvesting thermal fluctuations: Activation process induced by a nonlinear chain in thermal equilibrium
Authors: Reigada Ramon , Sarmiento Antonio , Romero Aldo H. , Sancho J. M. , Lindenberg Katja
Published: July 2002

We present a model in which the immediate environment of a bistable system is a molecular chain which in turn is connected to a thermal environment of the Langevin form. The molecular chain consists of masses connected by harmonic or by anharmonic springs. The distribution, intensity, and mobility of thermal fluctuations in these chains is strongly dependent on the nature of the springs and leads to different transition dynamics for the activated process. Thus, all else (temperature, damping, coupling parameters between the chain and the bistable system) being the same, the hard chain may provide an environment described as diffusion-limited and more effective in the activation process, while the soft chain may provide an environment described as energy-limited and less effective. The importance of a detailed understanding of the thermal environment toward the understanding of the activation process itself is thus highlighted.
Helix-coil transitions of amino-acid homo-oligomers in aqueous solution studied by multicanonical simulations
Authors: Mitsutake Ayori , Okamoto Yuko
Published: July 2002

Helix-coil transitions of homo-oligomers in aqueous solution are studied by multicanonical Monte Carlo simulations. The solvation effects are represented by the sum of the terms that are proportional to the solvent-accessible surface area of the atomic groups. Homo-oligomers of length 10 are considered for three characteristic amino acids, alanine, valine, and glycine, which are helix former, helix indifferent, and helix breaker, respectively. We calculated as a function of temperature the distributions of the backbone dihedral angles, the average values of total energy, and its component terms of the homo-oligomers. It is shown that for homo-alanine, the helix-coil transition exists and that the transition temperature in water is considerably lower than in gas phase, which implies that the effects of solvation tend to reduce helical content. Moreover, the helix propagation parameter s and nucleation parameter σ of the Zimm-Bragg model were calculated. The s values that were obtained from the simulations in aqueous solution are in remarkable agreement with the experimental results.
Anion–cation induction coupling in organic superconductors
Authors: Castet F. , Ducasse L. , Fritsch A.
Published: July 2002

Within the framework of the valence bond/Hartree–Fock (VB/HF) formalism, [Castet et al., J. Phys. I (France) 6, 583 (1996); L. Ducasse et al., Synth. Metals 85, 1627 (1997); F. Castet et al., Chem. Phys. 232, 37 (1998); Synth. Metals 103, 1799 (1999)] anion-cation induction interactions are evaluated in organic superconductors derived from the Bechgaard salts. The calculation scheme is based on an extension of the VB/HF model, so as to incorporate the effect of the distinct anion polarization states in the calculation of the VB Hamiltonian matrix elements. The induction mechanism involves a charge displacement on the counteranions in the electrostatic field of adjacent positively charged organic molecules. Anion-cation interactions are calculated for the β-BEDTTTF2I3 structure [A. J. Schultz et al., J. Am. Chem Soc. 108, 7853 (1986)], which involves highly polarizable anions.
Basis set convergence of correlated calculations on He, H2, and He2
Authors: Lee Jae Shin , Park Sun Yong
Published: July 2002

The convergence behavior of the total and correlation energies of He, H2, and He2 with the increase of basis quality in the correlation-consistent basis sets, cc-pVXZ and aug-cc-pVXZ(X=D,T,Q,5,6), was studied to search for a proper extrapolation scheme to predict the accurate complete basis set (CBS) limits at the MP2, CCSD, and CCSD(T) level. The functional form employed for extrapolation is a simple polynomial including inverse cubic power and higher-order terms of the cardinal number X in the correlation-consistent basis set as well as exponential function. It is found that a simple extrapolation of two successive correlation-consistent basis set energies (total or correlation energies) using (X+k)−3 [k=0 for MP2 and k=−1 for CCSD and CCSD(T) level] gives in general the most reliable (and accurate in case of total energy) estimates to the CBS limit energies. It is also shown that the choice of proper basis set, which can represent the electronic motions in the fragment and complex equally well, appears necessary for reliable estimate of the relative energies such as the binding energy of the complex. From the extrapolation of aug-cc-pV5Z and aug-cc-pV6Z energies with (X+k)−3, we obtained 21.3(21.4), 28.4(29.0) and 33.2(33.8) microhartrees as the CBS limit binding energy of He2 at the internuclear separation of 5.6 a.u. at the MP2, CCSD, and CCSD(T) level, respectively, with the values in parentheses representing the exact CBS limit binding energies.
On the propagation of the operator average in truncated space
Authors: Nomura Masao
Published: July 2002

