bluuebunny/crossref_metadata_2025 huggingface dataset:
The SO(7) polynomial basis for symmetric representations
Authors: De Wilde P. , De Meyer H. , Vanden Berghe G.
Published: March 2003

A polynomial basis is derived for the symmetric irreducible representations of the group SO (7). The reduction of SO(7) into [SU(2)]3 is considered. The SO(7) generators not belonging to [SU(2)]3 are grouped into a bispinor vector, of which matrix elements are calculated. An explicit expression for the state vector is given.
The isospectral property for a family of non-self-adjoint operators
Authors: de Castro Helena M. A. , Wreszinski Walter F.
Published: March 2003

We prove the isospectral property for certain families of linear non-self-adjoint operators which play a role in inverse scattering theory for a class of nonlinear evolution equations of interest in physics. These include the sine-Gordon and nonlinear Schrödinger equations.
Integrability of Hamiltonians with third- and fourth-degree polynomial potentials
Authors: Grammaticos B. , Dorizzi B. , Ramani A.
Published: March 2003

The weak-Painlevé property, as a criterion of integrability, is applied to the case of simple Hamiltonians describing the motion of a particle in two-dimensional polynomial potentials of degree three and four. This allows a complete identification of all the integrable cases of cubic potentials. In the case of quartic potentials, although our results are not exhaustive, some new integrable cases are discovered. In both cases the integrability is explicited by a direct calculation of the second integral of motion of the system.
Simple waves in quasilinear hyperbolic systems. I. Theory of simple waves and simple states. Examples of applications
Authors: Grundland Alfred M. , Żelazny Roman
Published: March 2003

This paper presents a new method of construction of solutions to nonlinear, nonelliptic systems of partial differential equations and especially nonhomogeneous ones. These equations have been considered from the point of view of integral elements. In particular the connections between the structure of the set of integral elements and the possibility of a construction of special classes of solutions have been studied. These classes consist of what is called simple waves and k waves (for homogeneous systems) and simple states (in the case of nonhomogeneous systems). They provide us with a possibility for a selection of simple integral elements from the set of all integral elements. Analyses have been performed using differential forms and Cartan theory of system in involution. The problem has been reduced to examining Pfaff forms. The Cauchy problem for Pfaff systems has been formulated and solved using the Riemann function. Some remarks concerning the notion of Bäcklund transformations for the case of k waves have been formulated. It is shown that, in contrast to simple wave, the simple state has no gradient catastrophy. The technique presented of constructing the solutions in form of simple states has been illustrated by the examples of Korteweg and de Vries and four-dimensional Klein–Gordon, sine–Gordon, and Liouville equations. It has been shown that the known soliton equations are closely connected with the elliptical functions and especially with the P–Weierstrass functions.
An SL(2,C)-invariant representation of the Dirac equation. II. Coulomb Green’s function
Authors: Hostler Levere C.
Published: March 2003

The Kepler problem for the Klein–Gordon type wave equation {ΠμΠμ+m2+ieσ⋅(ℰ+iB)}φ=0, investigated earlier [J. Math. Phys. 23, 1179 (1982)] and proven to be equivalent to the conventional Dirac equation, is discussed. In this equation φ is a 2×1 Pauli spinor and σa, a=1, 2, 3, are the usual 2×2 Pauli spin matrices. Quite simple expressions for the bound state Coulomb wavefunctions and for the Coulomb Green’s function are obtained by exploiting the concept of ‘‘coupling constant eigenfunction.’’ To facilitate the direct use of these simple expressions in Coulomb calculations, a stationary state perturbation theory appropriate for the Klein–Gordon type wave equation itself is described.
Infinitesimal symmetries and conserved currents for nonlinear Dirac equations
Authors: Kersten Paul H. M.
Published: March 2003

The complete algebras of infinitesimal symmetries for Dirac equations, Dirac equations with nonvanishing rest mass, and Dirac equations with a nonlinear term have been established. In addition, conserved currents associated to new symmetries have been constructed.
Symmetry of the complete second-order conductivity tensor in a Vlasov plasma
Authors: Larsson Jonas
Published: March 2003

This paper has two purposes. The first is to consider the origin of a recently derived symmetry property including the pole contributions of the second-order conductivity. The second is to show how certain general formulas for the conductivities easily lead to much more convenient expressions than those used in the above-mentioned derivation of the symmetry.
A new integral equation for summing Feynman graph series (general scalar Lagrangian case)
Authors: Gilain C. , Lévy D.
Published: March 2003

The Schwinger parameter formalism is used to derive a new integral equation verified by the ‘‘open’’ four-point amplitude built from any scalar Lagrangian. This integral equation is a generalization of the one already obtained and studied by the authors in the φ3 ladder graph case. One of the main results obtained here is a new representation of the Feynman amplitudes: the so-called β-representation, which expresses the Bethe–Salpeter structure of a graph in the Schwinger parameter space. The integrand of the β-representation satisfies a recurrence relation which is used to sum the perturbation series, and which leads to an integral equation for its sum. The expression of this integral equation is also given in some particular cases (particular values of the invariants, particular classes of graphs, etc.). The Mellin transform of the open amplitude satisfies a similar integral equation which may be used to describe the Regge behavior.
Quantum energy-entropy inequalities: A new method for proving the absence of symmetry breaking
Authors: Fannes M. , Vanheuverzwijn P. , Verbeure A.
Published: March 2003

