bluuebunny/crossref_metadata_2025 huggingface dataset:
Phase integral approximations for calculating energy bands
Authors: Floyd Edward R.
Published: March 2003

The phase integral approximation is modified to incorporate an energy-dependent effective potential that manifests the energy band character of lattice potentials. The resultant phase integral approximation because of its inherent renormalization demonstrates superior validity. Numerical examples which compare this approximation with other methods substantiate the superior convergence of this modified phase integral approximation.
Linear boson transformation coefficients
Authors: Vaidya Arvind Narayan
Published: March 2003

A simple expression for the coefficients which connect a Fock state containing an arbitrary number of quasiparticles with its tranformed state under a boson Bogoliubov transformation is obtained.
Some new identities of the Clebsch–Gordan coefficients and representation functions of SO(2,1) and SO(4)
Authors: Barut A. O. , Wilson Raj
Published: March 2003

A systematic derivation of various relations and identities among the Clebsch–Gordan coefficients and for the representation functions of SO(4) and SO(2,1), is given. These relations are essential in work involving the matrix elements of arbitrary group elements in higher noncompact groups such as O(4,2).
Consequences of scaling in nonlinear partial differential equations
Authors: Pereira Nino R.
Published: March 2003

Scaling of the form x=ax′, t=aht′, q=amQ of a nonlinear partial differential equation for q is connected with the form of the auxiliary functions in an inverse scattering method (AKNS scheme). Solvability of an equation by this scheme is treated. It is shown that only equations with m=2 are solvable by using the method of inverse scattering in conjunction with the Schrödinger eigenvalue equation. The criterion m=2 restricts the form of the terms in these equations. The terms, powers of q and its derivatives, can be found by inspection. A separate problem, the decay of a single soliton in the Korteweg–de Vries equation with damping, is solved using only scaling properties.
On the Schrödinger equation in fluid-dynamical form
Authors: Wong C. Y.
Published: March 2003

The fluid-dynamical form of the Schrödinger equations is studied to examine the nature of the quantum forces arising from the quantum potential of Madelung and Bohm. It is found that they are in the form of a stress tensor having diagonal and nondiagonal components. Future studies of these quantum stress tensors in a many-body system may shed some light on the mechanism of spontaneous symmetry breaking and the generation of vorticity in many nuclear systems.
The maximal solvable subalgebras of the real classical Lie algebras
Authors: Perroud Marcel
Published: March 2003

The classification of the maximal solvable subalgebras of sl(n,R), su* (n), so* (n), sp(n,R) and usp(p,q) is given, thus supplementing the cases su(p,q) and so(p,q) performed elsewhere.
Neutrinos and Bianchi I universes
Authors: Davis T. M. , Ray J. R.
Published: March 2003

We find that Bianchi I universes allow neutrinos only in the special case B=C≠A, and the neutrinos must be ’’ghost.’’ The solution is a special case of the Kasner solution. We also discuss massive neutrino solutions in Bianchi I universes. In an appendix we discuss the lack of a Birkhoff-type theorem for plane symmetry.
A spectral representation on ordinary linear difference equation with operator-valued coefficients of the second order
Authors: Fukushima Masahisa
Published: March 2003

The spectral theory associated with two-dimensional linear partial difference operators of the second order on the pseudo-Hilbert space originated by Berezanskii is studied. The present discussion, partly in Govindaraju’s style, is essentially based on the Kodaira’s method.
Iterative solution of the Hartree equations
Authors: Luning C. D. , Perry W. L.
Published: March 2003

An iterative scheme based on eigenpairs of Hilbert–Schmidt operators obtained from a Green’s function representation for solutions of a linearization of the Hartree equations, d2yi(r)/dr2 −[li(li+1)/r2]yi(r)+(2z/r) yi(r) −(2/r) ΣNj=1,j≠iYj(r) yi(r) =λ2iyi(r), Yi(r) =ℱr0y2i(s) ds+rℱ∞0s−1y2i(s) ds, yi(0) =0, yi(∞) =0, ℱ∞0y2i(s) ds=1, i=1,2,...,N, establishes existence of solutions to the Hartree equations and the sequence of eigenpairs generated converge subsequentially to a solution. In the case of the helium atom, for which we show some computational results, sequential convergence is obtained. Due to the Hilbert–Schmidt nature of the operators involved, the iterative method is implementable with Galerkin methods.
Nth order perturbation theory for hydrogen
Authors: Kelsey Edward J. , Macek Joseph
Published: March 2003