The propagation of the operator average is described in truncated space with some quantum number(s) being fixed. It is first shown that the propagation coefficient satisfies an analog of the Chapman–Kolmogorov equation. Next, particle-hole symmetry is incorporated into the propagation of the operator average. It yields an expression that facilitates evaluation of many-body trace. Fermion and boson systems are treated alike.
Symmetries of cosmological Cauchy horizons with exceptional orbits
Authors: Isenberg James , Moncrief Vincent
Published: July 2002

We show here that if an analytic space-time satisfying the vacuum (or electrovacuum) Einstein equations contains a compact null hypersurface with closed generators, then the space-time must have a nontrivial Killing vector field. This result is an extension of an earlier theorem, which required that the generators of the hypersurface must not only be closed, but in addition must satisfy a local product bundle (LPB) condition. This LPB condition (which is known to be violated in certain of the Kerr–Taub–NUT space-time models) is equivalent to the requirement that the generators must all be ordinary fibers of a Seifert fibration. We prove here that the LPB condition can be dropped. Thus we have stronger support for our conjecture that causality violations (as evidenced by Cauchy horizons) in cosmological solutions of the Einstein equations are essentially an artifact of symmetry, and are therefore nongeneric.
Finite hard rod systems and their thermodynamic limit. II. Ergodic properties, pair distribution function, and equation of state
Authors: Kasperkovitz P. , Reisenberger J.
Published: July 2002

Generalizing a trick used previously for one- and two-particle systems we obtain closed expressions for the positions and velocities of the hard rods as functions of time and the initial conditions. Using the corresponding solution of Liouville’s equation we show which ensembles can be used to calculate time averages and discuss the conditions under which an expectation value tends toward a stationary value. We also calculate the pair distribution function for almost all stationary distributions and the pressure, defined as the time average of the force exerted onto a specified particle by its left neighbor, for three kinds of stationary ensembles (smallest stationary, microcanonical, and canonical).
Global instability of a monoparametric family of vector fields representing the unfolding of a dissipative structure
Authors: Fernández Ariel
Published: July 2002

The continuous structural stability (CSS) of arcs of vector fields defined on a Banach space or, in general, on a normed space is introduced. It is shown that the nonequilibrium sensitivity of reaction-diffusion systems to external fields reflects itself in the lack of CSS for a family of arcs, which model the onset of two equally probable spatial organizations. It is therefore demonstrated that a universal model up to topological equivalence for the unfolding of a spatial dissipative structure does not exist. The results generalize some conclusions already available for bifurcation of stationary states in arcs of vector fields on compact manifolds.
Hydrodynamic self-similar cosmological models
Authors: Sanyal Abhik Kumar , Banerjee A. , Ray Dipankar
Published: July 2002

Hydrodynamic self-similar solutions, as obtained by Chi [J. Math. Phys. 24, 2532 (1983)] have been generalized by introducing new variables in place of the old space and time variables. A systematic procedure of obtaining a complete set of solutions has been suggested. The Newtonian analogs of all homogeneous isotropic Friedmann dust universes with spatial curvature k=0 and ±1 have been given.
Algebra and physics of the unitary multiplicity-free representations of ∼(SL)(4, R)
Authors: Šijački Dj. , Ne’eman Y.
Published: July 2002

