bluuebunny/crossref_metadata_2025 huggingface dataset:
Molecular-dynamics simulation of structural and conformational properties of poly(propylene oxide)
Authors: Ahlström Peter , Borodin Oleg , Wahnström Göran , Wensink Erik J. W. , Carlsson Patrik , Smith Grant D.
Published: July 2002

Molecular-dynamics simulations of poly(propylene oxide) (PPO) have been performed in the temperature range 300 K⩽T⩽450 K using a newly developed atomistic force field. Chains with 1, 11 and 45 repeat units have been considered. We find excellent agreement for the short and intermediate range order as deduced from x-ray and neutron diffraction measurements with deviations (excluding quantum mechanical effects for the nuclear motion) lying within experimental uncertainties. The static structure factor S(q) shows a first sharp diffraction peak due to interchain correlations which is shifted to smaller wave vectors with increasing temperature. The molecular weight dependence of the short and intermediate range order is found to be weak and the obtained density and thermal expansivity compare favorably with experimental data. The backbone dihedral angle distributions are essentially identical for PO11 and PO45, but deviate slightly from those for PO1, and the probability for gauche conformations is quite large resulting in a small characteristic ratio. The dihedral and bond angle distributions obtained from the present MD study are more closely related to experiments than those that have been achieved previously by combining experimental data with reverse Monte Carlo modeling.
Direction of the transition dipole moment of nitrobenzene determined from oriented molecules in a uniform electric field
Authors: Castle Karen J. , Abbott James , Peng Xianzhao , Kong Wei
Published: July 2002

The direction of the transition dipole moment of nitrobenzene between 230 and 250 nm was determined by orienting gas-phase molecules in a strong, uniform electric field. Oriented nitrobenzene was photodissociated with linearly polarized light, and the NO fragments were detected by resonantly enhanced multiphoton ionization (REMPI). When the polarization direction of the photolysis laser was perpendicular (rather than parallel) to the orientation field, a 44% enhancement in the NO signal was observed. This implies a predominantly perpendicular relationship between the transition dipole and the permanent dipole. However, the experimentally observed enhancement falls below that expected of a pure perpendicular transition, indicating the presence of a second potential-energy surface that is simultaneously accessed through a parallel transition. Quantitative analysis indicates that the parallel transition contributes 20% of the overall oscillator strength.
Immiscible two-phase flow in a porous medium: Utilization of a Laplace transform boost
Authors: King Michael J.
Published: July 2002

A boost operator is defined for the Laplace transform. It is used in conjunction with the Laplace transform to solve the diffusion equation on a domain with multiple moving boundaries. This problem arises in the study of immiscible multiphase flow in a finite medium, including end effects. Extensions of this method to the solution of other linear differential equations are conceivable.
Chiral fermions in non-Riemannian Kaluza–Klein theory
Authors: Moffat J. W.
Published: July 2002

The problem of obtaining left–right asymmetry of fermion quantum numbers in Kaluza–Klein theories is studied. A non-Riemannian Kaluza–Klein geometry, based on a nonsymmetric fundamental tensor gΣΛ, is shown to lead to zero modes of the Dirac operator and can possess a nonvanishing chirality index that permits a realistic description of fermions. Some specific models of unification and their group structures are considered.
Kantowski–Sachs cosmological models as big-bang models
Authors: Weber Edmond
Published: July 2002

In the presence of a nonzero cosmological constant Λ, we classify the anisotropic cosmological models of the Kantowski–Sachs type by means of the quantities ε20, q0, ∑0 corresponding, respectively, to the relative root-mean-square deviation from isotropy, the deceleration parameter, and the density parameter of the perfect fluid at a given time t=t0. We obtain for Λ>0 a set of big-bang models of zero measure as well as a set of cosmological models of nonzero measure evolving toward the de Sitter solution.
Scattering by a spherical inhomogeneity in a fluid-saturated porous medium
Authors: Berryman James G.
Published: July 2002

A fast compressional wave incident on an inhomogeneity in a fluid-saturated porous medium will produce three scattered elastic waves: a fast compressional wave, a slow compressional wave, and a shear wave. This problem is formulated as a multipole expansion using Biot’s equations of poroelasticity. The solution for the first term (n=0) in the multipole series involves a 4×4 system which is solved analytically in the long-wavelength limit. All higher-order terms (n≥1) require the solution of a 6×6 system. A procedure for solving these equations by splitting the problem into a 4×4 system and a 2×2 system and then iterating is introduced. The first iterate is just the solution of the elastic wave scattering problem in the absence of fluid effects. Higher iterates include the successive perturbation effects of fluid/solid interaction.
Conformal quantum Yang–Mills
Authors: Haidari A. D.
Published: July 2002

Conformally covariant quantization of non-Abelian gauge theory is presented, and the invariant propagators needed for perturbative calculations are found. The vector potential acquires a richer gauge structure displayed in the larger Gupta–Bleuler triplet whose center is occupied by conformal QED. Path integral formulation and BRS invariance are shown on a formal level in one covariant gauge.
Mathematical aspects of quantum fluids. II. Nonrotating 4He and Clebsch representations of symplectic two-cocycles
Authors: Kupershmidt B. A.
Published: July 2002

