bluuebunny/crossref_metadata_2025 huggingface dataset:
Magnetic coupling in neutral and charged Cr2, Mn2, and CrMn dimers
Authors: Desmarais N. , Reuse F. A. , Khanna S. N.
Published: July 2002

Theoretical ab initio studies of neutral, cationic and anionic Cr2, Mn2, and CrMn dimers have been carried out to explore the progression of magnetic coupling with the number of electrons. It is shown that while Cr2 and Cr2− have antiferromagnetically coupled atomic spins, Cr2+ has a ferromagnetic ground state closely followed by an antiferromagnetic state. On the other hand, all Mn2 dimers are ferromagnetic, irrespective of the charge. The neutral CrMn is ferrimagnetic while the charged CrMn are antiferromagnetic. In all cases, the charged dimers are found to be more stable than the neutral ones. The results are compared with available calculations and experiments and the difficulties associated with theoretical description and the experimental interpretations are discussed.
Effect of molecular bending on the photodissociation of OCS
Authors: Sugita Akihiro , Mashino Michio , Kawasaki Masahiro , Matsumi Yutaka , Bersohn Richard , Trott-Kriegeskorte Gundula , Gericke Karl-Heinz
Published: July 2002

At 230 nm, the photodissociation of OCS via a hot band and a triplet state was investigated by selective probing of high rotational levels of product CO (J=45–67) with photofragment imaging spectroscopy: OCS(v=0)+hν(UV)→CO(X 1Σ+,J⩾65)+S(3P), OCS(v=1)+hν(UV) →CO(X 1Σ+,J∼65)+S(1D). Additional two-photon IR excitation of the UV photoprepared OCS with intense 1.06 μm laser pulses bleaches the UV processes listed above and induces a new excitation channel of OCS: OCS(v=0)+hν(UV)→OCS*, OCS*+2hν(IR)→CO(X 1Σ+,J∼74)+S(1S). The bending mode of OCS in the excited states plays a central role in the excitation and dissociation dynamics. Additionally, the alignment effect of OCS by nonresonant infrared laser pulse, which appears on the angular distribution of the photofragment, is discussed.
Testing the identifiability of a model for reversible intermolecular two-state excited-state processes
Authors: Boens Noël , Szubiakowski Jacek , Novikov Eugene , Ameloot Marcel
Published: July 2002

The modeling of excited-state processes in photophysics can conveniently be done within the framework of compartmental analysis. In compartmental analysis substantial attention has been devoted to the study of deterministic identifiability, which verifies whether it is possible to determine the parameters of the compartmental model from error-free data. In this paper the similarity transformation approach is applied to the identifiability problem of the photophysical model for reversible intermolecular two-state excited-state processes. This method provides straightforward relations between the true and alternative sets of the system parameters. This allows one to explore directly the parameter space for identifiability. Since absolute values for the spectral parameters associated with excitation and emission are not available from time-resolved fluorescence experiments, the original similarity transformation approach to the identifiability problem was reformulated in terms of normalized spectral parameters, which are experimentally accessible. It is shown that six decay traces—measured at two coreactant concentrations and three emission wavelengths—are required for the model to be locally identifiable. Two sets of rate constants and associated spectral parameters may be found under these conditions. Enclosure in the analysis of the monoexponential decay at very low coreactant concentration results in global identifiability. The non-negativity requirement of the spectral parameters also can lead to the unique solution. If the fluorescence decays are independent of the emission wavelength, additional information about the photophysical system is necessary for identifiability.
Energy-dependent deposition processes of size-selected Ag nanoclusters on highly-oriented pyrolytic graphite
Authors: Yamaguchi W. , Yoshimura K. , Tai Y. , Maruyama Y. , Igarashi K. , Tanemura S. , Murakami J.
Published: July 2002

Singly charged cations of silver atoms and clusters (Agn+, n=1,3,5,7,9) were deposited on highly oriented pyrolytic graphite substrates at well-controlled, various collision energies. The total amount of Ag atoms remaining on the substrates after collision was quantified by measuring the Ag 3d5/2 photoelectron intensities. The collision energy dependence of the amount of deposited Ag atoms revealed that, for all the species, there are three distinct energy regions, for which soft landing, rebounding, or implantation is a dominant process, and that the energy ranges for the processes strongly depend on the cluster size. The deposition efficiency vs collision energy curve for each cluster is well fitted to that for Ag1, by considering the difference between the contact area of Ag1 with the surface and that of the cluster, reflecting the compactness of the clusters. Boundaries between the different deposition regimes for the clusters were less distinct than those for Ag1. Considering anisotropy in shape of a cluster, deposition efficiency around the implantation threshold was calculated, which well explains the indistinctness of the threshold observed in the experimental data. This supports the picture that the energy given to a unit surface area determines the collision process.
Trapping-mediated chemisorption of disilane on Si(100)-2×1
Authors: Ferguson B. A. , Reeves C. T. , Safarik D. J. , Mullins C. B.
Published: July 2002