The systematics of the multiplicity-free unitary irreducible representations of SL(4,↛) are restudied, and an amended list is presented. An automorphism essential to the physical application for particles and fields in Minkowski space is described.
Satake diagrams, Iwasawa decompositions, and representations of the exceptional Lie group F4(−20)
Authors: Sharma Veena , Tripathy K. C.
Published: July 2002

The parabolic subgroups of the noncompact, exceptional Lie group F4(−20) are computed from a systematic analysis of Iwasawa and Langlands decompositions. Satake diagrams have been used to determine the involutive automorphisms of F4(−20) which facilitate the Iwasawa decompositions. The polarizations associated with noncompact orbits with parabolic subgroups are computed. The representations so obtained for these polarizations using Kostant’s induction scheme yield the principal series representations of F4(−20).
Solution of the eigenvalue problem of an integral equation with the help of its associated differential equation applied to the calculation of diffraction losses in confocal resonators
Authors: Müller-Kirsten H. J. W. , Sattel E.
Published: July 2002

A problem in optics is chosen in order to develop a general method for solving the eigenvalue problem of a homogeneous integral equation with the help of the eigenfunctions of the associated differential equation. The problem chosen is that of the modes of optical resonators with circular, confocal mirrors which are given by the solutions of a homogeneous Fredholm integral equation which can be derived from Kirchhoff ’s diffraction formula. This integral equation can be converted into a hyperspheroidal differential equation supplemented by appropriate boundary conditions. The solutions and eigenvalues of this differential equation are studied in detail for both small and large values of a parameter called the Fresnel number. These eigenfunctions are then used for the computation of the eigenvalues of the original integral equation which measure the diffraction loss in the resonator. Throughout the same general perturbation method is used, and our emphasis is on the solution of the general problem of solving the eigenvalue problem of the homogeneous integral equation together with that of its related differential equation.
The action-angle variables for the massless relativistic string in 1+1 dimensions
Authors: Söderberg B. , Andersson B. , Gustafson G.
Published: July 2002

In this paper the Poisson bracket algebra for the open massless relativistic string in the one-space- and one-time-dimensional case is considered. In order to characterize the orbit of the system the directrix function, i.e., the orbit of one of the endpoints of the string, is used. It turns out that the Poisson bracket algebra is of a very simple form in terms of the parameters of the directrix function. We use these results to construct action-angle variables for the general motion of the string. The variables are different for different Lorentz frames, with a continuous dependence. The action-angle variables of the center-of-mass frame and of the light-cone frames are of particular interest with respect to the simplicity of the Poincaré generators and the physical interpretation. For the light-cone frame variables the equivalence to a set of indistinguishable oscillators is shown, for which an excitation corresponds to an instantaneous momentum transfer to an endpoint of the string.
Gauge fixing and Gupta–Bleuler triplets in de Sitter QED
Authors: Gazeau J. P.
Published: July 2002

Binegar et al. recently developed de Sitter QED within the frame of a particular gauge fixing c= (2)/(3) . Such a choice leads to the simplest possible structure of the Gupta–Bleuler triplets, with the SO(3,2) representations D(3,0) and D(1,1) appearing to describe special gauge solutions. The present work examines the general case c≠ (2)/(3) by considering explicitly the corresponding homogeneous propagators and some fundamental carrier states for the related indecomposable representations of SO(3,2). The latter expressions involve ‘‘logarithmic’’ gauge states which independently carry extensions of the D(3,0) and D(1,1) Lie algebra representations.
On a labeling for point group harmonics. II. Icosahedral group
Authors: Raynal Jacques
Published: July 2002

