bluuebunny/crossref_metadata_2025 huggingface dataset:
Electrostatically driven electronic molecular bistability: Ab initio calculation for a model (LiF)n system
Authors: Jagielska Anna , Piela Lucjan
Published: July 2002

Semiempirical theories predict that some donor–acceptor molecules may exhibit long-lived electronic metastable states. The states result from a cooperative effect of successive electron transfers from several donor to acceptor moieties of the molecule. Calculations within the Mo/ller–Plesset second-order perturbation theory following the unrestricted Hartree–Fock, projected unrestricted Hartree–Fock, and complete active space self-consistent field procedures confirm the effect for the first time at the ab initio level. An equidistant linear chain (DA)n, where the donor (D) and acceptor (A) subunits are the lithium and fluorine atoms, respectively, has been chosen as a model for a molecule with fixed in space D and A substituents. The nearest-neighbor LiF distance is set to be sufficiently large to assure the isolated DA pair has lower energy in the neutral DA state than in the ionic D+A− one, i.e., a single electron transfer to occur requires energy. In the (DA)n system, a single electron transfer from D to the nearest A requires a comparable amount of energy (ΔEn1). It is shown, however, that, due to the cooperative nature of the excitations, the excited state corresponding to m such electron transfers (m>ncrit) may have an excitation energy ΔEnm lower than ΔEn1. Due to this a multiply excited state may be close in energy scale to the nonexcited one, both states separated by energy barrier related to ncrit. The effect has been checked against perturbations that mimic dimerization of the chain and a lateral extension of the D+ and A− charge distribution. It turned out that the cooperative effect is likely to survive these perturbations.
Theory and simulation of adsorption in a templated porous material: Hard sphere systems
Authors: Zhang Linghui , Van Tassel Paul R.
Published: July 2002

An emerging strategy for controlling porosity in disordered materials is to employ a removable template during synthesis. We present here a theoretical description of adsorption in a templated porous material modeled as a collection of particles formed by an equilibrium quench of a binary mixture of matrix and template particles and subsequent removal of the template component. We show, using the replica method, that an adsorbed phase in the templated material is just the s=0 limit of a special s+2 component replica system. We present a set of Ornstein–Zernike equations relating the correlation functions of the matrix, template, and adsorbate components, solve these equations for the case of hard sphere interactions within the Percus–Yevick closure, and evaluate the system thermodynamics via the compressibility route. We also present a grand canonical Monte Carlo simulation of this model system and find good agreement between theory and simulation. We show that for systems of constant matrix+template volume fraction, templating always enhances adsorption and this enhancement is most pronounced when the template/matrix ratio is low and/or the template size is small.
Response to “Comment on ‘Effect of gravity on contact angle: A theoretical investigation’ ” [J. Chem. Phys. 112, 5511 (2000)]
Authors: Ward C. A. , Sasges M. R.
Published: July 2002

If two liquid phases are present in a closed cylinder, one above a vapor phase and one below, the upper contact angle is smaller than the lower contact angle when the system reaches thermodynamic equilibrium. This surprising theoretical prediction is supported by recent experimental studies.
Pattern formation in restricted geometries: The NO+CO reaction on Pt(100)
Authors: Hartmann Nils , Kevrekidis Yannis , Imbihl Ronald
Published: July 2002

Employing photoelectron emission microscopy (PEEM) as the spatially resolving technique, pattern formation during the catalytic reduction of NO with CO has been investigated on a microstructured Pt(100)/Ti/TiO2 surface in the 10−6 and 10−5 mbar range. The microstructured surface—initially created by a lithographic technique—shows restricted Pt(100) domains of varying size and geometry, such as circles, rings, and dumbbells, surrounded by an inert Ti/TiO2 layer. It is shown that pattern formation during the NO+CO reaction, i.e., the propagation of pulses on the Pt(100) surface, is significantly affected by the size and the geometry of these domains.
Monte Carlo simulation of the motions associated with a single Rouse segment
Authors: Lin Y.-H. , Luo Z.-H.
Published: July 2002

The validity of the Monte Carlo simulation for studying the dynamics of a Rouse chain with a finite number of beads, N, is established by showing the close agreement between the simulation results and the analytical solutions for the time-correlation function of the end-to-end vector. Then, the Monte Carlo simulation is used to calculate the dynamic functions associated with the bond vector b(t) or direction u(t)=b(t)/|b(t)| of an elastic dumbbell and a Rouse segment in a chain. The effect of chain connectivity on the motions of a single Rouse segment is studied. In particular, it is shown that the dynamic function 〈P2[u(0)⋅u(t)]〉2 over a wide dynamic range, which is the main region probed by the depolarized photon-correlation spectroscopy, is basically independent of the values of N⩾8 in agreement with the experimental results. Furthermore, the line shape of the depolarized photon-correlation functions of the concentrated solutions (≈60 wt. %) of polystyrene in cyclohexane at the theta point can be fully accounted for by including the effect of chain connectivity regardless of the crudeness of the Rouse segment relative to the chemical structure. From this study, the molecular weight for a Rouse segment of polystyrene in the concentrated solutions is estimated to be 1100, which is slightly larger than the values m=780–900 obtained for polystyrene in the melt state by other methods.
Slow modes in local polymer dynamics
Authors: Karatasos K. , Adolf D. B.
Published: July 2002