Disilane adsorption probabilities have been measured on Si(100)-2×1 over a wide range of incident kinetic energies, incident angles, and surface temperatures using supersonic molecular beam techniques. The trapping-mediated chemisorption mechanism is shown to be the dominant adsorption pathway under the conditions investigated. The first step in such a mechanism, namely trapping into the physical adsorption well, has been studied directly via measurements at a surface temperature of 77 K. As expected, the trapping probability drops with increasing kinetic energy, but nearly 50% of incident molecules trap at 1 eV incident energy, indicating that trapping is quite efficient over a wide range of translational energies. Chemisorption probability values measured at higher surface temperatures are fit to a simple trapping-mediated chemisorption model that can be used to predict adsorption probabilities over a wide range of conditions. Measurements of the chemisorption probability at 500 K are independent of incident angle at kinetic energies of 0.75 eV and below. However, trapping probabilities measured at 77 K are shown to decrease with increasing angle of incidence at kinetic energies of 0.6 eV and above. This unusual effect is discussed in terms of molecular scattering during parallel momentum accommodation. In order to investigate the effect of surface hydrogen formed as a result of disilane decomposition, adsorption probabilities were measured as a function of monohydride coverage as well. On a monohydride-saturated surface the trapping probability is found to be lower than on a bare surface, most likely due to a decreased disilane physical adsorption binding energy compared to the bare surface. Also, the trapping probability varies linearly with hydrogen coverage between bare-surface and monohydride-saturated values. On the other hand, the hydrogen coverage dependence of the chemisorption probability is found to follow a simple second-order kinetic scheme based on chemisorption occurring at two vacant surface sites.
Mapping of connections on bundles and gauge field theories
Authors: Sen D. K.
Published: July 2002

The problem of solving the combined gravitational and Yang–Mills field systems is regarded as a purely geometrical problem of determining a linear connection on the principal frame bundle L(M) from a connection on a SU(2) principal bundle over a space-time M. It is suggested that mapping theorems of connections on bundles may provide a means of actually solving ‘‘field equations.’’
The Gibbs phenomenon in generalized Padé approximation
Authors: Németh G. , Páris G.
Published: July 2002

The Gibbs phenomenon in generalized Padé approximation is discussed, and with the aid of some rational approximants the Gibbs constants are determined. In addition, the steepest of the rational approximants is calculated.
Ion-acoustic dispersion relation with direct fractional approximation for Z′(s)
Authors: Donoso Guillermo , Martín Pablo
Published: July 2002

A direct fractional approximation for the derivative Z′ of the plasma dispersion function Z(s) has been obtained by using the modified asymptotic Padé method. The dispersion relation for the ion-acoustic wave and for the ion-beam instability has been solved by the use of that fractional approximation yielding satisfactory results. A comparison is given between the dispersion relations calculated with (a) our approximation, (b) other approximations to Z′, and (c) the exact function.
Infinitesimal transformations about soliton solutions of sine–Gordon and modified Korteweg–de Vries equations
Authors: Rao Jyoti A. , Rangwala Abbas A.
Published: July 2002

Infinitesimal transformations about n-soliton solutions of sine-Gordon and modified Korteweg–de Vries equations are obtained using respective Bäcklund transformations. We also obtain the eigenfunctions of corresponding generalized Zakharov–Shabat systems.
Energy-momentum tensors and stress tensors in geometric field theories
Authors: Ferraris M. , Francaviglia M.
Published: July 2002

Lagrangian field theories of geometric objects are the most natural framework for investigating the notion of general covariance. We discuss here geometric theories of interacting fields, depending on Lagrangians of arbitrary order, and we give general definitions of energy flow, partial energy flows, energy-momentum tensors, and stress tensors. We also investigate the role which energy-momentum tensors and stress tensors play in formulating the natural conservation laws associated with the second theorem of Noether. Examples of application may be found elsewhere.
A pair of commuting scalars for G(2) ⊇ SU(2)×SU(2)
Authors: Hughes J. W. B. , Van der Jeugt J.
Published: July 2002

G(2) ⊇ SU(2)×SU(2) is a two-missing-labels problem, and therefore in order to give a complete and orthogonal specification of states of irreducible representations of G(2) in an SU(2)×SU(2) basis, one needs to find a pair of commuting Hermitian operators which are scalar with respect to the SU(2)×SU(2) subalgebra. A theorem due to Peccia and Sharp states that there are, apart from the Lie algebra invariants, twice as many functionally independent scalars as missing labels. Here two commuting SU(2)×SU(2) scalars are obtained, both of sixth order in the G(2) basis elements. They are in fact combinations of five scalars of different tensorial types, indicating that the functionally independent ones are in general insufficient to provide the lowest-order commuting scalars. An expression for the sixth-order invariant of G(2) is also obtained.
Inverse scattering by a local impurity in a periodic potential in one dimension. II
Authors: Newton Roger G.
Published: July 2002

This paper continues and completes the solution to the inverse scattering problem initiated in a recent paper. It allows for the existence of bound states in the band gaps and corrects a number of errors in the first paper.
Convergence of lattice sums and Madelung’s constant
Authors: Borwein David , Borwein Jonathan M. , Taylor Keith F.
Published: July 2002

The lattice sums involved in the definition of Madelung’s constant of an NaCl-type crystal lattice in two or three dimensions are investigated. The fundamental mathematical questions of convergence and uniqueness of the sum of these, not absolutely convergent, series are considered. It is shown that some of the simplest direct sum methods converge and some do not converge. In particular, the very common method of expressing Madelung’s constant by a series obtained from expanding spheres does not converge. The concept of analytic continuation of a complex function to provide a basis for an unambiguous mathematical definition of Madelung’s constant is introduced. By these means, the simple intuitive direct sum methods and the powerful integral transformation methods, which are based on theta function identities and the Mellin transform, are brought together. A brief analysis of a hexagonal lattice is also given.
Wavelength-dependent electromagnetic parameters for coherent propagation in correlated distributions of small-spaced scatterers
Authors: Twersky Victor
Published: July 2002