For nonrotating and rotating 4He, the formulas for the Poisson brackets and their canonical representations are shown to be particular cases of general Hamiltonian maps associated to symplectic two-cocycles on semidirect product Lie algebras of the type g⨷(W⊕V*⊕V).
On the formulation of the positive-energy theorem in Kaluza–Klein theories
Authors: Moreschi Osvaldo M. , Sparling George A. J.
Published: July 2002

The positive-energy theorem is formulated in the context of Kaluza–Klein theories. Different cases are considered, including the situation in which no symmetry is assumed. This work offers a new technique for stability considerations in Kaluza–Klein theories.
Linearization of the Hamilton–Jacobi equation
Authors: Espindola Maria L. , Espindola Oslim , Teixeira Nelson L.
Published: July 2002

Through a canonoid transformation the integration for the Hamilton–Jacobi equations is transformed into a two step procedure: the first being a linear problem and the second a quasilinear one. Examples are given.
Mean power reflection from a one-dimensional nonlinear random medium
Authors: Spigler Renato
Published: July 2002

A model of wave propagation in a slab 0≤x≤L of a nonlinear random medium is considered. The index of refraction is k[1+ε̃(x,w‖uε(x,L,w)‖2)]1/2, where ε̃(x,α)=εm(x)+ε2[(n(x) +iδ(x))α+θ(x)+iγ(x)], with ε a small parameter, m,n,δ,θ,γ suitable stochastic processes, uε(x,L,w) the wave field, and w≥0 the intensity of nonlinearity. The mean reflected power is evaluated from a certain nonlinear partial differential equation satisfied by the reflection coefficient Rε(L,w). An infinite system of ordinary differential equations for the coefficients Rεn(L), n=0,1,2,..., in the expansion of Rε(L,w) in powers of w, is then derived, and the infinitesimal generator for the process [R0 R*0 R1 R*1], Rn≡R0n(ε2L), is obtained, in the diffusion limit ε→0, L→∞, ε2L=const. This allows us to compute 〈‖R‖2〉≂〈‖R0‖2〉 +2w Re〈R0 R*1〉 as a function of ε2L. In the lossless case, δ=γ=0, there is no correction due to the nonlinearity, in such a limit, and this remains true at least up to the order O(w2). Some effects can be observed when dissipation (δ>0, γ>0) is taken into account. Numerical results are obtained and plots are given.
R-mer filling with general range-R cooperative effects
Authors: Mellein B.
Published: July 2002

An exact closed form solution is obtained for the time dependence of the coverage of a homogeneous, infinite, one-dimensional lattice filled irreversibly and cooperatively by R-mers. Cooperative effects, not assumed to be reflection invariant, may extend up to range R. Previously available exact solutions for random filling and nearest neighbor cooperative effects are recovered. For dimer filling with genuine range-2 cooperative effects it is found that autoretardative and autocatalytic rate regimes may lead to the same saturation coverage. Various adsorption schemes are considered.
An inverse problem for multidimensional first-order systems
Authors: Fokas A. S.
Published: July 2002

An inverse problem associated with N first-order equations in n+1 dimensions, n>1, is considered: Given appropriate inverse data T reconstruct the potential q(x0,x), where q is an N×N off-diagonal matrix. Although q depends on n+1 variables, it turns out that T depends on 3n−1 variables. This necessitates imposing certain constraints on T, i.e., T must be suitably characterized. The characterization problem for T is solved explicitly. Furthermore, the problem of reconstructing q is reduced to one for reconstructing a 2×2 matrix potential in two dimensions. The inverse data needed for the reduced problem are obtained in closed form from T. A method for solving two-dimensional inverse problems has recently appeared in the literature.
Differential geometry in the large and compactification of higher-dimensional gravity
Authors: Muzinich I. J.
Published: July 2002

Some well-known results from differential geometry are applied to some of the major issues of compactification of higher-dimensional gravity. The results apply both to the theories generally known as Kaluza–Klein and the recently more promising super string theories. These results are primarily due to Yano [K. Yano, Integral Formulas in Differential Geometry (Marcel Dekker, New York, 1970); Differential Geometry on Complex and Almost Complex Manifolds (Macmillian, New York, 1965)] and have profound implications for the Kaluza–Klein scenario with respect to the cosmological constant problem and the massless sector of the theory. While the results are well known in the mathematical literature, the present author has only seen a fragmentary account presented by a few physicists. The necessary introduction to complex manifolds is also provided including Kähler manifolds and their possible relevance to the problem of compactification. The Ricci tensor provides the central role in the discussion of metric isometries, holomorphy, and holonomy. The incumbent role of Calabi–Yau manifolds with Ricci flat curvature and SU(n) holonomy, which have been recently conjectured in regard to super string compactification, is also mentioned.
Separation of Dirac and Kähler equations in spherically symmetric space-times
Authors: Panahi M. , Tucker R. W.
Published: July 2002

The Dirac and Kähler equations are separated in a class of spherically symmetric space-times by using new techniques of Clifford analysis. New operators, which raise and lower the ‘‘spin weight’’ of spin-weighted functions by (1)/(2), are also introduced. The separated solutions enable us to analyze the distinction between spinor solutions to the Dirac separation equation and Kähler solutions.
Symmetry breaking of u(6/2 j+1) supersymmetric models
Authors: Baake M. , Reinicke P.
Published: July 2002