The expressions for the Γ2, Γ5, Γ6, Γ8, and Γ9 representations are given in terms of those of Γ1 representations for neighboring angular momenta. The coefficients of the Γ4 representations are expressed in terms of those of Γ7 representations. Therefore, with an arbitrary choice of orthonormal sets of Γ1, Γ3, and Γ7 representations, orthonormal sets of other kinds of representations are well defined and can be labeled with the labels of parent representations. All Clebsch–Gordan coefficients are expressed in terms of those between parent representations (and a few others). Tables of all nondegenerate Γ1, Γ3, and Γ7 representations are given, for the axes of quantization of order 5. With some degenerate Γ3 and Γ7 representations, which are also given, any representation of integer or half-integer angular momentum up to 27 can be obtained using some usual Clebsch–Gordan coefficients of SU(2).
Direct and inverse scattering in the time domain for a dissipative wave equation. I. Scattering operators
Authors: Kristensson G. , Krueger R. J.
Published: July 2002

This is the first part of a series of papers devoted to direct and inverse scattering of transient waves in lossy inhomogeneous media. The medium is assumed to be stratified, i.e., it varies only with depth. The wave propagation is modeled in an electromagnetic case with spatially varying permittivity and conductivity. The objective in this first paper is to analyze properties of the scattering operators (impulse responses) for the medium and to introduce the reader to the inverse problem, which is the subject of the second paper in this series. In particular, imbedding equations for the propagation operators are derived and the corresponding equations for the scattering operators are reviewed. The kernel representations of the propagation operators are shown to have compact support in the time variable. This property implies that transmission and reflection data can be extended from one round trip to arbitrary time intervals. The compact support of the propagator kernels also restricts the admissible set of transmission kernels consistent with the model employed in this paper. Special cases of scattering and propagation kernels that can be expressed in closed form are presented.
SO(4) Reduction of the SU(N) Yang–Mills–Dirac equations
Authors: Légaré M. , Harnad J.
Published: July 2002

The equations in compactified Minkowski space that describe SU(N) Yang–Mills fields minimally coupled to Dirac spinor fields transforming under the lowest-dimensional representation(s) of SU(N) are reduced by the action of an SO(4) subgroup of the conformal group of space-time. The reduced systems can be interpreted as Hamiltonian systems with symmetry constrained by a condition on the associated moment maps.
New classical properties of quantum coherent states
Authors: Emch Gérard G. , Hegerfeldt Gerhard C.
Published: July 2002

A noncommutative version of the Cramer theorem is used to show that if two quantum systems are prepared independently, and if their center of mass is found to be in a coherent state, then each of the component systems is also in a coherent state, centered around the position in phase space predicted by the classical theory. Thermal coherent states are also shown to possess properties similar to classical ones.
A Dyson-like expansion for solutions to the quantum Liouville equation
Authors: Narcowich Francis J.
Published: July 2002

Given a Hamiltonian of the form H=h+λv, the convergence of a Dyson-like expansion (in λ) is constructed and shown for the Wigner distribution function that solves the quantum Liouville equation that corresponds to H. Here, h is a quadratic polynomial in p, q; its coefficients may depend continuously on time. The potential v is a function of p and t as well as q; roughly speaking, it is the Fourier transform of a time-dependent measure.
Fluid sources for Bianchi I and III space-times
Authors: Bayin Selçuk Ş. , Krisch J. P.
Published: July 2002

Four analytic solutions to the Einstein field equations are presented. The solutions are parametrized to have either Bianchi I or Bianchi III symmetry. The associated fluid parameters are given and some of them are discussed in detail.
Time-ordered operators and Feynman–Dyson algebras
Authors: Gill Tepper L. , Zachary W. W.
Published: July 2002

An approach to time-ordered operators based upon von Neumann’s infinite tensor product Hilbert spaces is used to define Feynman–Dyson algebras. This theory is used to show that a one-to-one correspondence exists between path integrals and semigroups, which are integral operators defined by a kernel, the reproducing property of the kernel being a consequence of the semigroup property. For path integrals constructed from two semigroups, the results are more general than those obtained by the use of the Trotter–Kato formula. Perturbation series for the Feynman–Dyson operator calculus for time evolution and scattering operators are discussed, and it is pointed out that they are ‘‘asymptotic in the sense of Poincaré’’ as defined in the theory of semigroups, thereby giving a precise formulation to a well-known conjecture of Dyson stated many years ago in the context of quantum electrodynamics. Moreover, the series converge when these operators possess suitable holomorphy properties.
Branching rules for sp(2N ) algebra reduction on the chain sp(2N− 2)×sp(2)
Authors: Cerkaski Marcin
Published: July 2002