For quantum systems we develop a new method, based on a general energy-entropy inequality, to rule out spontaneous breaking of symmetries. The main advantage of our scheme consists in its clear-cut physical significance and its new areas of applicability; in particular we can handle discrete symmetry groups as well as continuous ones. Finally a few illustrations are discussed.
Transmutation as a minimizing procedure
Authors: Carroll Robert , Dolzycki Stanley
Published: March 2003

It is shown formally how transmutation kernels can be characterized via a minimizing procedure. The technique then can be extended to more general operators and transmutations.
Inverse scattering in dimension two
Authors: Cheney Margaret
Published: March 2003

The inverse scattering problem is solved for the two-dimensional time-independent Schrödinger equation. That is, the potential is reconstructed from the scattering amplitude, which is assumed to be known for all energies and angles.
Solution of multidimensional inverse transport problems
Authors: Larsen Edward W.
Published: March 2003

Formulas are derived for energy-dependent, steady-state, and time-dependent neutron transport problems, relating the surface neutron fluxes for a convex, homogeneous, three-dimensional region to the neutron scattering laws that apply within the region. In principle, these formulas can be used to deduce information about the scattering laws.
Vortex properties in first- and second-order formulations of abelian gauge theories
Authors: van der Hoek John , Lohe M. A.
Published: March 2003

Properties of noninteracting vortices in a class of models which generalize the Ginzburg–Landau model of superconductivity are described. Previous results of existence and uniqueness for solutions to the first-order equations are extended to cover the case in which the gauge photon and the scalar meson become massless, when long range interactions exist. Several properties of the solutions are also discussed. With some assumptions, and with restrictions on the class of models, all finite-energy solutions of the second-order equations are shown to be solutions of the first-order equations. The second-order equations are formulated in a gauge invariant way, resulting in a second-order elliptic system of two coupled nonlinear equations, which completely determine all gauge invariant quantities.
A gravitational Poincaré gauge theory and Higgs mechanism
Authors: McKellar R. J.
Published: March 2003

In this paper we shall construct the Lagrangian of a gravitational Poincaré gauge theory using degeneracy in the Euler–Lagrange expressions as a primary restriction. Such a generalization of a Lorentz gauge theory requires the addition of not only a translation gauge connection, but also a Goldstone field. The intractability of the field equations is lessened somewhat by means of a particular choice of gauge which acts like a Higgs mechanism. With one further assumption a complete reduction to the corresponding Lorentz theory can be made, and the Einstein vacuum field equations with cosmological term are recovered.
Remarks on inverse scattering in one dimension
Authors: Newton Roger G.
Published: March 2003

This paper answers the following questions: (1) what are the consequences in the matrix-Marchenko inversion scheme if a given S matrix lacks forward analyticity; and (2) in particular, does the condition known as the miracle depend on forward analyticity, and if not, what properties of S does it depend on? The answers are (1) if the input S matrix lacks forward analyticity then the output S matrix has it anyway, and (2) integrability of kRl,r is sufficient for the miracle to occur. It is also found that the matrix–Marchenko procedure simultaneously constructs the potentials for two scattering problems which differ only by the signs of their reflection coefficients.
Kruskal-like representation of the de Sitter metric
Authors: Beck Johanna Friedl , Inomata Akira
Published: March 2003

A new representation of the de Sitter metric is proposed, which is analogous to Kruskal’s coordinates for the Schwarzschild metric. The counterpart of Wheeler’s tortoise coordinate is also discussed.
Irreversible random and cooperative processes on lattices: Spatial correlations
Authors: Evans J. W. , Burgess D. R. , Hoffman D. K.
Published: March 2003

For processes where ‘‘filling’’ events occur irreversibly and, in general, cooperatively at the sites of a lattice, the minimal closed hierarchy of rate equations involves only probabilities for (effectively) connected subconfigurations of empty sites. Extended hierarchies of equations for (effectively) disconnected empty subconfigurations couple back to these. Here we consider a solution to the latter via previously developed exact and approximate truncation schemes based on a shielding property of empty sites. Numerical results for several processes are presented for correlation behavior in both autocatalytic and autoinhibitory rate regimes. The asymptotic large separation behavior of the spatial correlations is analyzed most easily by z-transforming the equations with respect to separations and is fundamentally different from that of equilibrium distributions.
A new class of Wick powers of generalized free fields
Authors: Brüning Erwin
Published: March 2003

In the frame of generalized Wick powers of generalized free fields a new realization of locality is presented in which locality of the field is not automatically ensured by locality of the two-point function and the well-known combinatorics of Fock space but instead an additional constraint expressing locality of the higher n-point functions has to be satisfied for locality of the field. By example it is shown that this class of models is fairly large.
Nonlinear Schrödinger-type field equation for the description of dissipative systems. III. Frictionally damped free motion as an example for an aperiodic motion
Authors: Schuch D. , Chung K.-M. , Hartmann H.
Published: March 2003