Molecular dynamics simulations of united atom nonentangled linear polyethylene models were utilized in order to systematically examine local orientational dynamics. In agreement with recent experiments and theoretical predictions, slow relaxation processes associated with motions of length scale of the order of chain dimensions are identified and analyzed with a method that allowed a model-free determination of their relative contribution to local orientational relaxation. Factors of intra- and intermolecular nature affecting their characteristics are discussed as well.
Elastic properties of surfactant monolayers at liquid–liquid interfaces: A molecular dynamics study
Authors: Laradji Mohamed , Mouritsen Ole G.
Published: July 2002

Using a simple molecular model based on the Lennard–Jones potential, we systematically study the elastic properties of liquid–liquid interfaces containing surfactant molecules by means of extensive and large-scale molecular dynamics simulations. The main elastic constants of the interface, corresponding to the interfacial tension and the mean bending modulus are determined from the analyses of the long-wavelength behavior of the structure factor of the capillary waves. We found that the interfacial tension decreases with increasing surfactant interfacial coverage and/or surfactant chain length. However, we found that the corresponding change in the bending rigidity is nonmonotonic. Specifically, we found that the bending rigidity decreases with increasing surfactant interfacial coverage for small surfactant interface coverages, but then it increases as the surfactant interface coverage is further increased. Using a Gaussian theory on an interfacial Ginzburg–Landau model of surfactants, we find that the initial decrease of the bending rigidity is attributed to coupling between fluctuations of the surfactant orientation field to those in the interfacial height.
A new iterative method for calculating energy levels and wave functions
Authors: Huang Shi-Wei , Carrington Tucker
Published: July 2002

We present an efficient iterative method for calculating energy levels and wave functions. The method requires storing only a small number of vectors but allows one to calculate energy levels and wave functions with far fewer matrix–vector products than the filter diagonalization method of Mandelshtam and Taylor. A zeroth-order Hamiltonian is used to precondition a spectral transform Lanczos method.
Triply resonant infrared-infrared-visible sum frequency generation: Three-dimensional vibronic spectroscopy for the investigation of vibrational and vibronic couplings
Authors: Cho Minhaeng
Published: July 2002

A theoretical description of the triply resonant (TR) infrared-infrared-visible sum frequency generation (IIV-SFG) is presented, which is an extension of the electronically off-resonant IIV-SFG to the case when the visible field is in resonance with the electronic transition. Since three injected field frequencies can be independently controlled, the measured susceptibility is a three-dimensional spectrum containing information on both the vibrational and vibronic couplings of a molecule in condensed phases. It is shown that the nonlinearities of the dipole moment in the ground electronic state with respect to vibrational coordinates can be separately measured by using the TR-IIV-SFG method. A series of numerical calculations of 2D vibrational and vibronic spectra for a model system are presented to show how the TR-IIV-SFG measurement can be of use in studying specific vibrational and vibronic coupling processes.
The Σu−3←X 3Σg− electronic spectrum of linear C4 in the gas phase
Authors: Linnartz Harold , Vaizert Olga , Motylewski Tomasz , Maier John P.
Published: July 2002

The Σ3Σu−←X 3Σg− electronic absorption spectrum of linear C4 has been detected in the gas phase. The origin and several vibronic transitions have been recorded by means of cavity ring down spectroscopy through a supersonic planar plasma. The origin band is found at 26 384.9(2) cm−1 (∼379 nm). A partly rotationally resolved origin band spectrum yields a value of B0′=0.1570(5) cm−1 for the electronically excited Σ3Σu− state.
Photodissociation of HBr adsorbed on the surface and embedded in large Arn clusters
Authors: Baumfalk Reinhard , Nahler Nils Hendrik , Buck Udo , Niv Masha Y. , Gerber R. Benny
Published: July 2002

Ultraviolet (UV) photodissociation experiments are carried out for Arn(HBr) clusters in which the HBr is adsorbed on the surface of the Arn, and also on isomers of these systems in which HBr is embedded within the rare-gas cluster. The mean size of the cluster distribution in the experiments is around n̄=130. The kinetic energy distribution (KED) of the hydrogen atoms that left the clusters is measured. Molecular dynamics (MD) simulations of the photodissociation of the chemically similar clusters Arn(HCl) are used to provide a qualitative interpretation of the experimental results. The clusters with embedded HBr give a very cold H-atom KED. The clusters with the surface-adsorbed HBr give a KED with two peaks, one corresponding to very low energy H atoms and the other pertaining to high energies, of the order of 1.35 eV. The theoretical simulations show that already for n=54, there is a strong cage effect for the “embedded” molecule case, resulting in slow H atoms. The surface-adsorbed case is interpreted as due to two types of possible adsorption sites of HX on Ar55: for a locally smooth adsorption site, the cage effect is relatively weak, and hot H atoms emerge. Sites where the HBr is adsorbed at a vacancy of Arn lead to “encapsulation” of the H atom produced, with a strong cage effect. A weak tail of H atoms with energies well above the HBr monomer excess energy is observed for the embedded case. Simulations support that this is due to a second photon absorption by recombined, but still vibrationally hot, HBr. The results throw light on the differences between the cage effect inside bulk structure and at surfaces.
Mobility of atomic chains on channeled surfaces
Authors: Montalenti F. , Ferrando R.
Published: July 2002

