bluuebunny/crossref_metadata_2025 huggingface dataset:
CASSCF and MRCI studies on the electronic excited states of CHBrO, CClBrO, and CBr2O
Authors: Li Yumin , Francisco Joseph S.
Published: July 2002

The potential energy curves for the low-lying excited states of CHBrO, CClBrO, and CBr2O have been computed using the complete active space self-consistent field (CASSCF) method. The vertical excitation energies for the excited states were calculated using the multireference internally contracted configuration interaction (MRCI) method with the cc-pVTZ and cc-pVTZ+spdf diffuse functions basis sets. The vertical excitation energies were also calculated with an ECP basis set. Results show that the first excited states for CHBrO, CClBrO, and CBr2O are slightly bound in the CX (X=H, Cl, and Br) coordinates. However, the first excited state exhibits predissociation (to ground state products) as a result of curve-crossing. Dissociation of CHBrO should result in Br atoms and HCO radicals, while in CClBrO, there are two competing channels for dissociation, namely, Cl+Br+CO and Br+ClCO. In CBr2O, photodissociation is predicted to result in the production of 2Br+CO.
Spin–orbit branching in the photodissociation of HF and DF. II. A time-dependent wave packet study of vibrationally mediated photodissociation
Authors: Brown Alex , Balint-Kurti Gabriel G.
Published: July 2002

The vibrationally mediated photodissociation dynamics of HF and DF, following A 1Π←X 1Σ+ electronic excitation, are examined using time-dependent wave packet techniques. Predictions of the branching fraction for the formation of excited state fluorine, F(2P1/2), are made for a wide range of excitation energies and for the initial vibrational states v=1, 2, and 3. The preceding article (Ref. 33) discusses the underlying theory and presents results for photodissociation from the ground vibrational state (v=0). The calculated branching fraction for HF photodissociation from the v=3 vibrational state agrees well with the value of 0.42±0.03 measured experimentally at 193.3 nm by Zhang et al. [J. Chem. Phys. 104, 7027 (1996)]. The results are discussed in context with the corresponding results for HCl and DCl.
Application of the adjacency matrix eigenvectors method to geometry determination of toroidal carbon molecules
Authors: Graovac Ante , Plavšić Dejan , Kaufman Matjaž , Pisanski Tomaž , Kirby Edward C.
Published: July 2002

Torusenes are defined as closed toroidal networks where every vertex or atom is 3-valent, and they can represent pure carbon tori. Here we study the geometries of two classes: hexagonal torusenes containing purely polyhex networks and the second class, 5,6,7-ring torusenes which besides hexagons contain also an equal number of 5- and 7-membered rings. As sophisticated quantum-mechanical methods for geometry determination are time consuming for large carbon cages, and having in mind the huge number of their isomers, one is interested in methods which are simple to apply but which are still able to produce plausible geometries. One of them is offered by the adjacency matrix elgenvectors (AME) method, which was proposed in this journal [D. E. Manolopoulos and P. W. Fowler, J. Chem. Phys. 96, 7603 (1992)]. The application of the AME method to fullerenes is based on an appropriately chosen triplet of eigenvectors. A rational choice may be made on the basis of their nodal properties. No rules have been formulated up to now on how to apply the AME method to torusenes. In order to find such a rule a systematic study of nodal properties of torusenes is crucial, and such a study is the subject of this paper. Theoretical and computer experimental considerations presented here suggest that a triplet a2,a3,aopt fulfills the task where the aopt should be checked for among those eigenvectors which possess no radial nodal plane but have one axial cut. In the present paper these findings have been elaborated for 5,6,7-ring torusenes with up to 270 atoms, and computer experiments have shown that similar findings hold for purely polyhex torusenes with up to 224 carbon atoms as well. In order to understand better these nodal properties, a quantum-mechanical study of free electrons on the surface of a torus was also undertaken.
Orientational phase transition of solid
ortho
-hydrogen
Authors: Fujii Ktsuhiko , Ohe Takashi , Nakamura Hiroaki
Published: July 2002

From the orientational dependence of the quadrupole energies, it is assumed that hydrogen molecules can take only four orientations characterized by the symmetry axis pointing to the [111] direction in the face-centered cubic lattice. It is shown that solid ortho-hydrogen undergoes the first-order phase transition for the molecular orientations. The transition temperature is derived in the mean-field approximation, and reexamined by means of the computer simulation. The intensity of x-ray diffuse scattering caused by orientational disorder shows an anomalous behavior at the transition temperature.
Internal structure of fermions
Authors: Bugajska Krystyna
Published: July 2002

We investigate the equations Pψ=kψ+h with the range of ψ contained in an appropriate Clifford algebra. Next we define, on the bundle ΨM of the minimal left ideals of the Clifford algebra, the unique connection ∇̃ which produces the Christoffel connection ∇ on M. To unify the whole picture we have to introduce an additional degree of freedom α which numerates the set of global fields of mutually annihilating primitive idempotents on M. Now the geometrical ‘‘duality’ of the spinor fields given by the primary as well as by the composed character of the sections of ΨM implies the existence of some internal gauge interaction Bμ which changes α. The generators of the holonomy group of ∇ that do not belong to the Crumeyrolle algebra are responsible for this internal interaction.
Symmetry chains and adaptation coefficients
Authors: Fritzer Harald P. , Gruber Bruno
Published: July 2002