In this paper branching rules for the reduction sp(2N) ■ sp(2N−2)×sp(2) are found, and a new pattern for labeling vectors belonging to the base for unitary irreducible representations BUIR’s is found.
Exact solutions for space-times with local rotational symmetry in which the Dirac equation separates
Authors: Iyer B. R. , Vishveshwara C. V.
Published: July 2002

The field equations for the class of perfect fluid space-times with local rotational symmetry which the authors had earlier shown the Dirac equation separates are studied. For the vacuum and dust cases all possible solutions are exhibited. Other solutions correspond to radiation, a stiff fluid, and a fluid with negative pressure.
Rotating rigid motion in general relativity
Authors: Mason D. P. , Pooe C. A.
Published: July 2002

Kinematic and dynamic expressions are derived for the Lie derivative of vorticity along a particle world line in a rigid motion. It is found that the evolution of vorticity in a rigid motion is governed by the electric part of the Weyl tensor. Necessary and sufficient kinematic and dynamic conditions are established for a rotating rigid motion to be isometric.
Nonlinear wave propagation in the Gauss–Bonnet extended Einstein theory
Authors: Tomimatsu A. , Ishihara H.
Published: July 2002

It is rather usual in general nonlinear fields that even if the waves begin to propagate under smooth initial conditions, after a finite time a shocklike discontinuity in the field quantities occurs at the wave front. Then the field theories fail to set a well-defined initial-value problem. By applying the method of characteristics, this propagation character of nonlinear gravitational waves which obey the lowest-order Gauss–Bonnet extended Einstein equations in higher-dimensional theory of gravity is studied. A diagonal metric tensor is assumed to be dependent on only two coordinate variables. It is found that the quadratic curvature terms added to the Einstein equations do not induce the occurrence of shock waves in the gravitational field.
Theorems on the Jordan–Schwinger representations of Lie algebras
Authors: Kim Shoon K.
Published: July 2002

The Jordan–Schwinger representations of Lie algebras are discussed based on the mixed sets of creation and annihilation operators of boson or fermion type. When the representation is Hermitian, the Lie algebra is shown to be unitary for the fermion case and pseudounitary for the boson case. It is also shown that the representation of a Lie algebra leads to a projective representation of the Lie group corresponding to the Lie algebra.
A formula on the Wiener–Hermite expansion
Authors: Nakayama J.
Published: July 2002

Two mathematical formulas are given in an explicit form: one develops a product of two different multiple Wiener integrals in a series of Wiener–Hermite expansions; the other one develops a product of two random variables, each of which is described by a Wiener–Hermite expansions, in a series of another Wiener–Hermite expansion.
An SU(8) model for the unification of superconductivity, charge, and spin density waves
Authors: Solomon Allan I. , Birman Joseph L.
Published: July 2002

A model Hamiltonian for a many-electron system which unifies superconductivity, charge density waves, and spin density waves is analyzed. It is shown that the spectrum generating algebra for this system is su(8), and all 63 generators of this Lie algebra are identified. The seven symmetry operators that are broken in transition to the condensed state are identified, together with 56 order operators, whose expectations give the order parameters of the various phases present in the model. The discrete symmetry properties of these operators are tabulated. A chain of subalgebras of submodels with corresponding decoupled phases is constructed. Finally, how the finite temperature Green’s functions may be obtained and used to solve the problem of self-consistency of the order parameters in the model is indicated.
The inverse of a Borel summable function
Authors: Boenkost W. , Constantinescu F. , Scharffenberger U.
Published: July 2002