We investigate the mobility of one-dimensional n-adatom chains deposited on the (110)(1×2) metal surface. All known diffusion mechanisms are taken into account; dissociation–reassociation processes are also included. On the missing-row reconstructed surface, diffusion may proceed via the leapfrog mechanism. Through a set of analytical calculations we find the law describing leapfrog-induced diffusion for every n. It turns out that in a wide range of n, at typical experimental temperatures, chain mobility may be independent of the chain length. As a consequence, even long chains are expected to display a significant mobility. On the contrary, on the (110)(1×1) surfaces, where the leapfrog diffusion mechanism is not present, tetramers are already practically motionless.
Reliability of the cluster model approach to the Stark tuning rate of adsorbates on metal surfaces: CO and OH− on Pt(111)
Authors: Garcı́a-Hernández Maite , Curulla Daniel , Clotet Anna , Illas Francesc
Published: July 2002

The Stark tuning rate, STR, of free and chemisorbed CO and OH− on Pt(111) is theoretically studied by means of a cluster model density functional theory, DFT, approach with the hybrid B3LYP potential for the exchange-correlation functional. The STR is obtained by explicit calculation of the corresponding vibrational frequencies and of their variation with respect to the intensity of a uniform external electric field. A point of special concern is the influence of the size of the model employed which has been tested by progressively increasing the number of metal atoms employed in the surface model. For both CO and OH− on Pt(111) results show that, except for extremely small cluster models, STR values do not appreciably vary with respect to cluster size. Therefore, the use of a cluster model does not introduce artefacts that may mislead the physical description of this property.
Potential energy surface and infrared spectrum of the Ar–H2Cl+ ionic complex
Authors: Dopfer Otto , Roth Doris , Maier John P.
Published: July 2002

The infrared photodissociation spectrum of the Ar–H2Cl+ dimer has been recorded in the vicinity of the Cl–H stretch fundamentals of bare H2Cl+. Eleven Q branches of a strong perpendicular transition of a (near) prolate symmetric top are observed. The position and rotational structure of the band are consistent with an assignment to the free Cl–H stretch fundamental of a proton-bound Ar–HClH+ dimer. The global minimum on the intermolecular potential energy surface of Ar–H2Cl+, calculated at the MP2/aug-cc-pVTZ# level of theory, corresponds to the proton-bound structure with an intermolecular separation of Re=1.97 Å and a well depth of De=1860 cm−1. The slightly nonlinear ionic hydrogen bond is directional with large barriers (Vb) for internal rotation of H2Cl+ via planar transition states with C2v symmetry: Vb∼750 and 1330 cm−1 for the bridged (Re=3.45 Å, De=1107 cm−1) and chlorine-bound (Re=3.38 Å, De=531 cm−1) structures. The molecular constants of the observed transition, ν0=2663.1 cm−1 and A=10.35 cm−1, are in good agreement with the values calculated for the proton-bound equilibrium geometry, ν0=2665.4 cm−1 and Ae=10.28 cm−1.
3-Ethylindole electronic spectroscopy: S1 and cation torsional potential surfaces
Authors: Pitts Jonathan D. , Basu Swarna , Knee J. L.
Published: July 2002

The tryptophan derivative 3-ethylindole was studied in the first excited electronic state and the cation ground state using resonance enhanced multiphoton ionization (REMPI) and zero electron kinetic energy (ZEKE) spectroscopy. Weakly bound clusters of 3-ethylindole with argon (n=1–3) have also been studied. The monomer spectroscopy revealed that two conformations of the 3-ethylindole exist in the jet cooled sample. Density-functional theory (DFT) calculations have been used to calculate the ground- and ionic-state geometries and energies. The calculations reveal the two conformations to be a planar and a nonplanar orientation of the ethyl substituent relative to the indole plane. The ZEKE spectrum of the nonplanar form has an extensive progression in the vibration associated with ethyl torsion and indicates a significant geometry change in the ethyl chain torsion upon ionization. The ethyl chain torsional potential is mapped out using DFT calculations, and the ion surface is adjusted such that calculated frequencies and Franck–Condon factors reproduce the experimental ZEKE spectra. The conformer interconversion barrier height is calculated in the ground and ion states. This is compared to an experimentally determined barrier height in the ion. The spectroscopy of the argon complexes reveals interesting results with regard to the cooling of the 3-ethylindole conformations.
Experimental and theoretical studies on different ionic states of ethylthio CH3CH2S radical
Authors: Ge Maofa , Wang Jing , Zhu Xinjiang , Sun Zheng , Wang Dianxun
Published: July 2002