Given a symmetry chain of physical significance it becomes necessary to obtain states which transform properly with respect to the symmetries of the chain. In this article we describe a method which permits us to calculate symmetry-adapted quantum states with relative ease. The coefficients for the symmetry-adapted linear combinations are obtained, in numerical form, in terms of the original states of the system and can thus be represented in the form of numerical tables. In addition, one also obtains automatically the matrix elements for the operators of the symmetry groups which are involved, and thus for any physical operator which can be expressed either as an element of the algebra or of the enveloping algebra. The method is well suited for computers once the physically relevant symmetry chain, or chains, have been defined. While the method to be described is generally applicable to any physical system for which semisimple Lie algebras play a role we choose here a familiar example in order to illustrate the method and to illuminate its simplicity. We choose the nuclear shell model for the case of two nucleons with orbital angular momentum l=1. While the states of the entire shell transform like the smallest spin representation of SO(25) we restrict our attention to its subgroup SU(6)×SU(2)T. We determine the symmetry chains which lead to total angular momentum SU(2)J and obtain the symmetry-adapted states for these chains.
On the infrared singularity of the resolvent of some Yang–Mills-type operators
Authors: Jensen Arne , Krüger Wolfgang
Published: July 2002

For operators of Yang–Mills type H=∑4j=1[−i(∂/∂xj)⊗1 +Aj(x)]2+W(x) in L2(R4)⊗𝒱 the infrared singularity of the resolvent (H−ζ)−1 is described completely in terms of asymptotic expansions as ζ→0. Aj(x) and W(x) are required to satisfy Aj(x)=O(‖x‖−2−δ), W(x) =O(‖x‖−2−δ), as ‖x‖→∞, δ>0.
On the body of supermanifolds
Authors: Catenacci Roberto , Reina Cesare , Teofilatto Paolo
Published: July 2002

The problem of constructing the body of a G∞ manifold is considered. It is shown that any such manifold is foliated, and the body is defined to be the space of the leaves of this foliation. Under certain regularity conditions on the foliation, the body is a smooth finite-dimensional real manifold.
Two-mode para-Bose coherent states
Authors: Saxena G. M. , Mehta C. L.
Published: July 2002

The construction of eigenstates of the square of annihilation operators for a two-mode para-Bose system is reported. Bose coherent states can be deduced from these eigenstates as a special case. These states are termed para-Bose coherent states. These states are degenerate. The expansion of the coherent states in terms of two-mode para-Bose energy eigenstates has been obtained and their salient properties are discussed. Also discussed is the uncertainty product of the square of position and momentum operators in the para-Bose coherent states for a two-mode system.
Character constraints on duality
Authors: Sullivan John J.
Published: July 2002

Duality identifies recoupling coefficients and isoscalar factors of the unitary groups with matrix elements of double coset representatives of the symmetric groups. When the double coset factorization is with respect to the same subgroup chain the matrix is that of the ordinary irreducible representation in a basis symmetry adapted to the subgroup chain. The invariant character of the symmetric group element then acts as a constraint on the magnitude, phase, and multiplicity resolution for diagonal elements. An algorithm for determining the content of this constraint is given and is shown to be consistent with a phase convention proposed previously.
First integrals for the modified Emden equation q̈+α(t) q̇+q
n =0
Authors: Leach P. G. L.
Published: July 2002

It is shown that the modified Emden equation q̈+α(t)q̇+qn=0 possesses first integrals for functions α(t) other than kt−1. The function α(t) is obtained explicitly in the case n=3 and parametrically for other n(≠2). The case n=2 is seen to be particularly difficult to solve.
On the algebras of local observables in the generalized sense in quantum mechanics
Authors: Wan K. Kong , McLean R. G. D.
Published: July 2002

The notion of observables localized with respect to a general spectral measure is introduced as a generalization of the localization with respect to the spectral measure of the position observable. The physical features of these observables are discussed and certain of their algebraic and lattice theoretic properties are presented.
Not necessary but sufficient condition for the positivity of generalized Wigner functions
Authors: Mourgues G. , Feix M. R. , Andrieux J. C. , Bertrand P.
Published: July 2002

Many authors, both in quantum mechanics and signal theory, are concerned with a condition of positivity for the generalized Wigner functions. They give (and use) as necessary and sufficient the condition that the kernel be the characteristic function of another Wigner function. It is shown that the condition is not necessary, but only sufficient.
The quantum normal form and its equivalents
Authors: Ali M. K.
Published: July 2002

A quantum analog, called the quantum normal form, of the classical Birkhoff–Gustavson normal form is presented. The algebraic relationship between the quantum and Birkhoff–Gustavson normal forms has been established by developing the latter using Lie transforms. It is shown that the Birkhoff–Gustavson normal form can be obtained from the quantum normal form. Using an anharmonic oscillator and a Henon–Heiles system as test cases, the equivalence between the quantum normal form and the Rayleigh–Schrödinger perturbation method is shown. This equivalence provides an algebraic connection between the Birkhoff–Gustavson normal form and the Rayleigh–Schrödinger perturbation approach. The question of Weyl and torus quantizations of the Birkhoff–Gustavson normal form is discussed in the light of the quantum normal form.
Remarks concerning functional integration on compact spaces
Authors: Patrascioiu Adrian , Richard Jean-Louis
Published: July 2002