A new theory for the description of dissipative systems by nonlinear Schrödinger-type field equations (NLSE’s) with logarithmic nonlinearity, which has been recently developed by the authors, is applied to investigate the frictionally damped free motion and similar spatially unrestricted aperiodic problems. Wave-packet solutions as well as time-dependent wave-function solutions are derived and discussed. In the limit of vanishing friction (friction constant γ→0) these solutions turn into the well-known solutions of the respective linear Schrödinger field equation. The same applies to the mean values of position, momentum, and energy, as well as to the uncertainty product of position and momentum. For γ≠0, however, interesting new effects appear. In contrast to the linear theory the uncertainty product of position and momentum does not diverge any more for infinitely long times, t→∞, but asymptotically approaches a definite constant value which depends on characteristic parameters of the system like its mass, initial width, and friction constant γ. Another effect, the faster spreading of the Gaussian wave-packet solution compared to the linear theory, can be explained with the help of a special property of our nonlinear differential equation. In a way similar to what is usually only known for linear differential equations, the wave-packet solutions of our NLSE can be obtained by superposition of the wave functions which are individually also solutions of the same NLSE. The properties of the time-dependent superposition coefficients appearing in this connection are discussed. The extension to the corresponding three-dimensional problem as well as the differences arising in the investigation of the NLSE’s of the free fall and the motion in a constant electric field are given. Concluding, some differences are discussed which appear applying our nonlinear field theory to describe periodic or aperiodic motions, respectively.
Plane-surface deformation in electrohydrostatics with electric double layer
Authors: Cade R.
Published: March 2003

General equations governing the static deformation of the surface of a conducting liquid under an electric field, when there is an electric double layer at the surface, are here applied to the general situation where the undeformed surface is a horizontal plane, and a number of specific problems are solved. The theory in this case has two features which distinguish it from other situations, studied previously, where the undeformed surface is curved. One feature requires a difference in the practical process of solution, while the other requires some careful theoretical examination in order to justify properly the solutions actually obtained.
A Lyapunov functional for the evolution of solutions to the porous medium equation to self-similarity. I
Authors: Newman William I.
Published: March 2003

We employ the transformation properties and the integral invariants of the porous medium equation in m dimensions to construct a Lyapunov functional which characterizes the evolution of the profile to its self-similar solution.
Low temperature expansions for the Gibbs states of quantum Ising lattice systems
Authors: Thomas Lawrence E. , Yin Zhong
Published: March 2003

By conditioning on a subalgebra of observables, we develop low temperature expansions for certain quantum Ising models, which include transverse Ising models and anisotropic xy models. These expansions are majorized by the series for functions solving certain nonlinear partial differential equations. Convergence for the majorizing series follows from Cauchy–Kowalevski theory applied to the partial differential equations. The low temperature expansions imply long-range order.
Discriminant, transmission coefficient, and stability bands of Hill’s equation
Authors: Keller Joseph B.
Published: March 2003

The discriminant Δ(k2) of Hill’s equation is shown to be related to the transmission coefficient T(k)eiθ(k) of one period of the potential by Δ(k2)=[2/T(k)]cos[kπ+θ(k)]. This result is used to find the boundaries of the stability bands.
Lax-pairs, spectral problems, and recursion operators
Authors: Strampp W.
Published: March 2003

We present various examples for the connection between Lax-pairs and recursion operators. From this connection a new method for constructing recursion operators is derived. As an application we find recursion operators to some integrable equations newly found by Wadati et al. [J. Phys. Soc. Jpn. Lett. 46, 1965 (1979); J. Phys. Soc. Jpn. 47, 1698 (1979)].
On the Schrödinger operator with periodic point interactions in the three-dimensional case
Authors: Fassari S.
Published: March 2003

We prove that it is possible to define the self-adjoint operator which gives sense to the merely formal expression −Δ−∑y∈Lλδ(⋅−y) (where L is a certain lattice of R3) as the limit when ε→0+ in the resolvent sense of the net Hε =−Δ+∑y∈L  λ(ε)ε−2V(⋅−y/ε) λ(ε) being a real-valued, C∞ [0,1] function with λ(0)=1 and V∈L ∞ is such that supp V is contained in the Wigner–Seitz cell. By using the direct integral decomposition, we reduce the problem to the convergence of the reduced Hamiltonian Hε (θ)=−Δθ +λ(ε)ε−2V(⋅/ε). In order to find the limit when ε→0+ of [Hε(θ)−E]−1, we also study the properties of its integral kernel.
Global reduction of a dynamical system on a foliated manifold
Authors: Gasparini Ida Cattaneo
Published: March 2003

Conditions for the global reductions of a dynamical system defined on foliated manifold M are given. They are expressed by a local condition on the topology of one single leaf and a global condition on the transverse bundle to the foliation. The link of this condition is shown with the existence of a normalizer of the Lie algebra of the vector fields tangent to the foliation in the Lie algebra of all the vector fields of M. This normalizer contains all the derivations of the functions constant on the leaves.
Post-Newtonian extensions of the Runge–Lenz vector
Authors: Argüeso F. , Sanz J. L.
Published: March 2003