This paper presents a simple reformulation of second order perturbation theory for hydrogen. We calculate first the perturbed wavefunction and then the perturbed matrix element. This procedure is repeated to obtain the nth order matrix element in terms of n−1 integrals. The parameters in the nth order matrix element are defined recursively. Schwinger’s representation of the Coulomb Green’s function follows immediately from our expression for the second order matrix element.
Propagation through an anisotropic random medium. An integro–differential formulation
Authors: Beran M. J. , McCoy J. J.
Published: March 2003

In a previous paper [J. Math. Phys. 15, 1901 (1975)] we derived an equation governing the mutual coherence function, {Γ̂}, of an initial plane wave signal propagating in an anisotropic random medium. In Eq. (49) of that paper we made a strong narrow-angle approximation which allowed us to derive an ordinary differential equation for {Γ̂}. Here we derive an integro–differential equation for {Γ̂} in which this approximation is not made. We show that for the horizontal scattering cases considered in the previous paper the approximation is valid. The vertical spectrum, however, is changed somewhat.
New representation of the Tomimatsu–Sato solution
Authors: Ernst Frederick J.
Published: March 2003

We devise a new representation of the simplest Tomimatsu–Sato solution of Einstein’s vacuum field equations. This permits us to dispose of the previously troublesome ’’directional singularities’’ through the introduction of an advanced (or retarded) time coordinate. In the neighborhood of the locations in question the T–S space is shown to possess a Killing tensor of valence two, which allows us to solve the geodesic problem in this neighborhood completely. Finally, we present for future analysis a plausible toroidal model of the material source for the T–S solution.
On the equivalence of nonrelativistic quantum mechanics based upon sharp and fuzzy measurements
Authors: Ali S. Twareque , Doebner H. D.
Published: March 2003

Starting from the idea that physical measurements may have residual imprecisions, the possibility of replacing the nonrelativistic, three-dimensional configuration space by a so-called fuzzy configuration space, having an isomorphic Borel structure, is discussed. A quantization procedure with respect to such a space is developed, and the invariance of nonrelativistic quantum mechanics under such Borel isomorphisms is exploited to prove the equivalence of this quantization procedure to the usual quantization procedure on a fuzzy-free configuration space. Further, any Galilean invariant dynamics is shown to be insensitive to such imprecisions in the measurements of position and momentum.
Remarks on conformal space
Authors: Bayen F. , Flato M.
Published: March 2003

Some remarks about a recent article dealing with Maxwell equations written on conformal space M4c are presented. The relevance of the manifold M4c in conformal physics, the cotransformation of fields under the conformal group, and the presence of external currents in Maxwell equations are discussed. A simple proof of the conformal covariance of a linear gauge condition for Maxwell equations is then exhibited.
Canonical symmetrization for the unitary bases. II. Boson and fermion bases
Authors: Patterson Chris W. , Harter William G.
Published: March 2003

The canonical Weyl basis described in Paper I is generalized to give a boson and fermion calculus which generates the symmetric and antisymmetric bases of U(nm) respectively contained in the irreducible bases of U(n) ×U(m). The boson calculus may be used to find the multiplicity free Clebsch–Gordan coefficients of U(n).
A crossed-channel expansion of a conformal invariant scattering amplitude
Authors: Meuldermans R.
Published: March 2003

We assume that a state out of a representation space of a irreducible representation of SO(4,2), in particular the E+(massless) and D+(massive) series of representation, fully describes a particle. Then, considering conformal invariant scattering amplitudes, we set up a crossed-channel expansion of the t matrix for elastic two-body scattering, by calculating the Clebsch–Gordan coefficients involved. The essential point is the reduction of the direct products E+×E− and D+×E−.
Modulational instability of cnoidal wave solutions of the modified Korteweg–de Vries equation
Authors: Driscoll C. F. , O’Neil T. M.
Published: March 2003

The stability of cnoidal wavetrain solutions of the modified Korteweg–de Vries equation is analyzed using Whitham’s modulational theory. The cnoidal waves are solutions of an oscillator equation obtained by twice integrating the modified Korteweg–de Vries equation. The stability of the cnoidal waves is determined by the roots of the polynomial in the oscillator equation. For real roots the waves are stable, whereas for complex roots the waves are unstable.
The energy levels of the one-dimensional potential well V (X) =a‖X‖ calculated by means of certain phase-integral approximations
Authors: Thidé Bo
Published: March 2003

The eigenvalue problem of the one-dimensional potential well V (X) =a‖X‖ is solved by means of certain higher-order phase-integral approximations. The purpose of this paper is to demonstrate numerically the applicability and accuracy of these approximations (which are related to, but not identical to, the higher-order JWKB approximations) and, therefore, a comparison is made with exact results. An upper bound for the absolute error in the first-order approximation is calculated analytically and found to be in accordance with the actual numerical results which are displayed in a table.
Coupled gravitational and electromagnetic perturbations around a charged black hole
Authors: Lee Chul Hoon
Published: March 2003