Certain technical subleties regarding the Feynman–Kac representation of the propagator for motion on compact spaces are discussed. A method of evaluation of the corresponding path integral is given. It produces the correct spectrum for the Hamiltonian, while the ordinary semiclassical method fails.
Bound states of N particles: A variational approach
Authors: Perez J. Fernando , Malta C. P. , Coutinho F. A. B.
Published: July 2002

Using a variational technique we provide sufficient conditions for the existence of a bound state in a system of N particles in one, two, and three dimensions. Our assumptions imply two bound clusters’ thresholds.
Static relativistic perfect fluids with spherical, plane, or hyperbolic symmetry
Authors: Collins C. B.
Published: July 2002

This article examines the Einstein field of equations of general relativity, when the source of the gravitational field is a perfect fluid, and the geometry is static and possesses spherical, plane, or hyperbolic symmetry. This examination unifies, extends, and amends some earlier works. It is shown that a previous qualitative treatment of static spherically symmetric perfect fluids that obey a γ-law equation of state can be extended to include the cases of plane and hyperbolic symmetry. In the case of plane symmetry, the exact solution is provided for general values of γ. This indicates defects in an earlier prescription that was given for a general equation of state.
Statistical theory of scattering and propagation through a rough boundary–The Bethe–Salpeter equation and applications
Authors: Furutsu K.
Published: July 2002

A systematic theory is given for a general class of scalar waves by introducing a surface Green’s function, which is a 2×2 matrix function governed by boundary equations, transferred onto two reference boundary planes enclosing the real boundary inside. It is subjected to several symmetries, including a relation eventually leading to optical relations. Governing equations of statistical surface Green’s functions of first and second orders are obtained unperturbatively in exactly the same way as for a random medium, on replacing the medium to a surface impedance. Two operator methods are introduced to obtain the surface impedance and integral equations of reflection–transmission coefficients exactly for a given boundary change. The space Green’s functions outside the boundary are obtained by a simple continuation of the surface Green’s functions, and scattering cross sections are obtained from their asymptotic expressions at large distances. Various quantities and equations associated with the incoherent waves are written exactly by the introduction of a scattering matrix, as contrasted with the conventional one for a coherent scatterer. A slightly rough boundary is investigated, with the cross sections for both reflected and transmitted waves, where obtained equations are significant also for higher-order effects, including multiple scattering. An application to boundary-value problems in layer transport is suggested.
Boson basis realization for shell-model fermion problem
Authors: Gambhir Y. K. , Nikam R. S. , Sarma C. R. , Sheikh J. A.
Published: July 2002

The boson basis for the fermion shell-model problem has been realized over a representation space Vn(n−1)/2 of the unitary group U(n(n−1)/2). A contraction of this space was found to yield the generator algebra of U(n). Based on this result it is shown that the transformations induced by the Dyson-mapped boson Hamiltonian on the Dyson boson basis are identical to the corresponding transformations by the fermion Hamiltonian on the shell-model basis.
A set of commuting missing label operators for SO(5)⊃SO(3)
Authors: De Meyer H. , Vanden Berghe G. , Van der Jeugt J. , De Wilde P.
Published: July 2002

The two-missing label problem for basis vectors of an SO(5) irreducible representation reduced according to the principal SO(3) subalgebra is considered. A pair of commuting Hermitian operators which are scalars with respect to the SO(3) subalgebra are explicitly constructed within the SO(5) enveloping algebra. One label generating operator is of fourth order and the other of sixth order in the SO(5) basis elements.
Generalized Stäckel matrices
Authors: Kalnins E. G. , Miller W.
Published: July 2002

Stäckel and differential-Stäckel matrices are generalized so that the matrix elements may be functions of the derivatives of the dependent variable as well as the independent variable. The inverses of these matrices are characterized and it is shown that for significant classes of linear and nonlinear partial differential equations, variable separation is accomplished via this generalized Stäckel mechanism.
Harmonic analysis of the Euclidean group in three-space. II
Authors: Rno Jung Sik
Published: July 2002

We develop the harmonic analysis for spinor functions which are defined by the matrix elements of the unitary irreducible representations of E(3) with the representation space on the translation subgroup.
Generalized FS×W versus Dyson’s classification of irreducible representations
Authors: Garola Claudio , Solombrino Luigi
Published: July 2002

We study the characterization of the 13 cases obtained in the classification of the irreducible linear–antilinear representations of semigroups in a finite-dimensional vector space X over an algebraically closed field K with a conjugation j (generalized Frobenius–Schur–Wigner, or FS×W, classification). It has already been shown that each case can be characterized by various equivalent properties, some of which can be endowed with a physical interpretation. We show here that, whenever K is the complex field C, each case can be characterized by the structure (in the sense specified by the Weyl theorem on the structure of the matrix algebras and their commutators) of a pair of suitable operator algebras over the real field R. This characterization coincides with the one given by Dyson for each case of his classification of symmetry groups. Thus, the latter classification is recovered under more general assumptions and in a generalized framework, and its one-to-one correspondence with the generalized FS×W classification is shown. In the process, we obtain a classification of the algebras over R generated by complex semigroup representations of the aforesaid kind, and inquire into the connections between some properties of the representations in X over C and the structure (in the Weyl sense) of the representations in the space XR over R obtained by decomplexification of the space X.
Second-order corrected Hadamard formulas
Authors: Epele L. N. , Fanchiotti H. , Canal C. A. García
Published: July 2002