Let B1 be the Borel transform of  f,  f(0)≠0. By means of an integral equation similar to that proposed by ’t Hooft [The Whys of Subnuclear Physics, edited by A. Zichichi (Plenum, New York, 1979)] an explicit representation of the Borel transform B2 of 1/f as a series in convolution powers of B1 and its derivative is given. It is proved that the singularities of B1, B2 on the circle of convergence coincide and have the same strength when approaching these singularities on a path inside their common analyticity domain, but possibly outside the circle of convergence of their power series representation (Borel circle).
The bi-Hamiltonian formulation of the Landau–Lifshiftz equation
Authors: Barouch E. , Fokas A. S. , Papageorgiou V. G.
Published: July 2002

The Landau–Lifshitz (LL) equation is a universal model for integrable magnetic systems. It contains the sine–Gordon (SG), nonlinear Schrödinger (NLS), and the Heisenberg model (HM) equations as particular or limiting cases. It is well known that the NLS, SG, and HM equations possess recursion operators. A recursion operator of an equation in Hamiltonian form generates (a) a hierarchy of integrable equations, and (b) a second Hamiltonian operator and more generally a hierarchy of Poisson structures. Here the recursion operator of the LL equation is obtained algorithmically, and hence its bi-Hamiltonian formulation is established.
Projector bases and algebraic spinors
Authors: Bergdolt G.
Published: July 2002

In the case of complex Clifford algebras a basis is constructed whose elements satisfy projector relations. The relations are sufficient conditions for the elements to span minimal ideals and hence to define algebraic spinors.
The brachistochrone in almost flat space
Authors: Kamath S. G.
Published: July 2002

This paper is an extension, within the framework of general relativity, of the relativistic brachistochrone discussed recently by Goldstein and Bender [J. Math. Phys. 27, 507 (1986)]. Assuming that the gravitational field due to a spherically symmetric source with mass M at equilibrium is weak, it is found that the brachistochrone, for a falling particle of mass m, described by Θ(r), with Θ an angle and r a distance measured from the center of symmetry, is in general a hyperelliptic integral. The latter integral can in one case be calculated exactly in terms of the normal elliptic integrals of the first and third kinds and the elementary transcendental functions. It is shown via a numerical computation using the sun’s gravitational field as a reference that one can recast this exact version into a simple form, viz., (r)1/2Θ=a, where a is a constant.
von Neumann lattices and magnetic orbitals in finite phase space
Authors: Zak J.
Published: July 2002

It is proven that in the finite phase space of dimensionality M, the number of independent von Neumann states is M−r, where r is the number of distinct zeros of the kq function. When applied to magnetic orbitals, this leads to a linear dependence between them for each zero of the corresponding kq function. Different interesting identities follow from the linear dependence of von Neumann states.
Static ‘‘semi-plane-symmetric’’ metrics yielded by plane-symmetric electromagnetic fields
Authors: Li Jian-zeng , Liang Can-bin
Published: July 2002

The task of seeking a general static solution to the Einstein–Maxwell equations representing ‘‘semi-plane-symmetric’’ metrics yielded by plane-symmetric electromagnetic fields is reduced to solving a single ordinary differential equation. A special solution is given, showing that there does exist some electrovac metric that does not share some of the symmetries of the electromagnetic fields.
N=3 extended supersymmetric gauge theories and an explicit construction of higher conservation laws
Authors: Devchand C.
Published: July 2002

A Lagrangian for the superfield equations of motion for supersymmetric gauge theories with N=3 extended supersymmetry is presented. A novel formulation of the previously constructed infinitely many spinorial continuity equations considerably clarifies their structure.
New gradings of sl(3,C) representations
Authors: Patera J. , Sharp R. T. , Van Der Jeugt J.
Published: July 2002