Coupled gravitational and electromagnetic perturbation equations are derived in the electrovacuum space around a charged rotating black hole using the Newman–Penrose formalism. When restricted to the nonrotating case, the equations separate in Schwarzschild coordinates. The asymptotic solutions at infinity and on the event horizon are obtained. In the coupled scattering of the electromagnetic and the gravitational waves on a Reissner–Nordström black hole, it is shown that the net energy flux is radially inward.
Multiplicative renormalization of composite operators
Authors: de Vega H. J. , Schaposnik F.
Published: March 2003

We study composite operators with the aid of dimensional regularization. Using Zimmermann ’’normal product algorithm,’’ we obtain a simple formula for any normal product in renormalized field theory and discuss some of its properties.
On generation of solutions of Einstein’s equations
Authors: Hoenselaers C.
Published: March 2003

The equations for two-Killing-vector solutions of Einstein’s equations are looked at from the point of view of the Lagrangian formalism. The original Lagrangian, written in terms of the metric, will undergo a Legendre transformation leading to the Ernst Lagrangian and from there by the same procedure to others. So one gets a sequence of Lagrangians, and by performing an invariance transformation at each step one obtains new solutions of Einstein’s equations. A convenient method for dealing with Lagrangians quadratic in the velocities is outlined.
Homothetic and conformal motions in spacelike slices of solutions of Einstein’s equations
Authors: Berger Beverly K.
Published: March 2003

Components of Killing’s equation are used to obtain constraints satisfied in a spacelike hypersurface by the intrinsic metric and extrinsic curvature in the presence of a spacetime conformal motion for a solution of Einstein’s equations. If the conformal motion is either a homothetic motion or a motion, it is shown that these Killing constraints are preserved by the Einstein evolution equations. It is then shown that the generator of the homothetic motion (homothetic Killing vector) can be constructed if the Killing constraints are satisfied by a set of initial data. It is shown that a homothetic motion in the intrinsic metric is a spacetime homothetic motion if the extrinsic curvature is transformed correctly under the spatial homothetic motion. Further restrictions on a proper conformal motion due to the fact that it is not identically a curvature collineation are obtained. Restrictions on the matter–stress–energy tensor are discussed. Examples are presented.
Measure-theoretic representations of the SU(2) ⊗SU(2) current algebra with PCAC
Authors: Haba Zbigniew
Published: March 2003

The SU(2) ⊗SU(2) current algebra, with scalar fields φa σ describing PCAC, is considered. The algebra is exponentiated in order to get a group 𝒞. These exponentiated currents are represented in the space ℒ2μ of functions defined on 𝒮′ (Gel’fand–Vilenkin formalism). The unitary representation is described by a quasi-invariant measure μ on 𝒮′. Then, the representation of the SU(2) ⊗SU(2) current algebra extended by the fields can be obtained, with currents and fields defined as self-adjoint operators with a dense invariant domain in Hilbert space. The Gaussian measure μB gives an example of a measure describing representations of the SU(2) ⊗SU(2) current algebra with conserved currents. Such a theory is nonrelativistic (ultralocal). In order to obtain chiral symmetry breaking and PCAC, the Gaussian measure is not sufficient and should be modified by the singular interaction factor giving a new measure dμ1=limh→1 {ℱ exp[−HI(h)]dμB}−1 exp[−HI(h)]dμB. This model is discussed, and the existence of the charges is shown.
Pseudo white noises: δ-correlated processes with finite memory
Authors: Brissaud A. , Léorat J. , Mazure A.
Published: March 2003

Stochastic processes are constructed from the trajectories of mutually independent particles subject to a central potential, and their characteristic functional is given. For a wide class of such processes, time dependence of the correlation function is found to follow a power law. Particular attention is paid to finite memory processes whose distribution function is a Dirac δ distribution, and an example of δ′ correlated processes is also given.
On space–time Killing tensors with a Segre characteristic [(11)(11)]
Authors: Hauser I. , Malhiot R. J.
Published: March 2003

We consider the set of all space–times which admit a Killing tensor Kαβ whose Segre characteristic is [(11)(11)] and whose eigenvalues λ1 and λ2 satisfy the condition that dλ1 - dλ2 is not null. We prove that there locally exist scalar fields φ3, φ4 such that λ1, λ2, φ3, φ4 constitute a chart, and dλ1⋅dλ2 =dλi⋅dφr=0 for i=1, 2 and r=3, 4. Also, relative to this coordinate system, the metric has the same general form as Carter’s Hamilton–Jacobi separable metric except that his arbitrary functions of λi are replaced by functions of λi, φ3, φ4. If Rαβ(∇αλ1)(∇βλ2) =0, there exists a two parameter Abelian group of isometries which commute with Kαβ; also (φ3,φ4) can be chosen so that ∂/∂φ3 and ∂/∂φ4 are the Killing vectors. Rαβ(∇αλ1)(∇βλ2) =0 is necessary and sufficient for Schrödinger equation separability in case (a) of Carter. A Newtonian analog of our results is discussed.
Cross between Born and WKB approximations: Variational solutions of nonlinear forms of the Schrödinger equation
Authors: Rau A. R. P.
Published: March 2003