The second-order correction to the Hadamard formulas for the Green’s function, harmonic measures, and period matrix of a two-dimensional domain is obtained in the context of the domain-variational theory.
On the convergence of the Rytov approximation for the reduced wave equation
Authors: Weston V. H.
Published: July 2002

The reduced wave equation Δu+k2n2(x)u=0 is treated where n(x) fluctuates about unity in a compact domain D, and is equal to unity in the region exterior to D. In the Rytov approximation the total field u(x) generated by an incident field ui(x) has the form u(x)∼ui(x)exp φ(x) where φ(x)ui(x)=(1/4π)∫D  (eik‖x−y‖/‖x−y‖)k2(n2−1) ×ui(y)dτy. It is shown that under suitable conditions on n(x) and restrictions on ui(x), the approximation is a leading term of a convergent expansion holding for all x in D. This is in contrast to previous theory, which treated the Rytov approximation as an asymptotic expansion valid in the forward-scattered direction.
Generalized Weyl-type gauge geometry
Authors: Bergmann Peter G. , Komar Arthur
Published: July 2002

Weyl-type gauge geometry based on gauging by GL(4, R) and presented in an earlier paper is developed from an alternative point of view, which emphasizes independent geometric objects as the building blocks. This approach avoids most of the elaborate calculations of the earlier paper, and thus contributes to an intuitive understanding. The new building blocks, which are the metric and two different affine connections, uniquely determine the tensorial structures of the earlier paper, and vice versa.
A prediction of the Cabibbo angle in the vector model for electroweak interactions
Authors: Reifler Frank , Morris Randall
Published: July 2002

In a recent paper we presented a vector model for the electroweak interactions which is similar to the Weinberg–Salam model but differs in the following features. (1) In the vector model all fermion wave functions are bispinors or equivalently isotropic Yang–Mills triplets (as opposed to a state vector composed of a spinor and bispinors in the Weinberg–Salam model). Particles are distinguished by their Higgs fields. (2) The vector model predicts that sin2 θW= 1/4 , where θW is the Weinberg angle. (3) The vector model accounts for conservation of lepton number, electric charge, and baryon number. (4) In the vector model an antiparticle is characterized by opposite lepton number, electric charge, and baryon number; yet both particles and antiparticles propagate forward in time with positive energies. In this paper we extend the vector theory to include interactions between fermions and the gauge bosons mediating the electroweak force. We model the bosons as Yang–Mills fields with their own Higgs fields. We further propose a specific configuration of Higgs fields for the u,d,s, and c quarks. With these features, the model accounts for electroweak transitions of quarks and leptons and predicts that cos θC=0.9744, where θC is the Cabibbo angle. We further show that the vector model accounts for the intrinsic parity of particles and antiparticles, and parity violations and CPT invariance for electroweak interactions.
Spherically symmetric vacuum field in the general scalar–tensor theory
Authors: Singh Tarkeshwar
Published: July 2002

The field equations in the general scalar–tensor theory of gravitation proposed by Nordtvedt are studied for a static and spherically symmetric vacuum field. Closed-form exact solutions of the field equations are presented for the scalar–tensor theories in the form given by Barker and Schwinger.
Comment on momentum in stochastic mechanics
Authors: Golin Simon
Published: July 2002

Stochastic mechanics is a probabilistic description of quantum systems in terms of stochastic differential equations. Davidson [M. Davidson, Lett. Math. Phys. 5, 523 (1981)] and de Falco, De Martino, and De Siena [D. de Falco, S. De Martino, and S. De Siena, Lett. Nuovo Cimento 36, 457 (1983)] have introduced momentum variables into this scheme. In this paper a discussion of this attempt is presented and some difficulties concerning the physical interpretation are pointed out.
Oscillating and absolute Maxwellians: Exact solutions for (d>1)-dimensional Boltzmann equations
Authors: Cornille Henri
Published: July 2002

A study of (d>1)-dimensional nonlinear Boltzmann equations is made for which both momentum and energy conservations hold. Maxwell particles in the presence of outside forces are assumed. For either linear spatial force or linear velocity force plus source term, a class of exact solutions for the homogeneous and inhomogeneous distributions is determined. In particular, a look is taken at oscillating external forces with a varying parameter and distributions relaxing towards oscillating Maxwellians are found. On the other hand, exact inhomogeneous distributions relaxing towards absolute Maxwellians are obtained. The exact solutions have asymptotic regimes that are solutions of the linear part of the Boltzmann equations and the relaxations towards these regimes are studied. Furthermore when equilibrium absolute Maxwellian states exist, whether the relaxation towards these states are from above or from below is investigated and the possibility of finding an overpopulation of high velocity particles at intermediate times is looked at.
Generalized Burgers equations and Euler–Painlevé transcendents. I
Authors: Sachdev P. L. , Nair K. R. C. , Tikekar V. G.
Published: July 2002