Earlier results for coherent propagation of electromagnetic waves in pair-correlated random distributions of scatterers (of radius a and physical parameters ε′,μ′) with minimum separation of centers b≥2a small compared to wavelength (2π/k) are generalized to obtain polarization, refraction, and absorption terms to order k2. The development includes multiple scattering and multipole coupling by electric and magnetic dipoles, as well as quadrupoles to appropriate order. The correlation aspects are determined by simple integrals of the statistical mechanics radial distribution function f for impenetrable particles (spheres, cylinders, and slabs) of diameter b. For slab scatterers, in terms of the exact Zernike–Prins f, the correlation integrals are expressed as algebraic functions of the volume fraction w; the resultant bulk values reduce to those of one particle at full packing, w=1. Similar results are obtained for spheres in terms of the Wertheim–Thiel solution of the Percus–Yevick approximation of f at the unrealizable bound w=1.
Simple physical models entailing inequivalent representations of the CCR
Authors: Warchall Henry A.
Published: July 2002

This paper analyzes a family of model quantum field theories for which a C*-algebraic viewpoint is essential because time-dependent scattering theory cannot be constructed in any one natural representation of the observable algebra. The models demonstrate, in an uncomplicated setting, mechanisms by which nonstandard representations of the canonical commutation relations (CCR) arise in the solution of the field theory. It is shown explicitly how sufficiently strong low-energy coupling between a massless quantum field and a quantum oscillator can result in the inequivalence of the free and interacting vacua, and in the failure of Møller wave operators to exist. It is also shown explicitly how an algebraic framework can be used to circumvent these representation-dependent difficulties and to easily construct an S matrix. The treatment relies on and illustrates the general theory developed in a preceding paper for scattering in models which are field-theoretic analogs to systems with finite numbers of degrees of freedom that are solvable by transformation to normal modes.
Realization of latent ensembles of the statistical operator
Authors: Leaf Boris
Published: July 2002

The statistical operator is a weighted sum, over eigenvalues of a complete commuting set of observables, of pure states each evolving unitarily from a microstate of the set. For every complete commuting set q̂ there is a latent ensemble, the diagonal projection of the statistical operator in q̂ representation, which determines the probabilities of observables in set q̂. When constraints imposed by a measurement situation makes these observables measurable, the latent q̂ ensemble is realized as the initial state of a new ensemble, which then evolves unitarily. Realization of a latent ensemble is an irreversible process with non-negative entropy increase. Reduced ensembles are realized when the constraints of the measurement situation permit only a subset of q̂ observables to be measurable. Successive realizations in response to changing measurement situations drive the system toward a state of maximum entropy. This mechanism explains the approach to equilibrium, and the change of an equilibrium system to an equilibrium state of increased entropy as constraints are relaxed.
Tiling, periodicity, and crystals
Authors: Radin Charles
Published: July 2002

A result on nonperiodic tilings is generalized and related to the problem of the origin of crystalline symmetry.
Multiply connected universes and inequivalent fields
Authors: Catenacci Roberto , Salmistraro Franco
Published: July 2002

Multiply connected universes with nice physical properties can be obtained from a standard model through identifications under discrete groups. We classify the possible transformation properties of matter and gauge fields under these groups. The example of zero-curvature models is analyzed giving the number of inequivalent fields.
Kinematics of the two-angle-dependent reactive infinite-order sudden approximation
Authors: Jellinek Julius
Published: July 2002

The so-called ‘‘matching problem’’ in the earlier formulations of the reactive infinite-order sudden approximation (RIOSA) is analyzed in detail. The kinematics of a new, two-angle-dependent RIOSA scheme, which is based on an independent selection of the ‘‘frozen’’ angles in the reactants and products channels, is derived. It is shown that the only pairs of these angles to be excluded from consideration are those which violate the ‘‘collinearity conservation rule.’’ The new scheme does not invoke any additional assumption which is not an inherent part of the RIOSA approach. It is free from the matching problem and treats the different arrangement channels in a completely symmetrical fashion.
Wave vector dependent susceptibility of a free electron gas in D dimensions and the singularity at 2kF
Authors: Sharma N. L. , Lee M. Howard
Published: July 2002

The static susceptibility of a free electron gas in D dimensions at T=0 is obtained by techniques of dimensional regularization. Our solutions for the susceptibility χ(k,D) are given in terms of the hypergeometric function. For any integer dimensions analytic expressions are possible. The high- and low-k series solutions are shown to be related by an analytic continuation if D is an odd integer, but not related if D is an even integer. The singularity at 2kF is a branch point, whereupon the series solutions are absolutely convergent, yielding χ(k=2kF,D)=(D−1)−1. The relationship of χkD has the appearance of a PVT diagram.
Hamiltonian and non-Hamiltonian perturbation theory for nearly periodic motion
Authors: Larsson Jonas
Published: July 2002