In this paper, the group theory of models with broken u(6/2 j+1) supersymmetry described by the chain u(6/2 j+1)⊇uB(6)×uF(2 j+1) ⊇uB(6)×spF(2 j+1) ⊇⋅⋅⋅ ⊇soB(3)×suF(2) ⊇suB+F(2), which has recently been suggested for application to nuclear physics, is presented. All invariants that are needed for the construction of the general Hamiltonian for this model are presented.
Mathematical aspects of quantum fluids. III. Interior Clebsch representations and transformations of symplectic two-cocycles for 4He
Authors: Kupershmidt B. A.
Published: July 2002

The symplectic two-cocycle on the semidirect product Lie algebra g⨷(W⊕V*⊕V) is shown to be canonically related to the dual spaces of the Lie algebras (a) g⨷(W⊕(g⨷V)) and (b) g⨷(W⊕(g⨷V*)). This fact (a) explains the second Poisson bracket for irrotational 4He and (b) leads to a derivation of a new nonlinear Poisson bracket for rotating 4He.
The generalized atypical supertableaux of the orthosymplectic groups OSP(2‖2p)
Authors: Gourdin Michel
Published: July 2002

The classification and the interpretation of the Young supertableaux of the orthosymplectic group OSP(2‖2p) are given. A particular emphasis is made on the generalized atypical supertableaux associated to nonfully reducible atypical representations.
Special solutions of singular nonlinear Schrödinger equations with polynomial nonlinearities
Authors: Brüll L. , Kapellen H.-J.
Published: July 2002

The singular nonlinear Schrödinger equation iut =−uxx +f(‖u‖2)u+χh(‖u‖2)h′(‖u‖2)u, where f has the form f(s)=asn, n≥1, a∈R, is investigated. A classification is given of those nonlinearities f and h that allow the existence of solitary waves and kink solutions. Further, in several cases the solutions are given in explicit form.
The free energy of the three-dimensional Zamolodchikov model
Authors: Glasser M. L.
Published: July 2002

Details are given for the reduction of Baxter’s expression for the exact partition function per site of the Zamolodchikov model to explicit form.
Physical state conditions and supersymmetry breaking in quantum mechanics
Authors: Fuchs Jürgen
Published: July 2002

It is shown, by giving an explicit example, how the conditions imposed on physically admissible states can affect the pattern of supersymmetry breaking and, as a consequence, the values of physically interesting quantities such as the Witten index. As a by-product an unusual kind of explicit supersymmetry breaking is observed, where the supersymmetry algebra still holds formally, as well as a spontaneous breakdown of supersymmetry, which is not induced by instantons.
Algebraic expressions for some multiplicity-free 6j symbols and isoscalar factors for G2
Authors: Judd B. R.
Published: July 2002

Generalized 6j symbols for G2 in which all four triangular conditions involve the seven-dimensional irreducible representation (irrep) (10) are multiplicity-free. Algebraic expressions depending on the highest weights of the accompanying irreps are found by using generalizations of the Racah-Wigner algebra. A rule is given for generalizing the SO(3) phase factors. The results are applied to finding algebraic expressions for a class of isoscalar factors for SO(7)⊇G2.
Theta series and magic numbers for diamond and certain ionic crystal structures
Authors: Sloane N. J. A.
Published: July 2002

Two earlier papers by Teo and the author [J. Chem. Phys. 83, 6520 (1985); Inorg. Chem. 25, 2315 (1986)] studied circular and spherical clusters in the simplest close-packed structures in two and three dimensions. The present work considers clusters in other fundamental structures (the hexagonal net, diamond), and applies the results to study clusters in related structures (Lonsdaleite, graphite) and in binary arrays with the structure of the idealized ionic crystals NaCl, CsCl, ZnS, CaF2, TiO2, O3Bi2.
Definition and general properties of a class of non-Markovian collision processes
Authors: Moreau M. , Gaveau B.
Published: July 2002

A class of non-Markovian stochastic processes is defined; it generalizes several anterior models, and allows a trajectorial description of collisions in dense fluids when the system loses all memory at each collision. The abstract formalism is studied here: an integral evolution equation is derived, as well as an integrodifferential equation that generalizes the master equation; some asymptotic properties of these processes are established. Applications to specific models will be treated in other articles.
Any physical, monopole equation of motion structure uniquely determines a projective inertial structure and an (n−1)-force
Authors: Coleman Robert Alan , Korte Herbert
Published: July 2002

It is proved that, in the context of a conformal causal structure, (a) any acceleration field decomposes uniquely into the sum of an affine structure that is compatible with the conformal structure and an n-force, and (b) any directing field, such that the n-force of the corresponding family of acceleration fields is due to tensor fields and is orthogonal to the n-velocity, uniquely decomposes into a projective structure that is compatible with the conformal structure and an (n−1)-force. Moreover, if there are no second clock effects and variable rest masses do not exist, there exists a unique pseudo-Riemannian metric on space-time that determines the unique standard of no acceleration for all massive monopoles. It follows from this that a non-null result for the Eötvös experiment entails the existence of a fifth force rather than a violation of the universality of free fall.
Indecomposable modules of the Poincaré algebra in an energy-cyclic angular momentum basis
Authors: Lenczewski Romuald
Published: July 2002