Initial-value problems for the generalized Burgers equation (GBE) ut+u βux+λuα =(δ/2)uxx are discussed for the single hump type of initial data—both continuous and discontinuous. The numerical solution is carried to the self-similar ‘‘intermediate asymptotic’’ regime when the solution is given analytically by the self-similar form. The nonlinear (transformed) ordinary differential equations (ODE’s) describing the self-similar form are generalizations of a class discussed by Euler and Painlevé and quoted by Kamke. These ODE’s are new, and it is postulated that they characterize GBE’s in the same manner as the Painlevé equations categorize the Kortweg–de Vries (KdV) type. A connection problem for some related ODE’s satisfying proper asymptotic conditions at x=±∞, is solved. The range of amplitude parameter is found for which the solution of the connection problem exists. The other solutions of the above GBE, which display several interesting features such as peaking, breaking, and a long shelf on the left for negative values of the damping coefficient λ, are also discussed. The results are compared with those holding for the modified KdV equation with damping.
The structure of the space of homogeneous Yang–Mills fields
Authors: Molelekoa Moshe
Published: July 2002

The structure of the space of solutions of Yang–Mills equations is examined for solutions that are required to have a specified set of infinitesimal space-time symmetries. It is shown that when the set consists of Killing vector fields, which are tangent to a compact spacelike Cauchy surface, the space is a smooth ILH manifold near each solution that has only trivial gauge symmetries.
A note on helicity and self-duality
Authors: Ashtekar Abhay
Published: July 2002

It is pointed out that, even if restricted to only self-dual (or anti-self-dual) fields, photon and linearized graviton states of both helicities can be constructed by dropping the restriction to positive-frequency fields. Consequently, contrary to the usual belief, it may not be necessary to work with both self-dual and anti-self-dual fields to obtain the Hilbert space of all quantum states in full quantum gravity.
On the completion of the post-Newtonian gravitational two-body problem with spin
Authors: Barker B. M. , O’Connell R. F.
Published: July 2002

Previous work by the authors [B. M. Barker and R. F. O’Connell, Phys. Rev. D 12, 329 (1975); 14, 861 (1976); B. M. Barker, G. G. Byrd, and R. F. O’Connell, Astrophys. J. (in press); B. M. Barker and R. F. O’Connell, Gen. Relativ. Gravit. (to be published)] on the post-Newtonian (order c−2) gravitational two-body problem with spin and parametrized post-Newtonian parameters γ and β was concerned with the relative position r=r1−r2. Here this work is completed by finding the individual positions r1 and r2, which is necessary for the interpretation of certain binary-system observations. First the center of inertia rCI is found. This makes it possible to obtain the positions r1 and r2 and the center of mass rCM as a function of the relative position r, relative velocity v, and spin angular momenta S(1) and S(2) of the two bodies. Thus, if a solution r=r(t) exists, then solutions r1=r1(t) and r2=r2(t) also exist. The final results are given in a very general coordinate system specified by four arbitrary dimensionless parameters. In particular, the spin-orbit potential energy terms VS1 and VS2 are given without going to a frame of reference where the total momentum is zero.
Correlation functions in finite memory-time reservoir theory
Authors: Arnoldus Henk F. , George Thomas F.
Published: July 2002

Interaction of a small system S with a large reservoir R amounts to thermal relaxation of the reduced system density operator ρS(t). The presence of the reservoir enters the equation of motion for ρS(t) through the reservoir correlation functions fkl(τ) (defined in the text), which decay to zero for τ→∞ on a time scale τc. Commonly, this τc is much smaller than the inverse relaxation constants for the time evolution of ρS(t). Then a series of approximations can be made, which lead to a Markovian equation of motion for ρS(t). In this paper the assumption of a small reservoir correlation time is removed. The equation of motion for ρS(t) is solved, and it appears that the memory effect, due to τc≂/0, can be incorporated in a frequency dependence of the relaxation operator Γ̃(ω). Subsequently, (unequal-time) quantum correlation functions of two system operators are considered, where explicit expressions for (the Laplace transform of) the correlation functions are obtained. They involve again the relaxation operator Γ̃(ω), which accounts for the time regression. Additionally it is found that an initial-correlation operator Υ̃(ω) arises, as a consequence of the fact that the equal-time correlation functions do not factorize as ρS(t) times the reservoir density operator. It is pointed out that the frequency dependence of Γ̃(ω) and the occurrence of a nonzero T̃(ω) both arise as a result of τc≂/0, and should therefore be treated on an equal footing. Explicit evaluation of Γ̃(ω) and Υ̃(ω) shows that their matrix elements can be expressed entirely in f̃kl(ω), just as in the Markov approximation. Hence no essential complications appear if one should go beyond the limits of a small reservoir correlation time τc.
Ion acoustic solitons in a warm magnetoplasma
Authors: Ghosh Kamal Kumar , Ray Dipankar
Published: July 2002

Kalita and Bujarbarua [J. Phys. A: Math. Gen. 16, 439 (1983)] obtained a set of equations to describe the nonlinear propagation of ion acoustic waves in a warm magnetoplasma and made a numerical study of these equations for particular values of the physical parameters. In this paper a rigorous and general analytical study is presented. Some simple necessary and sufficient conditions for solitary wave solutions are derived and it is also shown that cavity solutions are not possible.
Factorizations of vector operators for the isotropic harmonic oscillator in an angular momentum basis
Authors: de Lange O. L.
Published: July 2002