Kruskal’s asymptotic theory of nearly period motion [M. Kruskal, J. Math. Phys. 4, 806 (1962)] (with applications to nonlinear oscillators, guiding center motion, etc.) is generalized and modified. A new more natural recursive formula, with considerable advantages in applications, determining the averaging transformations and the drift equations is derived. Also almost quasiperiodic motion is considered. For a Hamiltonian system, a manifestly Hamiltonian extension of Kruskal’s theory is given by means of the phase-space Lagrangian formulation of Hamiltonian mechanics. By performing an averaging transformation on the phase-space Lagrangian for the system (L → L̄) and adding a total derivative dS/dτ, a nonoscillatory Lagrangian Λ=L̄+dS/dτ is obtained. The drift equations and the adiabatic invariant are now obtained from Λ. By truncating Λ to some finite order in the small parameter ε, manifestly Hamiltonian approximating systems are obtained. The utility of the method for treating the guiding-center motion is demonstrated in a separate paper.
Stability of forced nonlinear oscillators via Poincaré map
Authors: Liu K. L. , Young K.
Published: July 2002

The behavior of nonlinear oscillators x(t) driven by a periodic external force is completely determined by the corresponding Poincaré map, which loses stability only in certain well-known ways. These translate into different classes of perturbations ξ(t) of x(t) that must be considered. By choosing simple representatives in each class, the stability of approximate solutions can be studied analytically. The Duffing equation is considered as an example. An extra island of stability is predicted for a range of driving forces and this is confirmed by numerical computation.
Boson realization from quantum constraints
Authors: Iosifescu Mircea , Scutaru Horia
Published: July 2002

Generalized Holstein–Primakoff realizations deduced by Deenen, Quesne, and Papanicolaou are obtained directly from the algebraic identities satisfied in collective subspaces by the infinitesimal generators of the corresponding dynamical groups.
Two-loop Feynman integrals in the physical light-cone gauge
Authors: Leibbrandt George , Nyeo Su-Long
Published: July 2002

The feasibility of doing multiloop calculations in the noncovariant light-cone gauge nμAaμ=0, n2=0, is investigated by evaluating various Feynman integrals arising in a two-loop Yang–Mills self-energy. Application of a consistent prescription for (q ⋅ n)−1 is essential.
Determination of coexistence wave functions from two-neutron-transfer data
Authors: Carchidi M. , Fortune H. T.
Published: July 2002

An analysis of wave functions in a generalized two-state model for a series of even–even nuclei is presented here. With minimal assumptions, necessary and sufficient conditions for consistency in obtaining these from data on (p,t) and (t,p) cross-section ratios are exhibited.
Approximate solution of Fredholm integral equations by the maximum-entropy method
Authors: Mead Lawrence R.
Published: July 2002

An approximate means of solving Fredholm integral equations by the maximum-entropy method is developed. The Fredholm integral equation is converted to a generalized moment problem whose approximate solution by maximum-entropy methods has been successfully implemented in a previous paper by Mead and Papanicolaou [L. R. Mead and N. Papanicolaou, J. Math. Phys. 25, 2404 (1984)]. Several explicit examples are given of approximate maximum-entropy solutions of Fredholm integral equations of the first and second kinds and of the Wiener–Hopf type. Both the weaknesses and strengths of the method are discussed.
Sites and googly twistor spaces. I. Vacuum
Authors: Helfer Adam D.
Published: July 2002

(Anti-) self-dual Yang–Mills fields may be described by twistors of the same or opposite handedness as the fields. These are called the leg-break and googly descriptions, respectively. The leg-break twistor space is a complex manifold; the Yang–Mills field is given by a vector bundle over this manifold, and massless fields minimally coupled to the Yang–Mills field are given by elements of certain sheaf cohomology groups on the manifold. In this paper, the structure of the googly twistor space when no Yang–Mills field is present is elucidated. It is shown that the googly twistor space is a site. Sites are generalizations of topological spaces, in which the primitive concept is that of an open set rather than that of a point. The massless fields on space-time are given by the elements of a sheaf cohomology group on the site. Also, this site is isomorphic to a leg-break site, consisting of a family of open sets in the leg-break manifold. This provides a strong link between the googly and the leg-break spaces. The following paper treats the case where a Yang–Mills field is present.
Comment on a paper by Espindola, Teixeira, and Espindola [J. Math. Phys. 2
7, 151 (1986)]
Authors: Hojman Sergio
Published: July 2002

It is shown that the criterium to decide whether two Hamiltonians are equivalent given by Espíndola et al. [O. Espindola, N. L. Teixeira, and M. L. Espindola, J. Math. Phys. 27, 151 (1986)] is incorrect.
Charge operators without local commutativity
Authors: d’Emilio Emilio , Mintchev Mihail
Published: July 2002

A Goldstone-type theorem is proved for quantum field theories in any n≥2 space-time dimensions, without assuming local commutativity.
Exact localized solutions of a family of two-dimensional nonlinear spinor fields
Authors: Stubbe Joachim
Published: July 2002

The classical equations of motion for two-dimensional nonlinear spinor fields are investigated. Explicit solutions for monomial and logarithmic self-interactions are presented. Furthermore properties of these classical solutions are discussed.
Basis states for relativistic three-body calculations of particles with spin
Authors: Garcilazo Humberto
Published: July 2002