We obtain the most general post-Newtonian extension of the Runge–Lenz vector corresponding to a very large class of two-body relativistic systems whose equations of the relative motion can be derived from a post-Newtonian Hamiltonian depending on four parameters which include the electromagnetic and gravitational cases. Assuming a couple of conditions, we fix the arbitrariness and obtain a unique post-Newtonian Runge–Lenz vector, whose associated symmetries generate the same algebra as in the Keplerian case.
Geometrical models for quantum logics with conditioning
Authors: Deliyannis Platon C.
Published: March 2003

After obtaining a representation of a quantum logic by means of projection operators on the state space, geometrical conditions are imposed on a cone in an abstract Banach space which allow us to show that certain projections leaving this cone invariant will form a quantum logic with conditioning. Several examples are also presented.
Anharmonic oscillator with general polynomial potential
Authors: Sharma G. S. , Sharma L. K.
Published: March 2003

This paper derives simple analytical formulas for the energy eigenvalues En(λ) of one-dimensional anharmonic oscillators characterized by the potentials ω2x2+∑mα=2 λα x2α. For doubly anharmonic oscillators, over a wide range of n and λ, these energy values agree well with the numerical values calculated by earlier workers.
Exact solutions of the Schrödinger equation for a class of three-dimensional isotropic anharmonic oscillators
Authors: Leach P. G. L.
Published: March 2003

A mathematical explanation of how the Schrödinger equation for a class of three-dimensional isotropic anharmonic oscillators possesses exact solutions is given. The class of potentials is shown to be wider than at present found in the literature.
A rigorous derivation of the ‘‘miracle’’ identity of three-dimensional inverse scattering
Authors: Cheney Margaret
Published: March 2003

The large-energy asymptotic behavior of scattering solutions of the three-dimensional time-dependent Schrödinger equation is investigated. The second term of the expansion leads to the ‘‘miracle’’ of Newton’s three-dimensional inverse scattering theory.
Collectivity and geometry. III. The three-dimensional case in the Sp(6)⊇Sp(2)×𝒪(3) chain for closed shells
Authors: Castaños O. , Chacón E. , Moshinsky M.
Published: March 2003

As was indicated in previous papers, general Hamiltonians for systems of n particles in three-dimensional space can be formulated in the enveloping algebra of the symplectic group Sp(6n). This group admits, among others, the subgroup Sp(6)×O(n) and, as has been noticed by many authors, collective Hamiltonians can be formulated in the enveloping algebra of Sp(6), so that their eigenstates can be characterized by a definite irreducible representation (irrep) of this group. The mathematical problem is then to determine the matrix elements of the generators of Sp(6) in a basis characterized by irreps of this group as well as of appropriate subgroups. In the present series of papers the subgroups chosen where Sp(2)×𝒪(3) as the Casimir operator of Sp(2) when n → ∞ is formally related to the Bohr–Mottelson vibrational Hamiltonian (BMVH), while 𝒪(3) gives the angular momentum of the state. We give an algorithm for determining these states that closely parallels the procedure followed for the BMVH. Programs are being developed to convert our algorithm into a computational tool for determining collective excitations in nuclei.
Poisson bracket realizations of Lie algebras and subrepresentations of (ad⊗k)s
Authors: Iosifescu Mircea , Scutaru Horia
Published: March 2003

A procedure which associates Poisson bracket realizations of a Lie algebra L to subrepresentations of the extension (ad⊗k)s of the adjoint action to the algebra of polynomials defined on the dual space L* is pointed out. The procedure is applied, for k=2, to the real forms of the semisimple Lie algebras of types D3 and B2∼C2, in particular to the algebras so(4,2), so(4,1), and so(3,2)∼sp(4,R). The results obtained for the algebra sp(4,R) have led to an algebraic foundation for the constraints satisfied by the dynamical variables for the classical limit of the generalized helium problem.
The expression for the triple vector product solid harmonic
Authors: Antone T. A.
Published: March 2003

The solid harmonic yLM[(r1Λr2)Λr3] was expressed in terms of the spherical harmonics YL1M1(r̂1), YL2M2(r̂2), and YL3M3(r̂3), where the coefficients of the expansion were expressed in terms of 9j symbols. Here we present a simpler form of those coefficients expressed in terms of 6j symbols.
Liouville and Painlevé equations and Yang–Mills strings
Authors: Saçlioğlu Cihan K.
Published: March 2003

Stringlike solutions of the self-dual Yang–Mills equations (dimensionally reduced to R2) are sought. A multistring Ansatz results in the sinh–Gordon and Liouville equations. According to a general theorem, the solutions must be either real and singular and have infinite action, or complex and nonsingular, with zero action. In the Liouville case, explicit arbitrarily separated n-string solutions of both classes are given. The magnetic flux for these solutions is found to be the Chern class of a Kaehler manifold, and it consequently assumes quantized values 4πn/e. The axisymmetric version of the sinh–Gordon is solved by the third Painlevé transcendent P3, using the results on P3 by Wu et al. [Phys. Rev. B 13, 316 (1976)] and McCoy et al. [J. Math. Phys. 18, 10 (1977)]. The axisymmetric case can be cast into the Ernst equation framework for the generation of further solutions. In the Appendix, the Euclideanized Ernst equation is shown to give self-dual Gibbons–Hawking gravitational instantons.
First integrals via polynomial canonical transformations
Authors: Leach P. G. L.
Published: March 2003