The factorization of four vector operators, D±(ω) and D±(−ω), which occur in a representation-independent, spectrum-generating algebra for the three-dimensional, isotropic harmonic oscillator in an angular momentum basis, is considered (ω is the angular frequency of the oscillator). The D±(ω) are quantum-mechanical analogs of the classical vectors (1∓iL̂×)Fc (ω), where Fc(ω)=−Mωr×L+pL is constant in a frame rotating with angular velocity ωL̂. It is shown that these four vector operators can be factorized in two different ways to yield operators that, apart from their dependence on a constant of the motion (L2), are linear in either p or r. In this way 20 abstract operators are obtained. The properties of these operators are discussed: (i) Twelve are ladder operators for the quantum numbers l, and l and m, in the eigenkets ‖lm〉 of L2 and Lz. In linearized, differential form six of these operators are ladder operators for the spherical harmonics in the coordinate representation, while the other six are the corresponding operators in the momentum representation. (ii) The remaining eight operators factorize linear combinations of the Hamiltonian and the dimension operator. In linearized, differential form four of these operators are ladder operators for energy and angular momentum in the radial part of the coordinate-space wave functions, while the other four are the corresponding operators in the momentum representation.
An action principle combining electromagnetism and general relativity
Authors: Moyer H. Gardner
Published: July 2002

The stationary action problem for a single, classical, point particle in external gravitational and electromagnetic fields is written in optimal control format. The relativistic interval is the independent variable and time, space, and action are the five dependent variables. A general metric is used for the space-time manifold so that the equations are manifestly covariant. The form of the system equations guarantees that the particle moves with unit speed with respect to interval. The Lagrangian is a function of the metric tensor and the electromagnetic four-potential, but not of particle parameters such as electric charge q and mass m. The Hamiltonian is not identically zero, unlike those derived in many earlier analyses. A constant of the motion is found that is identified with q/mc2. An explanation is presented for the classical inequality m≥0. The trajectories can reduce to geodesics and even further to those governed by Fermat’s principle of stationary time.
The classification of complete sets of operators commuting with the Dirac operator in Minkowski space-time
Authors: Kamran N. , Légaré M. , McLenaghan R. G. , Winternitz P.
Published: July 2002

Under the action of the Poincaré group P(1,3) the three-, four-, and five-dimensional vector spaces of formally self-adjoint first-order matrix differential operators commuting among themselves and with the Dirac operator are classified. This gives a complete classification of the maximal subspaces of the vector space of first-order formally self-adjoint matrix differential operators commuting with the Dirac operator, which form an Abelian Lie algebra under the commutator.
Correlated states and collective transition operators for multilevel atomic systems. I
Authors: Rai Jagdish , Mehta C. L. , Mukunda N.
Published: July 2002

The correlated states of an assembly of N multilevel atoms interacting with resonant radiation fields are determined. On the basis of the duality between the permutation group and the linear group, one can construct the internal states for an assembly of N atoms, with n levels each. The possible states are determined by various allowed Young diagrams, corresponding to various representations of the permutation group SN. The collective transition operators are obtained as the generators of the group SU(n).
Space-group theory for a nonperiodic icosahedral quasilattice
Authors: Kramer Peter
Published: July 2002

The hypercubic lattice Y is considered in Euclidean space E6. Embedding of the icosahedral group A(5) determines a well-known noncrystallographic action of A(5) on an irreducible subspace E3. From boundaries of Y and its metrical dual Y*, new convex polytopes, called Klötze, are constructed in E6. The Klötze tile E6 periodically, but not face-to-face, and provide a new fundamental domain under the hypercubic translation group. All boundaries of a Klotz are parallel or perpendicular to the subspace E3. The intersection of the lattice Y with E3 determine a nonperiodic, face-to-face rhombohedral tiling of E3. A quasicrystal model is introduced in E6 and E3. The model has stable density supported on the rhombohedral tiles. Its Fourier transform yields sharp diffraction maxima and reduces to integrals in E3 over the representative tiles and their boundaries.
Some global properties and invariance of bundle metrics in the Kaluza–Klein scheme
Authors: Oh C. H. , Singh K. , Lai C. H.
Published: July 2002

It is shown that the transition functions that give the global structure of the fiber bundle play an important role in the construction of the metric. The invariance properties of this metric under general gauge transformations are discussed and it is found that the usual requirement of a gauge-invariant metric leads to severe constraints on the gauge fields. To avoid them, it is shown that the metric should instead be covariant with respect to these transformations. Moreover the existence of global actions that are essential in the context of the consistency problem is also discussed. The presence of such actions is studied in both the principal and their associated bundles. In the case of a homogeneous bundle with G/H as the typical fiber, it is shown that a ‘‘spliced’’ bundle with G×N(H)/H as the structure group has to be used. The unified space is then taken as the bundle space of its associated bundle.
Asymptotic decay of the free field covariance on a Riemannian manifold via heat kernel techniques
Authors: De Angelis Gian Fabrizio , de Falco Diego , Di Genova Glauco
Published: July 2002

It is demonstrated, via recent global estimates for the heat kernel found by Li and Yau [Acta Matematica 156, 153 (1986)], that the covariance of the mass m free field decays exponentially, at a rate m, with the geodesic distance on any complete, noncompact Riemannian manifold with non-negative Ricci curvature. The rate of the exponential decay is larger than m on simply connected manifolds with negative sectional curvature.
On constrained mechanical systems: D’Alembert’s and Gauss’ principles
Authors: Cardin Franco , Zanzotto Giovanni
Published: July 2002