Using a linear combination of the three-body helicity states constructed by Wick, a new set of basis states is constructed that can be used to perform three-body calculations with relativistic treatment of the spin. These states are diagonal in the usual angular momentum quantum numbers of a pair liSi ji, where li is the orbital angular momentum, Si the spin, and ji the total angular momentum of the pair jk. These states are used to write down the relativistic Faddeev equations obtaining two sets of uncoupled integral equations that are identified as corresponding to the states of positive and negative parity. It is also shown, by means of some simple examples, that the relativistic recoupling coefficients reduce to the usual nonrelativistic ones if one neglects the effects of relativity. Some possible applications involving particles off the mass shell are discussed.
Series representations for calculations in quantum statistics. II
Authors: Barker William A.
Published: July 2002

The methods developed in the first paper of this series (I) [J. Math. Phys. 27, 302 (1986)] are used to calculate the pressure in several cases of physical interest: conduction electrons inside and outside a heated tungsten cathode; helium atoms in liquid helium II and He vapor; electrons in a white dwarf star, and photons in a cavity. The latter two cases involve ultrarelativistic particles whose energy ε=pc. The formulation in I is extended to include particle speeds comparable to c. The grand potential is used to establish two useful, exact relationships between pressure and energy density: P=2u/3 and P=u/3, valid for v≪c and v≂c, respectively.
The quasiperiodic solutions to the discrete nonlinear Schrödinger equation
Authors: Ahmad Siraj , Roy Chowdhury A.
Published: July 2002

The quasiperiodic solutions to the discrete nonlinear Schrödinger equation are obtained by a variant of a method due to Date and Tanaka [E. Date and S. Tanaka, Suppl. Prog. Theor. Phys. 59, 107 (1976)]. It is shown explicitly that the nonlinear field variable at the different lattice points can be determined in a recursive fashion in terms of combinations of Reimann’s functions depending on lattice position and time.
Fourier transforms and the dilatation group
Authors: Hofstee P. , Tip A.
Published: July 2002

The Fourier transform g(k) of a square integrable function f(x), vanishing for x<0, is analytic in the upper half plane, so that, replacing k by k exp ζ, k≥0, 0<Im ζ<π, it can be associated with an operator K(ζ) in ℋ+=L2((0,∞),dx). The operator K(ζ) can be expressed in terms of the generator D of the dilatation group on ℋ+ and it can be shown that it is analytic in the strip 0<Im ζ<π with strong limits as Im ζ↓0 and ↑π. The Laplace transform (ζ=iπ/2) is an analytic vector for D. It is also found that D is not a spectral operator of scalar type on Lp((0,∞),dx), 1≤p<∞, p≠2. Applying the results obtained here to the time-evolution operator for a one-dimensional Sommerfeld model for the interaction between an electron and a metal, it is found that this operator has a complex-dilated analytic extension.
Nearest neighbor lattice statistics on semi-infinite two-dimensional rectangular lattices of various widths
Authors: Maeder J. M. , McQuistan R. B.
Published: July 2002

Recent results of the shift operator matrix technique are utilized to calculate an exact expression for the lattice coverage of simple indistinguishable interacting molecules adsorbed on a semi-infinite two-dimensional M×∞ rectangular lattice. As an illustrated example, parameters are chosen which most likely model the adsorption of the noble gas Ne on a graphite surface. The lattice coverage is determined as a function of the activity, temperature, and interaction potentials for lattices of increasing width (M=1–7).
Representation theory of the symplectic groups. I
Authors: Gould M. D.
Published: July 2002

Certain aspects of symplectic group representation theory are investigated. In particular, it is shown that every irreducible representation of Sp(n) admits a relatively large class of states, referred to herein as canonical states, which possess properties analogous to the Gelfand–Tsetlin states appearing in the theory of the orthogonal and unitary groups. The properties of canonical states are investigated and some matrix element formulas are derived.
Asymptotic velocities in classical mechanics
Authors: Gutkin Eugene
Published: July 2002

The scattering of a system of classical particles on the line with repulsive interactions is considered. The scattering is called regular if for any motion of the system the asymptotic velocities are distinct. It was known that the scattering is regular if the interactions decay sufficiently fast with the distance. Here the dynamics of repelling particles are put into the framework of Hamiltonians with cone potentials. The notion of regularity of scattering is defined for Hamiltonian systems with cone potentials and conditions for regularity are established that do not depend on the rate of decay of potentials at infinity. Then these results are applied to the scattering of repelling particles on the line.
On regularization ambiguities in fermionic models
Authors: Cabra D. , Schaposnik F. A.
Published: July 2002

Different regularization schemes based on the heat-kernel method using as samples the chiral Schwinger model and the Thirring model are discussed. As it happens with non-Abelian anomalies, it is shown that different physical contexts require different specifications of the fermionic generating functional. Also discussed is the introduction of an arbitrary parameter through the regularization and how this affects the resulting quantum theory.
Hamiltonian structure of the super evolution equation
Authors: Li Yi-shen , Zhang Li-ning
Published: July 2002

The constrained variational calculus proposed in previous papers [Y. Zheng, Y. Li, and D. Chen, Sci. Sinica A 24, 138 (1986); G. Tu, Kexue Tangbao 29, 1227 (1984)] is generalized to the supersymmetric case. Utilizing this method to some super AKNS system, which has soliton solutions and conserved quantities, their equations of motion with the Hamiltonian structure can be written as a 4×4 matrix. This is the supersymmetric symplectic matrix and hn are Hamiltonians of the system. The conserved quantities worked out in recent literature are just the first few terms of our analytic expression.
Normally ordered Fermi operator realization of the SUn group
Authors: Fan Hong-yi
Published: July 2002