A continuous flowing ethylthio CH3CH2S radical is produced in situ by pyrolysis of CH3CH2SSCH2CH3 at 242(±0.5) °C in a double heater inlet system on a double chamber UPS machine-II which was built specifically to detect transient species. By combining HeI photoelectron spectroscopic (PES) measurement with ab initio GAUSSIAN2 (G2) calculations on different ionic states of the CH3CH2S radical, we have concluded that the CH3CH2S radical has Cs symmetry and the ground state of the CH3CH2S+ cation is the A"3 state which comes from removal of an electron of the SHOMO 13a′ orbital for the CH3CH2S radical. The PES peak at the lowest ionization energy 9.08 eV with vibrational structure 700±60 cm−1 and corresponding with the G2 computed ionization energy 9.123 eV is designated to the A"3 ionic state. The removal of an electron of the HOMO 4a″ for the CH3CH2S radical leads to a very sharp peak at 10.31 eV, corresponding to ionization CH3CH2S+ (1A′)←CH3CH2S(X̃ 2A″) and the G2 computed ionization energy 10.322 eV. The A"1 ionic state caused by removal of the electron of the SHOMO 13a′ corresponds to the PES peak at 10.50 eV and the G2 computed ionization energy 10.448 eV. The assignment of the PES bands of the CH3CH2S radical in the high ionization energy region (>12.00 eV) is also supported by the G2 calculation. Both PES experiment and G2 calculations provide an evidence of existence of different ionic states for the CH3CH2S radical for the first time.
Glass transitions of thin polymeric films: Speed and load dependence in lateral force microscopy
Authors: Dinelli Franco , Buenviaje Cynthia , Overney René M.
Published: July 2002

The glass transition of thin polymeric films can be profitably studied using lateral force microscopy (LFM) if the system is calibrated regarding operational parameters, in particular the applied load and the scanning velocity. We have established that these two parameters significantly influence the occurrence of an apparent glass transition. In particular, we have found that the local pressure, applied by the LFM tip, is insufficient to generate a hydrostatic pressure effect causing an increase in the apparent transition temperature. In fact, at a constant scan velocity and for increased load, the apparent transition temperature decreases towards the actual bulk value. Further discussions in this article are based on viscoelastic theories. Critical time scales that are characteristic for sliding are compared to polymer relaxation times, and provide an estimate of the viscosity temperature dependence.
Spin–orbit branching in the photodissociation of HF and DF. I. A time-dependent wave packet study for excitation from v=0
Authors: Brown Alex , Balint-Kurti Gabriel G.
Published: July 2002

The photodissociation dynamics of HF and DF, following A 1Π←X 1Σ+ electronic excitation, are examined using time-dependent wave packet techniques. The calculations are based on new multireference configuration interaction calculations of the potential energy curves and complete active space self-consistent field calculations of the off-diagonal spin–orbit coupling matrix elements. The calculated branching fraction for the formation of excited state fluorine, F*(2P1/2), following excitation from the ground vibrational state (v=0) of HF, agrees well with the value of 0.41±0.08 measured experimentally at 121.6 nm by Zhang et al. [J. Chem. Phys. 104, 7027 (1996)]. Predictions are made for the excited spin–orbit state branching fraction for both HF and DF over a wide range of photon excitation energies. The results for HF and DF are discussed in context with the corresponding results for the photodissociation of HCl and DCl.
Static and stationary multiple soliton solutions to the Einstein equations
Authors: Letelier Patricio S.
Published: July 2002

The application of the Belinsky–Zakharov solution-generating technique, i.e., the inverse scattering method, to generate stationary axially symmetric solutions to the vacuum Einstein equations is reduced to a single quadrature when the seed solution is diagonal. The possibility of having real odd-number soliton solutions is investigated. These solutions represent solitonic perturbations of Euclidean metrics. The possibility of using instantons as seed solutions is also investigated. The one- and two-soliton solutions generated from a diagonal seed solution are studied. As an application, a unified derivation of some well-known static solutions, like the Schwarzschild metric and the Chazy–Curzon metric, as well as other new metrics is presented. By using these metrics as seed solutions, some known stationary solutions, like the Kerr-NUT metric, the double Kerr metric, and the rotating Weyl C-metric, as well as other new metrics are also derived in a unified way.
Fermi states of Bose systems in three space dimensions
Authors: Garbaczewski Piotr
Published: July 2002

Recently an exact spectral solution was constructed by Sudarshan and Tata for the (NΘ) Fermi version of the Lee model. We demonstrate that it provides a partial solution for the related pure Bose spectral problems. Moreover, the (NΘ) Bose (Bolsterli–Nelson) version of the Lee model is shown to possess Fermi partners, both exhibiting the partial solubility interplay: finding solutions in the Fermi case would presumably be easier than in the original Bose model. Fermi states of the underlying Bose systems in three space dimensions are explicitly identified.
Generating infinitesimal transformations with second-order-infinitesimal accuracy for proving covariance of commutation relations under finite transformations
Authors: Belinfante Frederik J.
Published: July 2002

As dynamical quantization of Einstein’s gravitational theory meets unsolved problems, it is worth considering the alternative method of quantization suggested by Fermi’s quantization of special-relativistic electrodynamics, which for that theory has been the starting point of most modern applications of quantum electrodynamics. This method avoids first-class constraints by an alteration of the Lagrangian. In physical formulas, this introduces unwanted terms, that are at the end equated weakly to zero by auxiliary conditions. By absence of first-class constraints, this theory could be quantized canonically, if it would not contain fermion fields. As shown by Dirac, in the presence of fermion fields the canonical commutation relations of the altered theory have to be replaced by modified commutation relations. The ultimate purpose of this and following papers is to prove the covariance of Dirac’s modified commutation relations, first under infinitesimal transformations, and thence under finite transformations. As usual, this requires the proof of existence of a conserved and invariant generator for the transformations admitted, here coordinate transformations and local Lorentz transformations of the tetrad field. For infinitesimal transformations, the conventional method of deriving from the Lagrangian density ℒ a generator T1 linear in the infinitesimal parameters that determine the transformations is used. However, for guaranteeing integrability of the procedure for generating transformations of the field variables, from infinitesimal transformations to finite transformations, it is necessary to show the existence of a more accurate generator T, no longer linear in the parameters, which will by eiTFe−iT−F generate the transformations δ̄F of the field variables F with second-order accuracy.