The universal enveloping algebra 𝒰=𝒰+𝒰−ℋ of the Poincaré algebra iso(3,1) is considered. Infinite-dimensional induced modules 𝒰+(Γ) are studied. Explicit formulas are obtained for 𝒰+(Γ) in the Poincaré–Birkhoff–Witt basis. Then a change of basis is performed to an energy-cyclic angular momentum basis. For any Γ∈C2, 𝒰+(Γ) turns out to be indecomposable. It can be represented as an infinite family of interacting Verma modules of the Lorentz algebra so(3,1). Finite-dimensional modules can be obtained as quotient modules of 𝒰+(Γ) if 2Γ∈Z2.
On unitary SU(N) ordered exponentials in a strong coupling limit
Authors: Fried H. M.
Published: July 2002

A construction is given of the leading, averaged output dependence of a unitary ordered exponential in the strong coupling limit of rapidly fluctuating input. While valid for any SU(N), the method does not provide ‘‘fine structure’’ corrections to the leading output behavior. Numerical illustrations are given using a simple SU(3) example.
Schrödinger-like equation for relativistic particles
Authors: Goldberg I. B. , Pratt R. H.
Published: July 2002

The Dirac equation in a spherically symmetric screened Coulomb potential is transformed to a modified Schrödinger equation of the form d2u/dr2+k2(r)u=0. This transformation is induced by expressing the Dirac function as a linear combination of the function u and its derivative du/dr. Various properties of the transformation and of the resulting equations are studied. The close similarity between the modified Schrödinger equation and the Schrödinger equation suggests that methods applied to the Schrödinger equation to derive nonrelativistic relations can be applied to the modified Schrödinger equation to derive the analogous relativistic relations. As an example, this approach is applied to the single channel quantum defect theory to give a new derivation of its relativistic form.
Nonlinear resonance for quasilinear hyperbolic equation
Authors: Liu Tai-Ping
Published: July 2002

The purpose of this paper is to study the wave behavior of hyperbolic conservation laws with a moving source. Resonance occurs when the speed of the source is too close to one of the characteristic speeds of the system. For the nonlinear system characteristic speeds depend on the basic dependence variables and resonance gives rise to nonlinear interactions which lead to rich wave phenomena. Motivated by physical examples a scalar model is proposed and analyzed to describe the qualitative behavior of waves for a general system in resonance with the source. Analytical understanding is used to design a numerical scheme based on the random choice method. An important physical example is transonic gas flow through a nozzle. This analysis provides a transparent and revealing qualitative understanding of wave behavior of gas flow, including such phenomena as nonlinear stability, instability, and changing types of waves.
Wiener analysis of a binary hysteresis system
Authors: Nakayama J. , Omori E.
Published: July 2002

Nonlinear transformation of an independent Gaussian sequence by a binary hysteresis is studied by Wiener’s method [Nonlinear Problems in Random Theory (MIT, Cambrige, MA, 1958)]. The output sequence of the hysteresis is represented by a series of Wiener–Hermite functionals, which are random and orthogonal (uncorrelated) to each other. From the hysteresis equation, a set of linear equations for the Wiener–Hermite functionals is derived without approximation. The equations directly show that the hysteresis is decomposed into equivalent subsystems consisting of static nonlinear elements, multipliers, adders, and linear filters. They are solved by use of random numbers generated in a computer in order to get a sample output sequence approximated by a finite sum of the Wiener–Hermite functionals. Another set of equations is derived for the mean-square values of the Wiener–Hermite functionals. In terms of its numerical solutions, the convergence property of the Wiener–Hermite functional series is discussed.
The existence of quantum fields for local nets of algebras of observables
Authors: Wollenberg Manfred
Published: July 2002

A necessary and sufficient criterion for the existence of quantum fields related to a given local net of algebras of observables is proved. This criterion is written in terms of the ‘‘conjugation operators’’ S𝒪 of the local algebras 𝒜(𝒪). It shows that the modular structure of the local algebras essentially determines the corresponding quantum field theory. In the case where the local net of algebras is conformally covariant the criterion gives the result that the existence of quantum fields depends only on the representation of the conformal group and does not depend on the concrete form of the algebras. For the proof of the criterion the fact that a quantum field related to a local net of algebras can be essentially characterized by one vector is used.
Partial waves for the linearized Yang–Mills equation about a monopole background
Authors: Majid Shahn
Published: July 2002

The properties of the monopole-vector spherical harmonics that are needed to transform covariant differential equations on charged vector fields in the presence of a monopole into purely radial ones are computed. This further extends the work of Wu and Yang [Nucl. Phys. B 107, 365 (1976)]. As an application, the complete set of partial waves of SU(2) Yang–Mills fluctuations about the U(1) monopole configuration are explicitly computed. They are generated from the scalar solutions to the covariant Laplacian by the covariant operators D and r×D, in analogy with the uncharged case.
The integral theorem for supersymmetric invariants
Authors: Constantinescu F. , de Groote H. F.
Published: July 2002

A supersymmetric integral theorem that extends results of Parisi, Sourlas, Efetov, Wegner, and others is rigorously proved. In particular, arbitrary generators are allowed in the integrand (instead of canonical ones) and the invariance condition is very much relaxed. The connection with Cauchy’s integral formula is made transparent. In passing, the unitary Lie supergroup is studied by using elementary methods. Applications in the theory of disordered systems are discussed.
A new derivation of the quadrupole formula for angular momentum
Authors: Nahmad-Achar E.
Published: July 2002