The mapping of the SUn group transformation in Grassmann number space into unitary normally ordered and antinormally ordered Fermi operator realizations in Hilbert space are investigated. The unitary Fermi operators are evaluated in fermion coherent state representation using the ‘‘integration within ordered product’’ technique for a fermionic system. Some new Fermi operator identities are thus obtained.
On the convergence of the Feynman path integral for a certain class of potentials
Authors: Papanicolaou Vassilis G.
Published: July 2002

A direct proof is given of the convergence of the discretized Feynman path integral to the fundamental solution of the (time-dependent) Schrödinger equation, for potentials which are bounded, integrable and continuous on the real line. No further smoothness assumptions are required.
Einstein–Maxwell equations and the groups of homothetic motion
Authors: Faridi Abbas M.
Published: July 2002

The Einstein–Maxwell field equations for a source-free, non-null electromagnetic field are studied under the assumption of admitting a nontrivial homothetic conformal motion, generating a homothetic bivector which is also non-null. It is shown that a space-time, whether vacuum or not, cannot admit a non-null homothetic vector field as a geodesic tangent. It is also shown that if a common principle null direction of the electromagnetic and the homothetic bivectors is geodesic and shear free, then the space-time must be algebraically special. Furthermore, it is found that if the electromagnetic and the homothetic bivectors have common principal null directions, then the vector field generating the homothetic bivector cannot be hypersurface orthogonal, unless it is a Killing vector field. Moreover, if these common principle null directions are also geodesics, then there exists no solution to the combined Einstein–Maxwell equations, unless, the non-null homothetic vector field is a Killing vector field. Finally, an example of a space-time admitting a non-null, nontrivial homothetic vector field generating a homothetic bivector which is also non-null is given.
On the BRS’s
Authors: Lusanna Luca
Published: July 2002

After an analysis of the concept of Lagrangian gauge fixing, it is shown that the arbitrariness in the parametrization of gauge transformations gives rise to a whole family of classical BRS transformations. This is explicitly shown for the free-relativistic particle. Two inequivalent classes of BRS Lagrangians are defined. While the former generates a Kato–Ogawa-like Hamiltonian BRS formalism, the latter gives rise to the Batalin–Fradkin–Vilkovisky theory. A comparison is made between these Hamiltonian theories, the multitemporal description of 1st-class constraints, the Konstant–Sternberg and Loll approaches, and the Bonora–Cotta Ramusino interpretation of ghosts. The relevance of an equivariance condition for the BRS observables is shown. The quantum BRS theory is briefly discussed.
Einstein gravity coupled to a massless conformal scalar field in arbitrary space-time dimensions
Authors: Xanthopoulos Basilis C. , Dialynas Thanassis E.
Published: July 2002

For space-times of arbitrary dimensionality two transformations are obtained that applied to any solution of the Einstein equations coupled to a minimally coupled scalar field construct a solution of the Einstein equations coupled to a conformal scalar field. The transformations are conformal for the metrics and algebraic for the reparametrization of the scalar fields. With these generating techniques static, spherically symmetric, asymptotically flat solutions of the Einstein-conformal scalar field equations in arbitrary space-time dimensions are obtained. Black hole solutions are systematically searched for and it is found that the only (nonvacuum) one exists in four space-time dimensions. This is the Bekenstein black hole for gravity coupled to a conformal scalar field.
Solutions to a spheroidal wave equation
Authors: Figueiredo B. D. B. , Novello M.
Published: July 2002

Fackerell–Crossman’s solutions to a generalized spheroidal wave equation are extended for the case in which there is no free parameter in that equation. The results, together with Leaver’s expansions in series of Coulomb wave functions, are used to find the time dependence of massive scalar test fields in nonflat Friedmann–Robertson–Walker models of universes with dust.
Parasupersymmetry in quantum mechanics
Authors: Khare Avinash
Published: July 2002

The various aspects of parasupersymmetric quantum mechanics of one boson and one parafermion of (arbitrary) order p are discussed in some detail. In particular it is shown that the parasupersymmetry algebra is given by Q1pQ1++Q1p−1Q1+Q1+...+Q1Q1+ Q1p−1+Q1+Q1p =2pQ1p−1H, [H,Q1]=0; Q1p+1=0 and the Hermitian conjugated relations where Q1 is the parasupercharge and H the Hamiltonian. It is also shown that such a system always possesses (p−1) other conserved parasupercharges and p bosonic constants. Further, a special case is pointed out when the above algebra takes a very simple form as given by Q1Q1+Q1=2Q1H, Q1pQ1++Q1+Q1p= 2Q1p−1H. A model of conformal parasupersymmetry of degree p is discussed and it is shown that in this case one has p supercharges, p conformal supercharges, and p bosonic constants which along with H, dilatation generator D, and conformal generator K form a closed algebra. A model of parasupersymmetry of degree p is discussed which is not conformal invariant and yet whose spectrum can be algebraically obtained by using the above conformally invariant supersymmetry model. Finally a model of parasupersymmetric quantum mechanics of one paraboson of (arbitrary) order q and one parafermion of order p is discussed.
Energy level degeneracy
Authors: Cohen Jeffrey M. , Kuharetz Boris
Published: July 2002