A geometric formulation of the classical principles of D’Alembert and Gauss in analytical mechanics is given, and their equivalence for possibly non-Riemannian mechanical systems is shown, in the case of ideal holonomic constraints. This is done by means of a Gauss’ function, which is defined in a natural way on the bundle of two-jets on the configuration space, and which gives the ‘‘intensity’’ of the ‘‘reaction forces’’ of the constraints. It is originated by a metric structure on the bundle of semibasic forms on the phase space determined by the Finslerian kinetic energy functions of the mechanical system.
An electron trapped in a rotating magnetic field
Authors: Mielnik Bogdan , Fernández C. David J.
Published: July 2002

The motion of the Schrödinger charged particle in a homogeneous, rotating magnetic field represents an exactly soluble model of the Schrödinger quantum dynamics. The Heisenberg motion trajectories are found and classified. It turns out that the rotating magnetic field of not too high intensity/frequency ratio forms a kind of trap, confining the nonrelativistic charged particle into a quasiperiodic motion. As the intensity/frequency ratio crosses a stability threshold, a sudden qualitative change of the Heisenberg trajectory occurs and the particle is expulsed out of the trap. It is shown that for some values of physical parameters our exact model simulates the behavior of the Schrödinger electron in the laser beam traps.
Boson operator realizations of su(2) and su(1,1) and unitarization
Authors: Doebner H. D. , Gruber Bruno , Lorente Miguel
Published: July 2002

Boson operator realizations of su(2) and su(1,1) are obtained. Scalar products are introduced on ‘‘Fock spaces’’ (Verma modules) spanned by generators of the Heisenberg algebra H and by generators of su(2). These scalar products unitarize certain of the representations of H, or of su(1,1). It is shown that the Gel’fand–Dyson realization of su(1,1) implies a scalar product that unitarizes H, while the Primakoff–Holstein realizations imply a scalar product that unitarizes su(1,1). The relationship between the Gel’fand–Dyson boson operators a° and the Primakoff–Holstein boson operators b° is obtained making use of the two distinct scalar products. Generalized ‘‘vacuum states’’ are defined that are formed by polynomials in the creation–annihilation operator pairs a°a. A representation ρ of H and su(1,1) on the states a°m and an is discussed. For this representation a1=a‖0〉≠0, but rather (a°a)‖0〉 =0. The states of this representation space consist of boson states and boson-hole states. All the familiar results of H and su(1,1) representation theory are preserved within the representation ρ.
Continuous subgroups of the generalized Schrödinger groups
Authors: Barannik L. F. , Fushchich W. I.
Published: July 2002

Some general results on the subalgebras of the Lie algebra ASch(n) of the generalized Schrödinger group Sch(n) and on the subalgebras of the Lie algebra ASch(n) of the generalized extended Schrödinger group Sch(n) have been obtained. The subalgebra structure of the algebras ASch(n) and ASch(n) are studied with respect to inner automorphisms of the groups Sch(n) and Sch(n), respectively. The maximal Abelian subalgebras and the one-dimensional subalgebras of the algebras ASch(n) and ASch(n) have been explicitly found. The full classification of the subalgebras of the algebras ASch(3), ASch(3), which are nonconjugate to the subalgebras of ASch(2), ASch(2), respectively, has been carried out.
Solution to boundary value problems using the method of maximum entropy
Authors: Baker-Jarvis James
Published: July 2002

The method of maximum entropy is used to solve a class of linear boundary value problems. The method is based on using various moments of the differential equation as constraints when maximizing the entropy. Various examples are presented and compared to exact solutions for varying numbers of moments. It is found that the maximum entropy approximation is, in many cases, better than a Fourier series solution for a given number of expansion terms and moments. The method is very general and will find applications in many areas of physics. A comparison of the amount of work necessary for the maximum entropy solution versus finite difference techniques is presented and it is found that the maximum entropy technique shows promise as an alternative solution technique.
Eigenvalue curves and boundary conditions
Authors: Spies Günther Otto
Published: July 2002

Nonlinear eigenvalue problems are considered which are defined by linear homogeneous systems of ordinary differential equations, subject to linear homogeneous boundary conditions, both depending analytically on a complex eigenvalue parameter ω, and on an additional small positive parameter ε such that all solutions have variation O(ε−1). There is, in general, a family of eigenvalues that, in the limit ε→0, become densely spaced and form a definite curve in the complex ω plane (exceptions arise only for some special boundary conditions). This eigenvalue curve is constructed for arbitrary nonsingular systems without turning points. It depends on no details of the boundary conditions other than their type (i.e., the numbers of boundary conditions involving only the left, only the right, or both end points of the interval). In the special cases of either only two-point boundary conditions (such as periodicity) or only one-point boundary conditions with equally many conditions at each end point, and of differential equations involving only even derivatives whose coefficients are constant to leading order, the curve is simply given by the roots of the local dispersion relation. The distance of the eigenvalues from the curve is O(ε) in general, but O(ε1/l log ε−1), with some positive integer l, in special cases.
Analytic solutions of a fourth-order differential equation with a second-order turning point
Authors: Åkerstedt Hans O.
Published: July 2002

Analytic solutions of a certain fourth-order differential equation with a second-order turning point are given. The solutions can be expressed in terms of products of the well-known parabolic-cylinder functions, and the equation might therefore be useful as a comparison equation in the theory of asymptotic expansions of ordinary differential equations.
Nonlinear evolution equations related to the first-order system: φx =λJφ+Pφ
Authors: Cavalcante J. A. , Silva J. A.
Published: July 2002