A new derivation of the farfield quadrupole formula for radiated angular momentum is presented, based on the gravitational Noether operator. Those metrics for which the angular momentum flux is well defined are characterized, and it is shown that this is free of the supertranslation ambiguity in the Newtonian approximation.
Extended gauge theories
Authors: Aldrovandi R.
Published: July 2002

A scheme inspired in Lie algebra extensions is introduced that enlarges gauge models to allow some coupling between space-time and gauge space. Everything may be written in terms of a generalized covariant derivative including usual differential plus purely algebraic terms. A noncovariant vacuum appears, introducing a natural symmetry breaking, but currents satisfy conservation laws alike those found in gauge theories.
Gauge transformations and fiber bundle theory
Authors: Socolovsky M.
Published: July 2002

The relationship between the group Γ of pure gauge transformations of Atiyah, Hitchin, and Singer [Proc. R. Soc. London Ser. A 362, 425 (1978)] of a principal fiber bundle and the group 𝒢 of gauge transformations consisting of the direct product of the local gauge groups on the base space is studied. Γ is an invariant subgroup of 𝒢 and the quotient 𝒢/Γ is identified with the group of inequivalent gauge transformations. In the framework of the category of principal fiber bundles with connections, a natural explanation for the relevance of the group Γ in the classical and quantum theories of gauge fields is presented. The paper is made self-contained by an introductory discussion of the concepts of principal coordinate fiber bundle (gauge fixed principal fiber bundle) and principal fiber bundle, and of the equivalence between the three different versions of the group of vertical automorphisms of the bundle.
The effective field approximation for Ising spin glasses on simply connected lattices
Authors: Zhang Guihua , Percus J. K.
Published: July 2002

A spin glass on a one-dimensional Ising lattice is considered. The entropy at fixed nonuniform bond and field energies is written down as a functional of singlet and pair spin expectations, in terms of which bond and field energies are then expressed. The solution is reformulated in terms of effective fields which, in a spin-glass ensemble, are distributed as in a Markov chain. This result, and the corresponding free energy, shows that the effective field approximation previously used is exact for such systems, an assertion which extends to Cayley trees.
Variation-iteration solution of the classical trajectory boundary value problem
Authors: Tikochinsky Y.
Published: July 2002

The general method of Gerjuoy, Rau, and Spruch [Rev. Mod. Phys. 55, 725 (1983)] for constructing variational principles is applied to the classical trajectory two-end point problem. A variational approximation to the trajectory is obtained as an initial value problem, suitable for numerical (and analytical) calculations. Iterations of the procedure converge rapidly to yield an accurate numerical trajectory. In cases where more than one trajectory passes through the given end points, the method can be used to discover these trajectories while other methods may fail. For the special case of potentials bilinear in the coordinates, a single iteration suffices to obtain the exact path.
Symmetric frames on Lorentzian spaces
Authors: Coll Bartolomé , Morales Juan Antonio
Published: July 2002

Symmetric frames (those whose vectors are metrically indistinguishable) are studied both, from the algebraic and differential points of view. Symmetric frames which, in addition, remain indistinguishable for a given set of concomitants of the metric are analyzed, and the necessary and sufficient conditions for a space-time to admit them are given. A new version of the cosmological principle then follows. Natural symmetric frames (induced by local charts) are also considered, and the space-times admitting them are obtained.
Transformations of some induced osp(3/2) modules in an so(3)⊕sp(2) basis
Authors: Ky Nguyen Anh , Palev Tchavdar D.
Published: July 2002

The modules of the orthosymplectic Lie superalgebra osp(3/2), induced from finite-dimensional irreducible submodules of the stability subalgebra so(3)⊕gl(1) are investigated. The corresponding infinite-dimensional irreducible or indecomposable modules, the Kac modules, and the related typical and atypical modules are studied in detail. Every such module is decomposed into a direct sum of either indecomposable or irreducible modules of the even subalgebra so(3)⊕sp(2). For each of these (infinite-dimensional or finite-dimensional, irreducible or indecomposable) modules relations are written down, giving the transformations of the basis under the action of the algebra generators.
Variational density of electrons for large closed shell atoms
Authors: Ullah Nazakat
Published: July 2002

An exact expression for the atomic form factor for closed shell atoms is derived using an antisymmetric multielectron wave function. It is shown that for large atoms it can be written as an integral over a Bessel function. Using the Hankel transform it gives an expression for the density of electrons which is of Thomas–Fermi form which was found earlier by Pucci and March.
The induction coefficients of the Hecke algebra and the Clebsch–Gordan coefficients of the quantum group SUq(N). II. General Gel’fand basis
Authors: Pan Feng , Chen Jin-Quan
Published: July 2002

The Clebsch–Gordan coefficients for the general Gel’fand basis of the quantum group SUq(N) are calculated from the induction coefficients of the Hecke algebra Hf(q) by the linear equation method. The advantage of this method is that the calculation of the SUq(N) Clebsch–Gordan coefficients is rank independent. The SUq(N) Clebsch–Gordan coefficients for the resulting irreps [f1,f2,f3] with f1+f2+f3≤4 are tabulated.
Generalization of the Szekeres results on perfect fluids with uΛkΛl=0 to uΛkΛl ≠ 0; Bianchi identities
Authors: García Alberto
Published: July 2002