The nondegeneracy theorem for one-dimensional systems is reviewed herein. After considering Loudon’s contention that this theorem does not apply in the presence of singular potentials, an example (in support of his assertion) which involves a singular potential with degenerate eigenstates is presented.
Reconstruction of Kubo–Martin–Schwinger structure from Euclidean Green functions
Authors: Gielerak R. , Jakóbczyk L. , Olkiewicz R.
Published: July 2002

The explicit form of the Poisson kernel for the strip Tβ={z∈C:0<Im z<β} is used to derive some conditions for a state ω on a given C*-algebra dynamical system (𝒜,αt) to be a Kubo–Martin–Schwinger (KMS) state. Reflection positivity and generalized periodicity of the Euclidean Green functions corresponding to ω are established and used for an analytic continuation to real time. Reflection positivity is also used for the construction of a cyclic and faithful representation of (𝒜,αt) on some Hilbert space. A sufficient condition for the identification of the constructed dynamics with the modular group of a von Neumann algebra generated by the representation is formulated in terms of the Euclidean Green functions.
Kerr–Schild metrics revisited. II. The complete vacuum solution
Authors: Gergely László Á. , Perjés Zoltán
Published: July 2002

The complete solution of Einstein’s gravitational equations with a vacuum–vacuum Kerr–Schild pencil of metrics gab+Vlalb is obtained. Our result generalizes the solution of the Kerr–Schild problem with a flat metric gab (represented by the Kerr theorem) to the case when gab is the metric of a curved space-time.
Algebraic structure of the gradient-holonomic algorithm for Lax integrable nonlinear dynamical systems. II. The reduction via Dirac and canonical quantization procedure
Authors: Prykarpatskyj A. K. , Samoilenko V. Hr. , Andrushkiw R. I.
Published: July 2002

The generalized theory of the ℛ-structure on affine operator Lie algebras is used to construct a complete theory of Lax integrable nonlinear dynamical systems in multidimensions. The operator bi-Hamiltonian structures and their functional reductions are discussed in great detail in the examples of operator Korteweg–de Vries and Benney–Kaup dynamical systems. As an important by-product of the developed algebraic theory, the Dirac canonical quantization problem is solved almost completely for the Neumann–Bogoliubov-type oscillatory dynamical system on spheres, associated via Moser with the spectral moment map on an affine associative metrized Lie coalgebra with a one-parameter gauge two-cocycle. Some remarks are given on the problem of extending the developed algebraic theory to the case of Lax integrable dynamical systems on discrete manifolds.
Symmetry properties of matrix elements of canonical SU(3) tensor operators
Authors: Biedenharn L. C. , Lohe M. A. , Williams H. T.
Published: July 2002

The symmetries of the SU(3) 3-j symbols, which are defined as symmetrized matrix elements of the canonical SU(3) tensor operators are investigated. The symmetries considered are those which in SU(2) correspond to the interchange of columns of the 3-j symbol, as well as the symmetry under conjugation. It is found that for each tensor operator in a multiplicity set the matrix elements (for a fixed operator pattern) carry a one-dimensional representation of the symmetric group S3.
Clebsch–Gordan coefficients for the quantum superalgebra Uq
(osp(1‖2))
Authors: Minnaert Pierre , Mozrzymas Marek
Published: July 2002

The structure of the finite-dimensional representations of the quantum superalgebra Uq(osp(1‖2)) is considered and the projection operator for this quantum superalgebra is derived. Application of the projection operator permits one to obtain an explicit analytical formula for the q analog of the Clebsch–Gordan coefficients. Pseudo-orthogonality relations and some other properties of Clebsch–Gordan coefficients are given.
Probabilistic computation of Poiseuille flow velocity fields
Authors: Hunt F. Y. , Douglas J. F. , Bernal J.
Published: July 2002

Velocity fields for Poiseuille flow through tubes having general cross section are calculated using a path integral method involving the first-passage times of random walks in the interior of the cross sectional domain 𝒟 of the pipe. This method is applied to a number of examples where exact results are available and to more complicated geometries of practical interest. These examples include a tube with ‘‘fractal’’ cross section and open channel flows. The calculations demonstrate the feasibility of the probabilistic method for pipe flow and other applications having an equivalent mathematical description (e.g., torsional rigidity of rods, membrane deflection). The example of flow through a fractal pipe shows an extended region of diminished flow velocity near the rough boundary which is similar to the suppressed vibration observed near the boundaries of fractal drums.
Asymptotic expansion of the Dirac–Coulomb radial Green’s function
Authors: Indelicato P. , Mohr Peter J.
Published: July 2002

An asymptotic expansion of the Whittaker function Mα,β(x), for β→∞, with α and x fixed, is employed to obtain the asymptotic expansion of the Dirac–Coulomb radial Green’s function Gκ(x2,x1,z) when the magnitude of the angular momentum quantum number κ is large. This result has application in numerical calculations of quantum electrodynamic effects in an external Coulomb field.
Generalized magnetic monopoles over contact manifolds
Authors: Itoh Mitsuhiro
Published: July 2002

A generalization of magnetic monopoles is given over an odd dimensional contact manifold and we discuss whether the Yang–Mills–Higgs functional attains at generalized monopoles the absolute minimal value, the topological invariant.
Nonexistence of global solutions of the initial-boundary value problem for the nonlinear Klein–Gordon equation
Authors: Bainov D. D. , Minchev E.
Published: July 2002