Let Ut =F(U,∂U/∂x,..., ∂rU/∂xr,t) or Uxt =F(U,∂U/∂x,...,∂rU/∂xr,t) be the nonlinear evolution equations that are the compatibility conditions between φx =λJφ+Pφ and φt =Aφ for P=U(x,t) or P=Ux(x,t), respectively. In this paper, it is proved that if A(Z0,...,Zr−1,t,λ) is a continuous function such that (∂A/∂Zk) (Z0,...,Zr−1,t,λ) k=0,1,..., exists (Zk=∂kU/∂xk), then for P=U(x,t), A is a polynomial in λ of degree r and for the case P=Ux, A=A−1/λ+A0+⋅⋅⋅+Ar−1λr−1. The case where P=Zm, m≥2 is also analyzed.
Refined asymptotic expansion for the partition function of unbounded quantum billiards
Authors: Steiner F. , Trillenberg P.
Published: July 2002

This paper presents a refined asymptotic expansion for the partition function Θ(t)=Tr etΔ of quantum billiards in the unbounded regions {0≤x,0≤yxμ≤1}, μ>0, and {0≤ye‖x‖≤1}⊆R2, where Δ is the Dirichlet Laplacian. Simon [Ann. Phys. 146, 209 (1983); J. Funct. Anal. 53, 84 (1983)] determined the leading divergence of the trace of the heat kernel for the first class of systems. Standard techniques are combined for the evaluation of Θ for bounded region billiards with results by Van den Berg [J. Funct. Anal. 71, 279 (1987)] for ‘‘horn-shaped regions’’ using an optimized way of dividing the region into ‘‘narrow’’ and ‘‘wide’’ parts to determine the first three terms in the asymptotic expansion of Θ. Results are also stated for bounded regions with cusps that can be obtained by the same method. As an application, the spectral staircase of the strongly chaotic billiard system defined in the region {0≤xy≤2,x≥0}, which has been discussed in connection with the Riemann ζ function and the search for quantum chaos is considered.
Sternberg construction and reduction
Authors: Razumov A. V.
Published: July 2002

A connection between the Sternberg construction, which allows one to introduce a symplectic structure on an associated fiber bundle with the base and the fiber being symplectic manifolds, and the reduction of symplectic manifolds is considered. It is shown that the Sternberg construction commutes with the reduction.
Exact solution of the Dirac equation in a reducible Einstein space
Authors: Villalba Víctor M.
Published: July 2002

In this paper, an exact solution of the Dirac equation in a static reducible Einstein space is presented. The asymptotic behavior of the spinor solution is analyzed.
A geometric approach to the path integral formalism of p-branes
Authors: Kafkalidis Menelaos S.
Published: July 2002

The configuration space for a path integral description of a p-brane is seen as a vector bundle over moduli spaces. The Einstein condition, applied to such vector bundles over compact Kähler manifolds, provides the required stability conditions. Consequently moduli spaces for such extended objects of higher dimensionality are constructed. Finally a Hermitian metric can be introduced in these moduli spaces.
Extremal properties of Synge’s world function and discrete geometry
Authors: Rylov Yu. A.
Published: July 2002

Properties of σ space [a set Ω of points P with a real function σ(P,P′) given on Ω] are investigated. A continuity of the set Ω is not necessary and, generally, geometry is discrete. The properties of the world function σ are investigated. At certain (extremal) world function properties the σ space is shown to be a subset of points of Euclidean space or Riemannian space. The presented approach has the peculiarity that no operation other than the function σ is given on σ space. In particular, all such operations as linear operation over vectors, constructing lines and planes, and dimension of the space are expressed through the world function σ and only through it (if it is extremal). A violation of the σ-space extremality leads to going out beyond the frames of Riemannian geometry (lines are substituted by tubes of lines, etc.). The presented approach can be useful in quantum gravitation, string models, and other problems, where the properties of the event space at small distances are important.
Test fields on compact space-times
Authors: Yurtsever Ulvi
Published: July 2002

In this paper, some basic aspects of (Lorentzian) field theory on compact Lorentz manifolds are studied. All compact space-times are acausal, i.e., possess closed timelike curves; this makes them a useful testbed in analyzing some new notions of causality that will be introduced for more general acausal space-times. In addition, studying compact space-times in their own right raises a wide range of fascinating mathematical problems some of which will be explored. It will be shown that it is reasonable to expect Lorentzian field theory on a compact space-time to provide information on the topology of the underlying manifold; if this is true, then this information is likely to be ‘‘orthogonal’’ (or complementary) to the information obtained through the study of Euclidean field theory.
New inhomogeneous boson realizations and inhomogeneous differential realizations of Lie algebras
Authors: Fu Hong-Chen , Sun Chang-Pu
Published: July 2002

The inhomogeneous boson realizations (IHBR) and the corresponding inhomogeneous differential realizations (IHDR) of Lie algebras, which play an important role in the search of quasi-exactly solvable problems (QESP) of quantum mechanics, are studied. All possible IHDR of semisimple Lie algebras can be obtained in this way. As examples, the IHBR and the corresponding IHDR of Lie algebras SU(2) and SU(3) are studied in detail.