Maharatna, Dutt, and Chattarji [J. Math. Phys. 20, 2221 (1979)] discussed the use of time-dependent canonical transformations for the determination of first integrals for time-dependent Hamiltonian systems. One particular proposal that successive time-dependent polynomial canonical transformations will enable first integrals to be found for a wider variety of time-dependent polynomial Hamiltonians than can be obtained using time-dependent linear canonical transformations is shown to be not true for the paradigm which they selected. It is suggested that their ansatz is ill-founded in general.
Nonexistence of asymptotically free solutions for a nonlinear Schrödinger equation
Authors: Barab Jacqueline E.
Published: March 2003

Let u be a nontrivial, smooth solution to iut=Δu−‖u‖ p−1u. If n=1 and 2<p≤3, then there does not exist any finite energy free solution v such that ∥u(t)−v(t)∥2→0 as t→+∞. This extends a theorem of Strauss in which the same result was proved for 1<p≤2.
A cosmological solution of Einstein’s equations
Authors: Wesson Paul S.
Published: March 2003

An exact solution of the equations of general relativity is given which tends to Einstein–de Sitter at late times. The energy density is inhomogeneous at early times, and is singular on two spherical surfaces which may be related to the ‘‘bubbles’’ typical of inflationary universe models.
Static space-time in general scalar tensor theory
Authors: Banerjee N. , Dutta Choudhury S. B. , Banerjee A.
Published: March 2003

The problem of the coupled Einstein–Maxwell scalar field in the framework of general scalar tensor theory of Nordtvedt is completely solved for plane symmetric static matter-free space-time. Special cases are considered for some special choices of ω as functions of the scalar field. Solutions are gien also in the absence of the electromagnetic field and these are shown to generate a few special cases of Bianchi I cosmological models when subject to a set of complex transformations of coordinates.
Probability measures and Hamiltonian models on Bethe lattices. I. Properties and construction of MRT probability measures
Authors: Peruggi Fulvio
Published: March 2003

The properties of one-step Markov, rotationally and m-step (m=1 or 2) translationally invariant (MRT) probability measures on q-state-site (qSS) Bethe lattices are studied. A theorem is proven, which completely defines such measures in terms of m(q2+q) fundamental probabilities. These are explicitly calculated for any MRT–qSS Hamiltonian model. As a consequence of our approach, the dychotomy between alternative solutions of Hamiltonian models on Bethe lattices is solved.
A new set of Euler angles for the generalized Lorentz group
Authors: Syed Ansaruddin
Published: March 2003

A new set of Euler angles for the generalized Lorentz group O+( p,n−p) are defined, which turn out to be much simpler than the ones defined in a couple of earlier papers, and have the useful property that each factor in the factorization of a general element itself belongs to the same group.
A generating function for Chew–Mandelstam functions
Authors: Reid J. H. , Trofimenkoff N. N.
Published: March 2003

We have obtained the generating function for Chew–Mandelstam functions for arbitrary integral angular momentum. From this a closed formula for the Chew–Mandelstam functions is derived in both the simple equal mass case and in the more complicated case of unequal masses.
A certain class of solutions of the nonlinear wave equation
Authors: Cieciura Grzegorz , Grundland Alfred
Published: March 2003

In this paper are investigated some differential geometry methods in the theory of the nonlinear wave equation ∇2u=Φ(u,(∇u‖∇u)). A special class of solutions is discussed for which (∇u‖∇u) is constant on each level of the function u. It is proved that levels of such solutions form in the space of independent variable’s hypersurfaces with all principal curvatures constant. The general form of such hypersurfaces is given. Then it is proved that via the method of characteristics it is possible to construct (in principle) all the solutions of the discussed class. They may be obtained by integration of an ODE of second order using a special class of the polynomial functions. Some new solutions are given for equations⧠v=4Av3+3Bv2+2cv+D, ⧠v=μ exp v, ⧠v=sin v, ⧠v=cosh v, and ⧠v=sinh v.
Hamiltonians with high-order integrals and the ‘‘weak-Painlevé’’ concept
Authors: Grammaticos B. , Dorizzi B. , Ramani A.
Published: March 2003

We examine the singularity structure of the equations of motion associated to integrable two-dimensional Hamiltonians with second integrals of order higher than 2. We show in these specific examples that the integrability is associated to a singularity expansion of the ‘‘weak-Painlevé’’ type. New cases of integrability are discovered, with still higher-order integrals which are explicitly computed.
Multifrequency inverse problem for the reduced wave equation: Resolution cell and stability
Authors: Weston V. H.
Published: March 2003

The multifrequency inverse problem associated with the reduced wave equation Δu+k2n2(x)u=0, x ∈ R3 is examined for the case where the data set is sparse. The resolution cell or solution set is examined in detail and is shown to be an infinite-dimensional manifold. The concept of stability is introduced. It is shown that the intrinsic condition of structural stability to the inverse process selects out a preferred set of solutions from the solution set. The structural stability of various iterative schemes used in the inverse process are examined.
Self-gravitating fluids of class one with nonvanishing Weyl tensor
Authors: Gupta Y. K. , Sharma S. P. , Gupta R. S.
Published: March 2003