The Szekeres results concerning the shear and ray curvature properties of the congruences of eigenvectors of the conformal curvature tensor with a perfect fluid source are generalized. The fluid vector u is assumed to be outside of the two-space spanned by two eigenvectors k and l of the Weyl tensor; uΛkΛl≠0. The full Bianchi identities, referred to a preferred null tetrad basis with k and l being the real null vectors, are analyzed in detail. Particular attention is paid to the Bianchi identities for algebraically special gravitational fields. An extension of the Wainwright results for type D fields is given. The Szekeres results with uΛkΛl=0 are derived as limiting transitions. The main conclusion of this work can be summarized by the statement: The shear and refraction properties of a repeated eigendirection of the Weyl tensor of algebraically special gravitational fields are determined completely by the energy density gradient, the rotation, and shear of the fluid.
Lie algebras for the Dirac–Clifford ring
Authors: Mignaco Juan Alberto , Linhares Cesar Augusto
Published: July 2002

It is shown in general that the Dirac–Clifford ring formed by the Dirac matrices and all their products, for all even and odd space–time dimensions D, span the commutation algebras su(2D/2) for even D and su(2(D−1)/2)⊕su(2(D−1)/2) for odd D. Some physical consequences of these results are discussed herein.
A new completely integrable Liouville’s system produced by the Kaup–Newell eigenvalue problem
Authors: Qiao Zhijun
Published: July 2002

Under the constraint between the potentials and eigenfunctions, the Kaup–Newell eigenvalue problem is nonlinearized as a new completely integrable Hamiltonian system (R2N,dpΛdq,H): H=i〈Λ2p,q〉+1/2〈Λq,q〉〈Λp,p〉. Furthermore, the involutive solution of the high-order Kaup–Newell equation is obtained. Specifically, the involutive solution of the well-known derivative Schrödinger equation ut=1/2iuxx+1/2(u‖u‖2)x is developed.
Bargmann- and Calogero-type bounds for the Dirac equation
Authors: Martin A. , Stubbe J.
Published: July 2002

The Dirac equation for a particle of mass m submitted to a spherically symmetric vector potential is considered. Similar to the Schrödinger case, a nodal characterization of solutions for energies in the spectral gap (−m,m) is shown. As a consequence some bounds on the number of bound states which reduce in the nonrelativistic limit to the classical bounds of Bargmann and Calogero are proven.
The spectrum of radial adiabatic stellar oscillations
Authors: Beyer Horst R.
Published: July 2002

The stability analysis with respect to ‘‘small’’ radial adiabatic perturbations of spherically symmetric stellar equilibrium models which are polytropic with a constant adiabatic index only near the center and the boundary of the star leads to the consideration of a class of singular minimal Sturm–Liouville operators. It is shown that the physical boundary conditions choose in a unique way the corresponding Friedrichs extensions. Moreover, all linear self-adjoint extensions of the members of the class are determined and are shown to have a purely discrete spectrum.
Bi-Hamiltonian formulation for the Korteweg–de Vries hierarchy with sources
Authors: Bl/aszak Maciej
Published: July 2002

The first Hamiltonian structure is constructed for the Korteweg–de Vries (KdV) hierarchy with sources and for the respective modified systems. Applying the appropriate Miura map the second Hamiltonian structure for the KdV hierarchy with sources is derived. Stationary projection of considered system gives so-called restricted flows of the KdV hierarchy as well as its bi-Hamiltonian structure.
Tau-function formalism for supersymmetric KP hierarchies
Authors: Martínez Alonso Luis , Medina Reus Elena
Published: July 2002

We consider the Manin–Radul and Jacobian supersymmetric KP hierarchies from the point of view of the tau-function formalism. Solutions of their associated systems of Sato equations are characterized in terms of correlation functions of supersymmetric vertex operators of superghost type. The expression of the wave functions of these hierarchies in terms of tau-functions is obtained and the corresponding bilinear identities are established. Explicit methods for generating soliton and rational solutions are given.
Recursive recovery of a family of Markov transition probabilities from boundary value data
Authors: Patch S. K.
Published: July 2002

Recent developments in optical imaging inspired the model of photon transport discussed below. (Infrared radiation is used to image relatively soft and homogeneous tissue.) The difficulty of solving Maxwell’s equations, or even linear transport equations, led to this ‘‘diffuse tomographic’’ model. A recursive scheme for solving the two-dimensional problem is sketched and the first recursive step is detailed.
Operator formalism on the Z
n symmetric algebraic curves
Authors: Ferrari F. , Sobczyk J. , Urbanik W.
Published: July 2002

On Zn symmetric algebraic curves of any genus the Hilbert space of analytic free fields with integer spin is constructed. As an application, an operator formalism for the b–c systems is developed. The physical states are expressed in terms of creation and annihilation operators as in the complex plane and the correlation functions are evaluated exploiting simple normal ordering rules. The formalism is very suitable for performing explicit calculations on Riemann surfaces and, moreover, it gives some insight into the nature of two-dimensional field theories on a manifold. It is proven, in fact, that the b–c systems on a Zn symmetric algebraic curve are equivalent to a conformal field theory on the complex plane having as primary operators twist fields and free ghosts. Some consequences of the interplay between topology and statistics are also discussed.
Solutions of A∞ Toda equations based on noncompact group SU(1,1) and infinite-dimensional Grassmann manifolds
Authors: Fujii Kazuyuki
Published: July 2002