While it is left to a following paper to discuss the exact form of Dirac’s modified commutation relations and to prove the conservation and covariance of the generator T and to prove that the conventional first-order generator T1 will, this time by Dirac’s modified commutation relations, generate the first-order substantial variations δ̄1F of the field variables, in the present paper formulas are derived for expressing the second-order-infinitesimal terms in the transformation formulas by means of the first-order terms, and a method is derived for obtaining from T1 the more accurate generator T. Finally, it is verified that the transformations F(x)→F′(x′) =F(x)+δ̄F generated by the generators T do satisfy the transformation group property with second-order accuracy.
An inverse problem in crystallography
Authors: Rubinstein R. , Fitzgerald J. E.
Published: July 2002

Coordinate-independent formulations are derived for the conditions satisfied by the elastic modulus tensor of materials with trigonal, hexagonal, and cubic symmetry. Analogous results for two-dimensional modulus tensors are also derived.
Solution of an extremum problem pertaining to analytic extrapolation techniques
Authors: Auberson G. , Ciulli S.
Published: July 2002

A preliminary problem appearing in analytic extrapolation procedures when the ‘‘physical data’’ are given on a line contained in the analyticity domain and their errors are measured through the norm of the supremum is solved. As an interesting by-product, Blaschke functions are constructed, which, in some sense, generalize the usual Chebyshev polynomials.
Explicit form of the Haar measure of U(n) and differential operators
Authors: Maekawa Takayoshi
Published: July 2002

The Haar measure of the group U(n) is explicitly introduced using the Euler-like parameters, and the differential operators of the first- and second-parameter groups are given. The D-matrix elements are defined through the Gel’fand and Tsetlin basis and the orthogonality and the completeness relations for the d-matrix elements are given explicitly.
Global aspects of shear-free perfect fluids in general relativity
Authors: Collins C. B.
Published: July 2002

In an earlier investigation of the class of shear-free expanding (or contracting) irrotational perfect fluids obeying a barotropic equation of state p=p( μ), and satisfying the field equations of general relativity, it was shown that the space-times form three distinct classes. In one class, the fluid acceleration is zero (i.e., the flow is geodesic), and the space-times are the well-known spatially homogeneous and isotropic Friedmann–Robertson–Walker (FRW) models. In the other two classes, the acceleration is nonzero, and the space-times are spatially anisotropic and are less familiar. One of these classes consists of the spherically symmetric Wyman solutions, whereas models that are plane symmetric, and either spatially or temporally homogeneous, constitute the final class. Analytic forms for these anisotropic space-time metrics were given, although in each case their exact determination would depend upon the solution of a single nonlinear ordinary differential equation, which has not been achieved. The purpose of the present article is to provide a pictorial description of the solutions of these equations, to depict qualitatively similar and distinct subclasses of solution, and hence to discover in some detail all possible global behaviors of the associated space-times. In all cases, it is found that, when the space-time is sufficiently extended, the fluid exhibits unphysical properties. The conclusion is that shear-free expanding (or contracting) relativistic perfect fluids that obey an equation of state p=p( μ) must be FRW, or else must be restricted to ‘‘local’’ regions, by means of a suitable extension in which at least one of the conditions defining the entire family is relaxed.
Explicit forms of Bäcklund transformations for the Grassmannian and C
P N−1 sigma models
Authors: Sasaki R.
Published: July 2002

A fairly wide class of classical solutions of the Euclidean two-dimensional Grassmannian and CPN−1 sigma models has been constructed explicitly and elementarily by the present author. Starting from these classical solutions we derive the explicit forms of the Bäcklund transformations following Harnad et al. Properties of the Bäcklund transformations for the Grassmannian models are discussed. In particular, a simple interpretation of the Bäcklund transformations for the CPN−1 model is obtained. Generalization of these results to the noncompact Grassmannian sigma models is straightforward.
An alternate approach to finding and using the Lie group of the Vlasov equation
Authors: Roberts Dana
Published: July 2002

Two recent methods for finding exact solutions to the Vlasov–Maxwell equations using Lie group theory are compared by the introduction of an ‘‘intermediate’’ approach. In the latter, the Lie group and general similarity solutions of the Vlasov equation are found through a method which treats independent and dependent variables as forms that are on an essentially equal footing. A Maxwell equation is then used to constrain the solutions further. The procedure is shown to illustrate a more general theorem that implies that the reduction of the number of variables in a set of equations through the use of canonical variables generated from the Lie group invariance of one equation in the set leads to the same solutions as are found by considering the invariance of the entire set.
Abelian integrals and the reduction method for an integrable Hamiltonian system
Authors: Gagnon L. , Harnad J. , Winternitz P. , Hurtubise J.
Published: July 2002