Sufficient conditions are given so that the solutions of the initial-boundary value problem for the nonlinear Klein–Gordon equation do not exist for all t≳0.
Particle motion in the gravitational field of a charged, radiating body
Authors: Koberlein Brian D. , Mallett Ronald L.
Published: July 2002

The motion of test bodies is examined in the framework of the Vaidya–Bonner model of a charged, radiating mass. The null and time-like geodesic equations are obtained exactly. Similar equations are obtained exactly for the case of charged test particles. It is demonstrated that the luminosity of the central body induces a relative motion between positive and negative test charges, leading to accretion disk temperatures for luminous bodies which are higher than those of non-radiating bodies.
Classical and quantum sl(1‖2) superalgebras, Casimir operators and quantum chain Hamiltonians
Authors: Arnaudon Daniel , Chryssomalakos Chryssomalis , Frappat Luc
Published: July 2002

We examine in this paper the two parameter deformed superalgebra 𝒰qs(sl(1‖2)) and use the results in the construction of quantum chain Hamiltonians. This study is done both in the framework of the Serre presentation and in the R-matrix scheme of Faddeev, Reshetikhin, and Takhtajan (FRT). We show that there exists an infinite number of Casimir operators, indexed by integers p≥2 in the undeformed case and by p∈Z in the deformed case, which obey quadratic relations. The construction of the dual superalgebra of functions of SLqs(1‖2) is also given and higher tensor product representations are discussed. Finally, we construct quantum chain Hamiltonians based on the Casimir operators. In the deformed case we find two Hamiltonians which describe deformed t−J models.
Symmetries of Clebsch–Gordan coefficients of the quantum group U
q(n)
Authors: Klimyk A. U.
Published: July 2002

Permutation symmetries for Clebsch–Gordan coefficients of the quantum group Uq(n) and for Uq(n−1)-reduced Clebsch–Gordan coefficients of Uq(n) are derived. In particular, the formula relating Clebsch–Gordan coefficients for the tensor product Tm1⊗Tm2 with Clebsch–Gordan coefficients for the tensor product with permuted representations Tm1 and Tm is obtained, where Tm is one of the irreducible representations in the decomposition of Tm1⊗Tm2. Contrary to the classical case, coefficients connecting these Clebsch–Gordan coefficients depend on Gel’fand–Tsetlin patterns of one of irreducible representations. This dependence is explicitly determined.
On the time decay of a wave packet in a one-dimensional finite band periodic lattice
Authors: Firsova N. E.
Published: July 2002

Nonstationary Schrödinger equation with a periodic finite band potential p(x) is considered. The Green’s function G(x,x′,t) of this equation is investigated when t→∞. Asymptotics for G(x,x′,t) are specified. It is shown that for large ‘‘velocities’’ v=(x−x′)/t the principal term in asymptotics of G(x,x′,t), t→∞ coincides with the Green’s function for p=0. The principal term in the asymptotics of G(x,x′,t) in the case v→∞ is equal to a sum of Green’s functions of unperturbed problems for particles whose masses are equal to effective masses of the Hill operator under investigation.
Classical mechanics with lapse
Authors: Schmidt Hans-Jürgen
Published: July 2002

Mechanics is developed over a differentiable manifold as space of possible positions. Time is considered to fill a one-dimensional Riemannian manifold, so having the metric as lapse. Then the system is quantized with covariant instead of partial derivatives in the Schrödinger operator.
Solvable (nonrelativistic, classical) n-body problems on the line. II
Authors: Calogero F.
Published: July 2002

A solvable n-body problem is exhibited, which features equations of motion of Newtonian type, mjẍj=Fj, j=1,...,n, with ‘‘forces’’ Fj that are linear and quadratic in the particle velocities, Fj=ẋj{∑k=1n[fjk(1)(x) +ẋkfjk(2)(x)]}, and depend highly nonlinearly on the positions xk≡xk(t), k=1,...,n, of the n ‘‘particles’’ on the line. Explicit expressions of the functions fjk(i)(x), in terms of elliptic functions, are given; they contain n+4 arbitrary constants, in addition to the n ‘‘masses’’ mk and to n arbitrary functions gk(xk). Special cases in which the elliptic functions reduce to trigonometric or rational functions are of course included. The technique whereby this model has been arrived at entails that its initial-value problem is solvable by quadratures [for any n and arbitrary initial data x(0) and ẋ(0)]. A discussion of the actual behavior of the solution, and of special cases, is postponed to future papers.
A formula for obtaining new hereditary symmetries and new integrable equations
Authors: Lu Bao Qun
Published: July 2002

In this paper we give a simple formula to obtain hereditary symmetries related to the isospectral eigenvalue problem of integrable equations. Using this formula, (i) we prove that eigenfunctions of hereditary strong symmetry are symmetries for the whole hierarchy, which improves the result of Fokas and Anderson [J. Math. Phys. 23, 1066 (1982)]; (ii) we find new integrable equations; and (iii) we give strong symmetries of these new integrable equations and various equations for eigenfunctions of the isospectral eigenvalue problems.
Projective group representations in quaternionic Hilbert space
Authors: Adler Stephen L.
Published: July 2002

We extend the discussion of projective group representations in quaternionic Hilbert space that was given in our recent book. The associativity condition for quaternionic projective representations is formulated in terms of unitary operators and then analyzed in terms of their generator structure. The multi-centrality and centrality assumptions are also analyzed in generator terms, and implications of this analysis are discussed.