All the Zeldovich fluids of imbedding class one with nonvanishing Weyl tensor have been obtained by solving equations of continuity and equations of motion. All of them are found to be irrotational and therefore can be termed as self-gravitating fluids with pressure equal to energy density.
Constraints on the nature of inertial motion arising from the universality of free fall and the conformal causal structure of space-time
Authors: Coleman Robert Alan , Korte Herbert
Published: March 2003

According to the principle of the universality of free fall, the motions of all neutral monopole particles are governed by one common path structure. This principle does not, however, require the path structure to be geodesic; that is, the path structure need not be a projective structure. It is shown that any equation of motion structure (either a curve or a path structure) that has sufficient microisotropy to be compatible with the conformal causal structure of space-time must be geodesic and must be unique. Hence, the empirically well-supported principles of conformal causality and of the universality of free fall together require the existence of a unique Weyl structure on space-time.
Superposition of solutions to Bäcklund transformations for the SU(n) principal σ-model
Authors: Harnad J. , Saint-Aubin Y. , Shnider S.
Published: March 2003

We show that the Bäcklund transformations for the SU(n) principal σ-model may be linearized using a geometrical interpretation of these equations involving the minimal orbit of SU(n, n) in the Grassmann manifold Gn (C2n). Linearization puts the equations in Zakharov–Mikhailov–Shabat (ZMS) form. Using this form of the equations, we prove inductively a nonlinear superposition law and a permutability theorem for iterated Bäcklund transformations analogous to known results in the theory of the sine–Gordon and KdV equations. From the superposition law we get an explicit form for multisoliton solutions to the σ-model.
On the construction of state spaces for classical dynamical systems with a time-dependent Hamilton function
Authors: Braunss Günter
Published: March 2003

The damped linear and the forced harmonic oscillator are used as standard examples for a dynamical system with a time-dependent Hamilton function to investigate the problem of constructing a Hilbert state space and evolution operators in this space.
The forced Toda lattice: An example of an almost integrable system
Authors: Kaup D. J.
Published: March 2003

A method for solving forced integrable systems is presented. The method requires the knowledge of at least one piece of information about the solution. Once this is known, one may then construct the remainder of the solution. In this sense these systems are ‘‘almost integrable.’’ The forced semi-infinite Toda lattice is used as an example and to illustrate the method.
The soliton birth rate in the forced Toda lattice
Authors: Kaup D. J. , Neuberger D. H.
Published: March 2003

The soliton birth rate in the semi-infinite Toda lattice is studied. The lattice is forced by driving the zeroth particle with a constant velocity into the remainder of the lattice. An approximate solution for the soliton birth rate is derived and it is shown to compare quite favorably with the actual birth rate.
Semiregular induction of group representations
Authors: Klein D. J.
Published: March 2003

The method of inducing an irreducible representation of a group from that of a subgroup is extended. This generalized induction process is illustrated to occur in applications and to account for some occurrences of ‘‘intermediate’’ or ‘‘hidden’’ symmetry. Some general results are proved, including a reciprocity theorem relating general induction and subduction processes.
Variational bounds on the temperature distribution
Authors: Kalikstein Kalman , Spruch Larry , Baider Alberto
Published: March 2003

Upper and lower stationary or variational bounds are obtained for functions which satisfy parabolic linear differential equations. (The error in the bound, that is, the difference between the bound on the function and the function itself, is of second order in the error in the input function, and the error is of known sign.) The method is applicable to a range of functions associated with equalization processes, including heat conduction, mass diffusion, electric conduction, fluid friction, the slowing down of neutrons, and certain limiting forms of the random walk problem, under conditions which are not unduly restrictive: in heat conduction, for example, we do not allow the thermal coefficients or the boundary conditions to depend upon the temperature, but the thermal coefficients can be functions of space and time and the geometry is unrestricted. The variational bounds follow from a maximum principle obeyed by the solutions of these equations.
Coulomb-modified nuclear scattering. III
Authors: Talukdar B. , Ghosh D. K. , Sasakawa T.
Published: March 2003

Scattering by the Coulomb plus Graz separable potential is studied by employing a coordinate space approach to the problem. Exact analytical expressions for on- and off-shell Jost functions fl(k) and fl(k,q) are constructed and certain useful checks are made with regard to their limiting behavior and on-shell discontinuity.
A fully crossing symmetric vertex function
Authors: Gering M. Z. I. , Heiss W. D.
Published: March 2003

A fully crossing symmetric vertex function was calculated in an exactly soluble model. It has branch points in the interaction strength whose positions are independent of the energy variables. The irreducible vertex parts entering the Bethe–Salpeter equations are more involved than the vertex function itself.
Isometries compatible with gravitational radiation
Authors: Bičák J. , Schmidt B. G.
Published: March 2003

Isometries compatible with asymptotic flatness and admitting radiation are studied by using Bondi’s formalism. In axially symmetric space-times, the only second allowable symmetry that does not exclude radiation is boost symmetry. The boost-rotation symmetric solutions describe ‘‘uniformly accelerated particles’’ of various kinds. The news function is restricted by a differential equation; however, it need not vanish, as has been claimed in the literature. If two Killing fields corresponding to null rotations at null infinity are present, then it is shown that the vacuum field equations imply a further isometry. The resulting space-time is a plane wave.
The detailed balance condition in quantum statistical mechanics
Authors: Majewski W. A.
Published: March 2003