Special solutions of A∞ Toda equations are constructed based on noncompact group SU(1,1). These solutions are derived from the holomorphic construction of infinite-dimensional nonlinear Grassmann σ models. It is also shown that the solutions give a family of solutions of self-dual Einstein equations in a certain continuum limit.
Determination of the permittivity and conductivity in R3 using wave splitting of Maxwell’s equations
Authors: He Sailing , Weston Vaughan H.
Published: July 2002

Time domain wave-splitting of Maxwell’s equations is applied to the inverse problem of determining the permittivity and conductivity in three dimensions (where the reflected field is produced by an impulse dipole, exterior to the scattering medium). The structure of the fundamental solution is analyzed, and the transport equation is used to derive a condition for the reconstruction. A numerical scheme to reconstruct the permittivity and conductivity simultaneously is given, using the tangential reflection fields due to a dipole with a fixed position and orientation.
Quantum Heisenberg group and algebra: Contraction, left and right regular representations
Authors: Ellinas Demosthenes , Sobczyk Jan
Published: July 2002

It is shown that the quantum Heisenberg group Hq(1) can be obtained by means of contraction from the quantum SUq(2) group. Its dual Hopf algebra is the quantum Heisenberg algebra Uq(h(1)). Left and right regular representations for Uq(h(1)) as acting on its dual Hq(1) are derived. By imposing conditions on the right representation, the left representation is reduced to an irreducible holomorphic representation with an associated quantum coherent state. By duality, left and right regular representations for quantum Heisenberg group, with the quantum Heisenberg algebra as a representation module are also constructed. As before, the reduction of left representations leads to finite-dimensional irreducible ones for which the intertwining operator is also investigated.
Symmetries of the stationary Einstein–Maxwell-dilaton–axion system
Authors: Gal’tsov Dmitri , García Alberto , Kechkin Oleg
Published: July 2002

Sigma-model representation is derived for the stationary four-dimensional Einstein–Maxwell-dilaton–axion system arising in the low-energy limit of the heterotic string theory. Killing equations for the corresponding target space metric are solved and a closed ten-parameter algebra of isometrics is described. Finite symmetry transformations are obtained by a direct integration from infinitesimal ones. They include Ehlers–Harrison-type transformations involving dilaton and axion fields, as well as the dilaton–axion SL(2,R) duality. The solution generating technique is used to construct dilaton black holes and a stringy Kerr dyon solution starting from vacuum Schwarzschild and Kerr metrics.
Lie bialgebra contractions and quantum deformations of quasi-orthogonal algebras
Authors: Ballesteros A. , Gromov N. A. , Herranz F. J. , del Olmo M. A. , Santander M.
Published: July 2002

Lie bialgebra contractions are introduced and classified. A non-degenerate coboundary bialgebra structure is implemented into all pseudo-orthogonal real algebras so(p,q) starting from the one corresponding to so(N+1). It allows us to introduce a set of Lie bialgebra contractions which leads to Lie bialgebras of quasi-orthogonal algebras. This construction is explicitly given for N=2,3,4. All Lie bialgebra contractions studied in this paper define Hopf algebra contractions for the Drinfel’d–Jimbo deformations Uzso(p,q). They are explicitly used to generate new non-semisimple quantum algebras as it is the case for the Euclidean, Poincaré, and Galilean algebras.
Quantum random walk for U
q(su(2)) and a new example of quantum noise
Authors: Lenczewski Romuald
Published: July 2002

We derive the quantum version of the central limit theorem for sample sums of q-independent q-identically distributed quantum variables for q∈R+−{1}. In particular, we consider Uq(su(2)), for which we obtain in the limit a state Ψ on the algebra generated by q-commuting q-oscillators indexed by pairs of real numbers (r,s), where 0≤r<s, giving a new example of non-additive quantum noise.
Comments on a recent paper by S. Adler on projective group representations in quaternionic Hilbert spaces
Authors: Emch Gérard G.
Published: July 2002

A version of Schur’s lemma is proven that elucidates some issues raised by that paper.
Aharonov–Bohm scattering: The role of the incident wave
Authors: Sakoda Seiji , Omote Minoru
Published: July 2002

The scattering problem under the influence of the Aharonov–Bohm (AB) potential is reconsidered. By solving the Lippmann–Schwinger (LS) equation we obtain the wave function of the scattering state in this system. In spite of working with a plane wave as an incident wave we obtain the same wave function as was given by Aharonov and Bohm. Another method to solve the scattering problem is given by making use of a modified version of Gordon’s idea, which was invented to consider the scattering by the Coulomb potential. These two methods give the same result, which guarantees the validity of taking an incident plane wave as usual to make an analysis of this scattering problem. The scattering problem by a solenoid of finite radius is also discussed, and we find that the vector potential of the solenoid affects the charged particles, even when the magnitude of the flux is an odd integer as well as a noninteger. It is shown that the unitarity of the S matrix holds provided that a plane wave is taken to be an incident one.
Spectral theory of thermal relaxation
Authors: Jakšić Vojkan , Pillet Claude-Alain
Published: July 2002