A classical finite-dimensional integrable Hamiltonian system, corresponding to the motion of a particle constrained to an n-dimensional sphere ∑nμ=0 x2μ=1, with the Hamiltonian H=∑μ( (1)/(2) y2μ+u2μ/x2μ +εαμx2μ) (where uμ, αμ, and ε are constants and yμ are the momenta conjugate to xμ), is integrated using several different methods. These are the following: (1) The projection of geodesic (free) flow on a larger space, namely the sphere S2n+1 (for ε=0). The flow is obtained in terms of elementary functions. (2) Separation of variables in the Hamilton–Jacobi equation in elliptic coordinates or, alternatively, the use of a complete set of integrals of motion in involution to reduce Hamilton’s equations to quadratures. The flow is obtained in terms of Abelian integrals which are then inverted in terms of generalized θ functions. The relation between the different methods and results is clarified using methods of algebraic geometry, in particular the geometry of quadrics.
A class of solvable second-order ordinary differential equations with variable coefficients
Authors: Takayama Ken
Published: July 2002

This paper treats the problem of solving the second-order ordinary differential equations with variable coefficients of the form d2x/dt2+(q1(t)+λq2(t))x=0. It is shown that if the initial equation d2x/dt2+q1(t)x=0 is in analytically solvable form and q2(t) is the inverse square function of a solution for the nonlinear auxiliary equation 1/2 x d2x/dt2− 1/4 (dx/dt)2+q1(t)x2 =1, there are exact solutions. Using an inner relationship between solutions for the initial equation and the auxiliary equation, an infinite sequence of analytically solvable differential equations is constructed step by step. Typical examples of such a sequence are shown.
On a property of a classical solution of the nonlinear mass transport equation u
t=u
x
x/1+u
x 2
Authors: Kitada Akihiko
Published: July 2002

A mechanism of smoothing due to evaporation–condensation of the roughly perturbed surface of solid is described by Mullins [W. W. Mullins, J. Appl. Phys. 28, 333 (1957); 30, 77 (1959)] in terms of the Cauchy problem (P) in R1 (real line) of a nonlinear parabolic equation for u(x,t) representing the evolution of the profile of the surface: ut=uxx/1+ux2, (x,t)∈ R1×(0,∞); u(x,0)=α(x), x∈ R1[model (P)]. In the present paper, it is demonstrated that each peak height of the initial surface α(x) in Mullins’ model (P) does not increase with time.
The group-theoretical treatment of aberrating systems. II. Axis-symmetric inhomogeneous systems and fiber optics in third aberration order
Authors: Wolf Kurt Bernardo
Published: July 2002

The group-theoretical description of geometrical optical systems whose elements are, in general, inhomogeneous but axis symmetric, in third aberration order, is presented. Closed algebraic expressions are given for fiber elements, i.e., media homogeneous under translations along the optical axis, and refracting interfaces between them.
On Diophantine equations and nontrivial Racah coefficients
Authors: Bremner Andrew
Published: July 2002

Some families of zeros of weight-1 6j coefficients are given, each in terms of four parameters. They arise from a geometrical investigation of certain Diophantine equations. Some general remarks on the solutions of Diophantine equations are also made.
On the linearization problem for ultraspherical polynomials
Authors: Bassetti B. , Montaldi E. , Raciti M.
Published: July 2002

A direct proof of a formula established by Bressoud in 1981 [D. M. Bressoud, SIAM J. Math. Anal. 12, 161 (1981)], equivalent to the linearization formula for the ultraspherical polynomials, is given. Some related results are briefly discussed.
The one-dimensional inverse scattering problem for an increasing potential
Authors: Kristensson Gerhard
Published: July 2002

The one-dimensional inverse scattering problem is considered for potentials that grow without limit for large values of x. The Marchenko method is established for this class of potentials, and several properties of the solution to the Schrödinger equation are developed. In the derivation of the Marchenko equation an extension of the triangularity condition is used. Some brief remarks on the relation to the inverse radial problem and the generalization to hard core potentials are made.
Soliton solutions to the vacuum Einstein equations obtained from a nondiagonal seed solution
Authors: Letelier Patricio S.
Published: July 2002

The one- and two-soliton solutions obtained by using the Belinsky–Zakharov inverse scattering method in the particular case where the seed solution is taken as the one due to van Stockum are studied. For the above-mentioned particular case the inverse scattering problem is solved in terms of a single quadrature.
Variational calculus on supermanifolds and invariance properties of superspace field theories
Authors: Bruzzo Ugo , Cianci Roberto
Published: July 2002

The foundations of a variational calculus on fibered supermanifolds are outlined, giving applications to the formulation of superspace field theories. Utiyama theorems and conservation laws related to local gauge and general invariance of the theory are proved.
Some remarks on scattering theory in supersymmetric quantum systems
Authors: Arai Asao
Published: July 2002

First it is shown in an abstract mathematical framework of supersymmetric quantum theory that, under some conditions for the perturbation, the wave and the scattering operators on bosonic states have some connections with those on fermionic ones. In particular, a unitary equivalence between the two scattering operators is proved. Then, a class of supersymmetric quantum mechanical models on Rn is discussed and the abstract general results are applied to obtain some more explicit results on the supersymmetric potential scattering.
Transmission coefficients in anharmonic symmetrical potentials
Authors: Caballero Carretero J. A. , Martín Sánchez A.
Published: July 2002

Barrier transmission in potentials of the type V(x)=Ax2+Bx4 is studied using the phase integral method, the same as the JWKB approximation in lower orders. Elliptic functions are used for the classical solutions. The transmission coefficient is calculated for all signs and values of A and B that give a potential barrier.
Fractional approximation to elliptic functions
Authors: Visentin Kley , Martin Pablo
Published: July 2002