The generalization of the detailed balance condition is discussed in the framework of algebraic quantum statistical mechanics.
Reduction of the Poincaré gauge field equations by means of duality rotations
Authors: Mielke Eckehard W.
Published: March 2003

A rather general procedure is developed in order to reduce the two field equations of the Poincaré gauge theory of gravity by a modified ansatz for the curvature tensor involving double duality. In the case of quasilinear Lagrangians of the Yang–Mills type it is shown that nontrivial torsion solutions with duality properties necessarily ‘‘live’’ on an Einstein space as metrical background.
Generating differential operators for the basis functions in the variational LCAO-type methods
Authors: Niukkanen A. W.
Published: March 2003

The analytical expressions for operators, which allow us to generate the basis functions from the simplest (ground) states by means of differentiating by parameters, are obtained. Some important properties of these operators are indicated. This approach allows us to simplify the structure of molecular matrix elements, whose calculation presents considerable difficulties in the variational LCAO-type methods.
First integrals for some nonlinear time-dependent Hamiltonian systems
Authors: Leach P. G. L. , Lewis H. R. , Sarlet W.
Published: March 2003

An observation of a simple property of canonical transformations leads to a procedure for determining first integrals for classes of Hamiltonians. In illustrative examples the most general result presently known from other methods is recovered, a new result presented, and a generalization to more than one degree of freedom discussed.
Generalized variational principles and nondifferentiable potentials in analytical mechanics
Authors: May Helge-Otmar
Published: March 2003

The present paper deals with variational principles in terms of hemivariational inequalities and with multivalued differential equations which are called differential inclusions in analytical mechanics. Such inequalities and inclusions are received when no restrictions of differentiability are considered.
Specializations of integrable systems and affine Lie algebras
Authors: Guerrero F. Guil
Published: March 2003

We analyze a number of restrictions on the evolution systems associated with the zero-curvature equations corresponding to the extended Dynkin diagram A(1)n−1. The resulting specialized evolution systems contain exponential terms, like a third-order differential equation previously derived in Ref. 5.
Finite quantum processes
Authors: Gudder Stanley P.
Published: March 2003

A model for quantum dynamics is presented in terms of a generalization of Markov chains. We first consider measurements and events on an amplitude space. Markov amplitude chains on an amplitude space are then studied. Quantum chains are defined and characterized by a Markov and weak stationarity property. We then consider random phase transformations and study the changes that result in an amplitude space and in the quantum chains due to such transformations. A perturbation expansion involving a potential perturbing the ‘‘free’’ motion is proved. Quantum processes are defined and their relation to quantum chains is discussed. The existence of an arbitrary quantum chain is proved using path chains.
Quantization of three-dimensional space
Authors: Leaf Boris
Published: March 2003

Geometrical properties of space are described by relations between quantum observables, functions of generalized coordinate and momentum operators of a physical system. Space comprises the set of eigenvalues of the coordinate observables, which may be a discrete set of points instead of the continuum of classical geometry. Differentiation on coordinates and momenta is defined by commutation operations. Well-known formulas from classical geometry for gradient and divergence operators, connections, covariant differentiation, tangent vectors, geodesics, and the Riemann curvature tensor are derived as relations between quantum operators. The quantum formulation retains the symmetry between coordinate and momentum representations required by the principle of complementarity.
Unitary equivalence and scattering theory for Stark-like Hamiltonians
Authors: Ben-Artzi Matania
Published: March 2003

Let H0=−Δ+V0( x1), H=H0+V( x) be self-adjoint in L2(Rn). V0 depends only on one coordinate and tends monotonically to ∓∞ as x1→±∞. V is a real H0-compact potential, short range with respect to V0. In particular, the cases V0( x1)=−(sgn x1)‖x1‖α, 0<α≤2 and ‖V( x)‖≤C‖x‖−1 are included (α=1 being the Stark effect). It is shown that (a) H is spectrally absolutely continuous over the entire real axis apart from a possible discrete sequence of eigenvalues of finite multiplicity and rapidly decaying eigenfunctions (H0 has no eigenvalues) and (b) the wave operators W±(H,H0) exist and are complete.
The minimum potential strength for the existence of bound states
Authors: Sidharth B. G.
Published: March 2003

Bounds are deduced for both the minimum potential strength for the existence of bound states and the scattering length for everywhere attractive potentials which fall off faster than (1/r3) for large r. These bounds are the second Born approximations. A variational calculation is then invoked to prove that, interestingly, these bounds are actually good estimates when a specified sufficiency condition is satisfied. The estimates are then shown to compare favorably with known results for a number of potentials of practical interest, viz., the square-well, Morse, exponential, and Yukawa potentials.
On quantum solitons and their classical relatives: Reducible quantum fields and infinite constituent ‘‘elementary’’ systems
Authors: Garbaczewski Piotr
Published: March 2003