We review some results obtained in a recent series of papers on thermal relaxation in classical and quantum dissipative systems. We consider models where a small system ℐ, with a finite number of degrees of freedom, interacts with a large environment ℛ in thermal equilibrium at positive temperature T. The zeroth law of thermodynamics postulates that, independently of its initial configuration, the system ℐ approaches a unique stationary state as t→∞. By definition, this limiting state is the equilibrium state of ℐ at temperature T. Statistical mechanics further identifies this state with the Gibbs canonical ensemble associated with ℐ. For simple models we prove that the above picture is correct, provided the equilibrium state of the environment ℛ is itself given by its canonical ensemble. In the quantum case we also obtain an exact formula for the thermal relaxation time.
Time-reversal symmetry breaking and the field theory of quantum chaos
Authors: Simons B. D. , Agam O. , Andreev A. V.
Published: July 2002

Recent studies have shown that the quantum statistical properties of systems which are chaotic in their classical limit can be expressed in terms of an effective field theory. Within this description, spectral properties are determined by low energy relaxation modes of the classical evolution operator. It is in the interaction of these modes that quantum interference effects are encoded. In this paper we review this general approach and discuss how the theory is modified to account for time-reversal symmetry breaking. To keep our discussion general, we will also briefly describe how the theory is modified by the presence of an additional discrete symmetry such as inversion. Throughout, parallels are drawn between quantum chaotic systems and the properties of weakly disordered conductors.
Global effects due to a chiral cone
Authors: Bezerra Valdir B.
Published: July 2002

Scalar and spinor quantum particles are considered in the background space–time generated by a chiral cosmic string. It is shown that in this chiral conical space–time, the wave functions, the energy spectra, and the scattering amplitude associated with a quantum scalar particle depend on the global features of this space–time. In the case of a spinor particle, we study this dependence on the wave functions, energy, and current. These dependences represent gravitational analogues of the well-known Aharonov–Bohm effect in electrodynamics. Using the Hamilton–Jacobi equations, we also look into the motion of light rays and show how the effective potential depends on the global features of the chiral conical space–time.
The status of diffeomorphism superselection in Euclidean 2+1 gravity
Authors: Marolf Donald , Mourão José , Thiemann Thomas
Published: July 2002

This work addresses a specific technical question of relevance to canonical quantization of gravity using the so-called new variables and loop-based techniques of Ashtekar, Rovelli, and Smolin. In particular, certain “superselection laws” that arise in current applications of these techniques to solving the diffeomorphism constraint are considered. Their status is elucidated by studying an analogous system: 2+1 Euclidean gravity. For that system, these superselection laws are shown to be spurious. This, however, is only a technical difficulty. The usual quantum theory may still be obtained from a loop representation and the technique known as “Refined Algebraic Quantization.”
The geometry of self-dual two-forms
Authors: Bilge Ayşe Hümeyra , Dereli Tekin , Koçak Şahin
Published: July 2002

We show that self-dual two-forms in 2n-dimensional spaces determine a n2−n+1-dimensional manifold 𝒮2n and the dimension of the maximal linear subspaces of 𝒮2n is equal to the (Radon–Hurwitz) number of linearly independent vector fields on the sphere S2n−1. We provide a direct proof that for n odd 𝒮2n has only one-dimensional linear submanifolds. We exhibit 2c−1-dimensional subspaces in dimensions which are multiples of 2c, for c=1,2,3. In particular, we demonstrate that the seven-dimensional linear subspaces of 𝒮8 also include among many other interesting classes of self-dual two-forms, the self-dual two-forms of Corrigan, Devchand, Fairlie, and Nuyts [Nucl. Phys. B 214, 452 (1983)] and a representation of 𝒞l7 given by octonionic multiplication. We discuss the relation of the linear subspaces with the representations of Clifford algebras.
Green’s matrix from Jacobi-matrix Hamiltonian
Authors: Kónya B. , Lévai G. , Papp Z.
Published: July 2002

We propose two ways for determining the Green’s matrix for problems admitting Hamiltonians that have infinite symmetric tridiagonal (i.e., Jacobi) matrix form on some basis representation. In addition to the recurrence relation coming from the Jacobi-matrix, the first approach also requires the matrix elements of the Green’s operator between the first elements of the basis. In the second approach the recurrence relation is solved directly by continued fractions and the solution is continued analytically to the whole complex plane. Both approaches are illustrated with the non-trivial but calculable example of the D-dimensional Coulomb Green’s matrix. We give the corresponding formulas for the D-dimensional harmonic oscillator as well.
Fermion doubling on a lattice and topological aspects of chiral anomaly
Authors: Goswami G. , Bandyopadhyay P.
Published: July 2002

The problem of fermion doubling on a lattice has been discussed here from the specific geometrical properties of a lattice structure and topological aspects of chiral anomaly. It is argued that there cannot be chiral anomaly on a lattice and as such there cannot be any conserved charge. This unveils the root cause of fermion doubling, and the unwanted fermions just reflect the geometrical properties of a lattice and may be viewed as to represent the “fictitious” chiral spinors associated with the lattice structure which make chiral fermions anomaly free.
A natural basis for spinor and vector fields on the noncommutative sphere
Authors: Gratus J.
Published: July 2002

The product of two Heisenberg–Weil algebras contains the Jordan–Schwinger representation of su(2). This algebra is quotiented by the square-root of the Casimir to produce a nonassociative algebra denoted by Ψ. This algebra may be viewed as the right-module over one of its associative subalgebras which corresponds to the algebra of scalar fields on the noncommutative sphere. It is now possible to interpret other subspaces as the space of spinor or vector fields on the noncommutative sphere. A natural basis of Ψ is given which may be interpreted as the deformed entries in the rotation matrices of SU(2).