The Jacobi functions sn(x/m) have been approximated by a quotient of polynomials of first to fourth degrees. The method used here is an extension to nonlinear differential equations of one previously published for first- and second-order linear differential equations. That method uses power series and asymptotic expansions simultaneously. The accuracy here obtained is very good (the absolute error is lower than 10−8 for m<0.8) except for values of the parameter m near 1. They are much better for several orders of magnitude than those based on the Padé method for the same number of parameters to be determined.
The group-theoretical treatment of aberrating systems. III. The classification of asymmetric aberrations
Authors: Wolf Kurt Bernardo
Published: July 2002

A Lie-theoretical classification of the aberrations of systems modeled by asymmetric optical devices is given. The classification is done on the basis of aberration order and axial symmetry of the first-order part. This leads to finite-dimensional (nonunitary) representations of sp(4,R) reduced with respect to its sp (2,R) subalgebra, with helicity and ‘‘symplectic spin’’ labels. Based on pure-magnifier systems, a weight label reproduces and completes Seidel’s traditional classification of axis-symmetric aberrations. Based on other first-order systems such as optical fibers, other classification schemes are indicated.
Effective conductivity of periodic composites composed of two very unequal conductors
Authors: Keller Joseph B.
Published: July 2002

The effective conductivity tensor is calculated for a periodic composite composed of alternating rectangular blocks of two very unequal conductors. The two-dimensional case of a checkerboard pattern of rectangles is also treated, and Gautesen’s result for it is obtained. The checkerboard of parallelograms is treated, too. The method can be applied to alternating parallelepipeds and to certain other configurations.
The ‘‘spectral Wronskian’’ tool and the ∂̄ investigation of the KdV hierarchy
Authors: Jaulent M. , Manna M.
Published: July 2002

The recently introduced ‘‘spatial transform’’ (ST) method for providing solutions to nonlinear evolution equations is developed when the basic ∂̄ equation is the ‘‘spectral Schrödinger’’ equation (S). A fundamental tool is the ‘‘spectral Wronskian,’’ which allows one to take advantage of the structure of a two-dimensional module for some set of solutions of (S). This leads easily to the KdV hierarchy. Contrary to the usual spectral transform (or inverse scattering transform) method there is no a priori assumption on the long distance behavior of the solutions. A recursion operator is exhibited. Local conservation laws and Bäcklund relations are also derived.
Baker–Campbell–Hausdorff relations for the super-Poincaré group
Authors: Kostelecký V. Alan , Truax D. Rodney
Published: July 2002

Baker–Campbell–Hausdorff relations are obtained for the connected supergroup associated with the super-Poincaré algebra iosp(1‖4).
Tensors with icosahedral symmetry that are invariant under a certain wreath product
Authors: Kerber Adalbert , Scharf Thomas
Published: July 2002

Faithful icosahedral symmetry exists only for tensors of rank higher than 5. The most relevant tensor of this type is the one for third-order elastic constants C(3)ijklmn defined by the series expansion Tij=C(2)ijklεkl+ 1/2 C(3)ijklmnεklεmn +⋅⋅⋅ of the stress tensor T in terms of the deformation tensor ε. A basis for those tensors in (R3)⊗6 that are invariant under a certain action of both the icosahedral group S2×A5 and the wreath product S2∼S3 of the symmetric groups S2 and S3 are evaluated.
Semilinear operators
Authors: Sharma C. S. , Almeida D. F.
Published: July 2002

Semilinear operators on a complex Hilbert space are studied in a part of a program that aims to develop the theories of additive operators on complex and quaternionic Hilbert spaces for application to problems in mathematical physics. The more notable among the new results proved on the eigenvalue problem for semilinear operators are the following: (i) if α is an eigenvalue of a semilinear operator then so also is any complex number which has the same modulus as α; (ii) if a normal semilinear operator has two eigenvectors belonging to different eigenvalues, then either the two eigenvectors are orthogonal or two eigenvalues have the same moduli; and (iii) a normal semilinear operator has a complete set of eigenvectors if and only if it is self-adjoint. Further, it is shown that there exists a norm-preserving semilinear isomorphism between the spaces of bounded linear and semilinear operators on a complex Hilbert space. Finally it is demonstrated how the theory of semilinear operators can be exploited to solve the problems of finding three involutive mutually anticommuting self-adjoint two-by-two matrices and four four-by-four matrices with the same properties: the unusual and remarkably easy solution of this old familiar exercise establishes the relevance of the theory being developed here to physics.
BRST quantization of the spinning particle
Authors: Thomi P.
Published: July 2002

Using rigged Hilbert space techniques, the spinning particle is BRST quantized. It is shown that there is a unique admissible Hermitian form on the extended phase space. With respect to it, the BRST operator is anti-Hermitian. The doubling of the BRST cohomology is removed by choosing a subspace on which the Hermitian form is positive definite.
Equations of motion and wave functions in spherical coordinates for an integrable Hamiltonian system
Authors: Gagnon L.
Published: July 2002