We demonstrate that the emergence of translation modes in the quantization of some at least nonlinear field theory models (like, e.g., φ4 or the sine–Gordon systems) implies a specific structure of their state spaces namely this of the direct integral Hilbert space, which follows from the reducibility of the involved quantum field canonical commutation relations (CCR) algebras. As a special manifestation of this structure, one recovers infinite constituent ‘‘elementary’’ quantum systems living in the commutant of the CCR algebra, which appear as the Schrödinger or the two level ones. The corresponding Hamiltonians are derived. In addition, we propose a modification of the standard infrared Hilbert (photon field) space construction employed in quantum electrodynamics. We demonstrate that, in principle, Fermi (CAR) generators, carrying the spin–charge–momentum labels of Dirac particles, can be defined as operators in the electromagnetic (photon field) Hilbert space. The photon field (CCR) algebra is highly reducible, and in the present case fermions arise in the commutant of it, playing the role of intertwining operators.
On-shell singularities of the off-shell Jost functions and Jost solutions for long-range potentials
Authors: Dušek Jan
Published: March 2003

Using the known form of the on-shell singularities of the off-shell incoming and outgoing wave solutions, we investigate the on-shell singularities of the off-shell Jost solutions and off- and half-shell Jost functions for local central potentials vanishing at infinity as cr−α, where αε(0,1]. We show that all the singularities can be expressed via the renormalization factors of the incoming and outgoing wave solutions. The obtained results explain the singular term appearing for long-range potentials in the partial waves of the half-shell scattering amplitude in the neighborhood of the energy shell.
The positivity of the Lyapunov exponent and the absence of the absolutely continuous spectrum for the almost-Mathieu equation
Authors: Figotin A. L. , Pastur L. A.
Published: March 2003

This paper contains the rigorous proof of the formulated by Andre and Aubry following statement: the Cauchy solutions of the discrete Schrödinger equation with the potential qn=g cos(2πnθ+φ) grow exponentially for every irrational θ, g>1 and almost every φε[0,2π). According to known this fact implies the absence of the absolutely continuous component of the spectrum for the corresponding operator.
On the solution of the two-dimensional Helmholtz equation
Authors: Singh G. S. , Kothari L. S.
Published: March 2003

The solution of the two-dimensional Helmholtz equation has been obtained in the annular region having eccentric circular boundaries. It is shown that in the limit of eccentricity zero, the solution reduces to that corresponding to the case of concentric circular boundaries.
Convergence of a crossing-symmetric perturbation series for the four-point vertex
Authors: Davis E. D. , Heiss W. D.
Published: March 2003

A finite radius of convergence is established for a perturbation expansion of the crossing-symmetric vertex function in a discrete model.
Planar coherent states
Authors: Fuller William Roger
Published: March 2003

Planar coherent states with domains in the complex plane are defined by means of ladder operators acting in a separable Hilbert space. Some properties of the states are derived and examples provided to indicate areas of possible applications.
Generalized supermanifolds. II. Analysis on superspaces
Authors: Hoyos J. , Quirós M. , Ramírez Mittelbrunn J. , de Urríes F. J.
Published: March 2003

The analysis on generalized superspaces is studied. G-differentiability of functions and indetermination of partial G-derivatives are treated in detail. A canonical expansion for supersmooth functions and a particular choice of partial G-derivatives are given, and their properties studied. Existence of (nonanalytic) G∞ -functions is proved.
Generalized supermanifolds. III. ρ-supermanifolds
Authors: Hoyos J. , Quirós M. , Ramírez Mittelbrunn J. , de Urríes F. J.
Published: March 2003

ρ-supermanifolds are characterized as supermanifolds modeled in a superspace S having a well-behaved body. Tangent, cotangent, and tensor bundles to ρ-supermanifolds are discussed. The elements of the theory of Lie supergroups and principal superfiber bundles as ρ-supermanifolds are given.
Symmetries and stable periodic orbits for one-dimensional maps
Authors: Vilela Mendes R.
Published: March 2003

Global φ−1 ■ f ■ φ=f and infinitesimal α ■ f=Df(α) symmetries are considered for dynamical maps f. The general solution of α ■ f(x)=f′(x)α(x); x∈[a,b]⊆ R is constructed, and for S-unimodal maps, the existence of a nontrivial continuous solution is shown to be equivalent to the existence of a stable periodic orbit.
Fermion diffusions
Authors: Applebaum D. , Hudson R. L.
Published: March 2003

We determine the form and solutions of all possible stochastic differential equations driven by fermion Brownian motion for a fermion system of one degree of freedom.
Evaluation of an integral involving associated Legendre polynomials and inverse powers of (1−X2)
Authors: Ullah Nazakat
Published: March 2003

An integral involving the product of two associated Legendre polynomials and inverse powers of (1−X2) is carried out using the operator form of Taylor’s theorem and an integral over a single associated Legendre polynomial.
On the limit from the intermediate long wave equation to the Benjamin–Ono equation
Authors: Santini P. M. , Ablowitz M. J. , Fokas A. S.
Published: March 2003

The intermediate long wave equation is a physically important singular integrodifferential equation containing a parameter, referred to here as δ. For δ → ∞ it reduces to the Benjamin–Ono equation. It has been recently shown that the inverse scattering transform schemes of the above equations have certain significant differences. Here it is shown that for δ → ∞, the inverse scattering transform scheme of the intermediate long wave equation reduces to that of the Benjamin–Ono equation.