Two new gradings of the Lie algebra sl(3,C) are the refined sl(2,C) and o(3) gradings. The grading in each case utilizes the sl(2,C), or o(3), weight together with a new additive modular label. A complete set of sl(3,C) representation basis states labeled by each to the two sets of additive quantum numbers is found. The newlabeling operator in both cases fails to commute with the cubic sl(3,C) Casimir operator, and hence mixes states of the contragredient representations (p,q) and (q,p)
Canonical formalism for path-dependent Lagrangians. Coupling constant expansions
Authors: Jaén X. , Jáuregui R. , Llosa J. , Molina A.
Published: July 2002

A canonical formalism obtained for path-dependent Lagrangians is applied to Fokker-type Lagrangians. The results are specialized for coupling constant expansions and later on are applied to relativistic systems of particles interacting through symmetric scalar and vector mesodynamics and electrodynamics.
Some classes of general solutions of the U(N) chiral σ models in two dimensions
Authors: Piette Bernard , Zakrzewski Wojciech J.
Published: July 2002

The factorization theorems of Uhlenbeck and Wood are used to derive various finite action solutions to the classical equations of motion of the Euclidean U(N) chiral model in two dimensions. They are obtained by adding a general basic uniton to solutions of the Grassmannian models. A brief comment is made on the properties of these solutions.
Spherically symmetric solutions in higher dimensions
Authors: Krori K. D. , Borgohain P. , Das Kanika
Published: July 2002

An exact general solution of Einstein’s equations for spherically symmetric distribution of a perfect fluid in N dimensions is presented from which the whole class of spherically symmetric solutions may be obtained. As examples, some particular solutions obtainable from a general solution are presented.
Conservation of momentum for systems of charged particles
Authors: Willis Barton L.
Published: July 2002

It is shown that the interaction part of the symmetric energy-momentum tensor for a system of charged particles is integrable over any forward light cone. A covariant definition of the mechanical momentum is then given and conservation of momentum is shown.
The Φ4 equations of motion. II. The zero-, one-, and two-dimensional solutions
Authors: Manolessou Marietta
Published: July 2002

This is the second paper of the series concerning the solution of the system of Φ4 equations of motion for the Schwinger functions by a fixed-point method. These works constitute a part of a general program towards the construction of a Φ44 Wightman quantum field theory (QFT). In the previous paper [J. Math. Phys. 29, 2092 (1988)] (Paper I), a general outline of the program has been presented. Moreover, the ‘‘nice’’ properties of signs, splitting, and norms revealed ‘‘experimentally’’ by the Φ iteration have been analyzed. We have shown how this iterative procedure converges to the solution (if the coupling constant is fixed positive and smaller than a finite value) thanks to the conservation of these properties, which constitute in fact a complete system of self-consistent conditions. Taking into account this information, in the present paper, the answer to the zero-, one-, and two-dimensional problems is given. To be precise, the fixed-point method is constructed by formulating the properties of signs and splitting of the Φ iteration in terms of particular subsets Φ0Λ ⊆ℬ0 (zero dimensions) and ΦΛ⊆ℬ (one and two dimensions) of the appropriated Banach spaces ℬ0 and ℬ, defined exactly with the norms provided by the Φ iteration. The basic ingredients, both introduced already in I, are, on the one hand, the bounded positive sequences of the splitting constants and, on the other hand, the sweeping factors, which carry all the combinatorial information for the global terms. Their absolute and relative bounds yield the stability of the corresponding subsets and the conservation of the norms.

F o r the zero-dimensional problem a simpler equivalent system (nonlinear map) of equations in the space of the splitting sequences is solved by ensuring the existence of the solution (resp. contractivity) inside the corresponding subset when the coupling constant Λ satisfies 0<Λ≲0.1 (resp. 0<Λ≲0.01). For the two- (or one-) dimensional problem it is shown that when 0<Λ≲0.006, the subset ΦΛ is stable under the nonlinear mapping (represented by the equations of motion), which in turn is contractive inside ΦΛ under weaker conditions on Λ. By this last result the convergence of the Φ iteration to the unique fixed point (presented in I) is reobtained in a direct way.