The classical equations of motion for the Hamiltonian H=∑nμ=0 (y2μ/2+u2μ/x2μ) (where ∑μ x2μ=1, yμ is the conjugate momentum to xμ, and uμ is constant) are solved by separation of variables, in spherical coordinates, in the Hamilton–Jacobi equation. This flow is related to the one obtained from the projection of geodesic (free) flow on the sphere S2n+1. Wave functions for the quantum case together with the level degeneracy for the generic case uμ≠0 are also given.
Global quantities in algebraic quantum mechanics of infinite systems: Classical observables or parameters?
Authors: Pöttinger Jürgen
Published: July 2002

Local observables of an infinite system are described by a quasilocal C*-algebra A. Traditionally classical observables are introduced as parameters that can be assigned to certain states on the local observables. As fundamental theories should be essentially free of parameters this can hardly be regarded as satisfactory. In the present paper classical observables are introduced explicitly as operators by a transitive system of imprimitivity of a kinematical group in the center of the W*-algebra π(A)″ belonging to a representation π of A. The states of the system are represented by linear functionals on π(A)″, which are dispersion-free on the center of π(A)″. For classical observables related to a kinematical group a W*-description—with algebra π(A)″ and its associated linear functionals that are dispersion-free on the center and normal on the noncentral part of π(A)″—is equivalent to a C*-description—with algebra A and a distinguished family of linear functionals on A, determined uniquely by π. The implications of these results on the interpretation of quantum mechanics of infinite systems are discussed.
A family of inhomogeneous cosmological Einstein–Rosen metrics
Authors: Oliver Gabriel , Verdaguer Enric
Published: July 2002

Some generalized soliton solutions of the cosmological Einstein–Rosen type defined in the space-time region t2≥z2 in terms of canonical coordinates are considered. Vacuum solutions are studied and interpreted as cosmological models. Fluid solutions are also considered and are seen to represent inhomogeneous cosmological models that become homogeneous at t→∞. A subset of them evolve toward isotropic Friedmann–Robertson–Walker metrics.
The relativistic coma aberration. I. Geometrical optics
Authors: Atakishiyev Natig M. , Lassner Wolfgang , Wolf Kurt Bernardo
Published: July 2002

It is shown, in the framework of Hamilton–Lie geometrical optics, that the image on a moving screen undergoes comatic aberration as the conjugate sphere of ray directions distorts under Lorentz boosts.
Berry’s phase for photons and topology in Maxwell’s theory
Authors: Cai Y. Q. , Papini G. , Wood W. R.
Published: July 2002

The classical nature of Berry’s phase for photons is shown to arise from the intrinsic topological structure of Maxwell’s theory. The phase is developed in the context of fiber-bundle theory and is discussed in some detail.
Wave functions of bound states of a fermion and a Dirac dyon and matrix elements in an external electromagnetic field
Authors: Zhang Jian-zu , Qi Yong-chang
Published: July 2002

Wave functions of bound states for a fermion and a Dirac dyon with charge Zd<Zcd and for j≥‖q‖+ 1/2 are obtained. Matrix elements of this system in the external electromagnetic field are calculated and the corresponding selection rules are shown.
Lie group symmetries and invariants of the Hénon–Heiles equations
Authors: Abraham-Shrauner Barbara
Published: July 2002

Lie group symmetries and invariants of the generalized Hénon–Heiles equations are found. The coupled second-order equations are invariant under translations in time, in general, and the stretching group (dilation) if the linear terms in the ‘‘force’’ are absent. The equivalent set of four coupled first-order equations is found to be invariant under a one-parameter group for three cases and the group generators are given. Three different approaches are reported: the ‘‘classical method’’ for determining Lie group symmetries, a modified method for finding Lie group symmetries with vector fields and the direct method for calculating the invariants. For the Hénon–Heiles equations the direct method is the most efficient.
Some aspects of quantum groups and supergroups
Authors: Corrigan E. , Fairlie D. B. , Fletcher P. , Sasaki R.
Published: July 2002

Some features of Manin’s construction of quantum groups are developed and extended to supergroups.
Stochastic action of dynamical systems on curved manifolds. The geodesic interpolation
Authors: Aldrovandi Ettore , Dohrn Daniela , Guerra Francesco
Published: July 2002

Dynamical systems on curved manifolds, with a Lagrangian at most quadratic in the velocity, are considered. The classical action functional, on some finite time interval, is well defined for any smooth trial trajectory in configuration space. The action functional is at the basis of Lagrangian variational principles, from which all dynamical properties of the system can be derived. Here the problem of extending the action functional from the smooth deterministic trajectories of classical mechanics to the very irregular random trajectories of diffusions in configuration space is considered. In this way the action becomes a functional of the trial diffusion processes and can be put at the basis of stochastic variational principles. Since the problem is beset with ultraviolet divergences, the general strategy of renormalization theory is followed, by regularizing the trial diffusion processes through piecewise smooth geodesic lines for a generic given connection on the manifold. After cutoff removal and infinite counterterm subtraction, the quadratic part of the action shows a residual dependence on the generic regularizing connection field. Therefore, in the frame of this geodesic interpolation strategy, it is shown that a change in the connection field is equivalent to a well-defined renormalization of the scalar potential. These results apply to the problem of quantization of generic dynamical systems on curved manifolds, in particular to the definition of Feynman path integrals on curved configuration spaces.
Fourier transforms on 𝒜/𝒢 and knot invariants
Authors: Majid Shahn
Published: July 2002

Fourier transformation on 𝒜/𝒢 leads to some elementary insight into Witten’s expression for the Jones polynomial.