Dashen, taking as his starting point the fact that the Born approximation for the phase shift has a wider range of applicability than would be expected from the usual criterion that the phase shift should be small, investigated a nonlinear form of the ’’one-dimensional’’ Schrödinger equation and arrived at an expression which can best be described as ’’a cross between the Born and WKB approximations.’’ This expression for the phase shift reduces to the Born result even when the phase shift is not small. We investigate this result from a different point of view and establish that the Dashen expression is a variational principle for the nonlinear equation considered by him. This serves to explain the accuracy of the approximation. We also construct similar variational expressions for the more usual nonlinear Riccati equation and contrast it with the WKB series solution and recently proposed alternatives to this series. Contact is made between the techniques of functional analysis that Dashen used in arriving at his result and the unified formulation of variational principles that we adopt. An appendix deals with the principles of ’’invariant imbedding’’ in the particular context of such nonlinear versions of the one-dimensional Schrödinger equation.
Inverse scattering problems in absorbing media
Authors: Jaulent M.
Published: March 2003

We study inverse scattering problems which occur in various fields of physics (transmission lines theory, electromagnetism, elasticity theory), and in which the inhomogeneous media considered are absorbing. We suppose that waves propagate in a z direction from z=0 to z=∞ and are totally reflected at z=0, the input data being the values of the reflection coefficient to the right S+(k) for all frequencies k (note that the case where waves propagate from z=−∞ to z=∞ can be studied in a similar way). These problems are reduced to an inverse scattering problem for the radial s-wave Schrödinger equation with an energy-dependent potential. The case where S+(k) is close to 1 and the case where the absorption is weak are specially investigated, and a class of exactly solvable examples is given.
SU(2)  × SU(2) scalars in the enveloping algebra of SU(4)
Authors: Quesne C.
Published: March 2003

We build an integrity basis for the SU(2)  × SU(2) scalars belonging to the enveloping algebra of SU(4). We prove that it contains seven independent invariants in addition to the Casimir operators of SU(4) and SU(2)  × SU(2). We form a complete set of commuting operators by adding to the latter two linear combinations of the former the operators Ω and Φ first introduced by Moshinsky and Nagel. We then solve the state labeling problem that occurs in the reduction SU(4)  ⊆ SU(2)  × SU(2) by diagonalizing simultaneously Ω and Φ. Their eigenvalues are calculated numerically in all irreducible representations of SU(4) that are encountered in light nuclei up to and including the s–d shell. Finally we build the propagation operators for the widths of the fixed supermultiplet, spin and isospin spectral distributions by taking appropriate linear combinations of SU(2)  × SU(2) invariants of degree less than or equal to four, and we tabulate the averages of these operators in the above-mentioned irreducible representations of SU(4).
Asymptotic radiation from spinning charged particles
Authors: Cohn J. , Wiebe H.
Published: March 2003

A manifestly covariant expression for the asymptotic energy–momentum and angular momentum emitted by a charged spinning particle in arbitrary motion is found. A center of energy theorem is discussed and it is also shown that, for spinning particles, the radiation rate is not an invariant.
Exact closed evolution equation for the electron density operator averaged over impurity configurations
Authors: Fujita Shigeji
Published: March 2003

The exact Markoffian evolution equation for the electron density operator n (t) averaged over impurity configurations (describing a grand ensemble of non-interacting electrons in the potential fields of impurities fixed in space) is not closed. The interaction term, that is, the integral involving the electron-impurity interaction and the electron-impurity density operator is analyzed with the aid of diagrams after its evolution operator is expanded in perturbation and its initial density operators are expanded in terms of correlation operators. A closed non-Markoffian equation for n (t) is obtained without introducing any approximations. This equation contains infinite sets of collision and initial correlation terms which are most conveniently represented by connected diagrams, and which can be expressed in terms of n (t) and initial correlation operators arbitrarily given. The equation is found to be identical with the closed evolution equation obtained earlier in the fixed-particle-number ensemble theory with the bulk limit.
Sum rules for the optical constants
Authors: King Frederick W.
Published: March 2003

A number of sum rules for the optical constants, in particular, the refractive index of a nonconducting medium, are obtained. Some of the sum rule constraints are highly damped for large frequencies, exponentially in one particular case. Formal integral relationships for the index of refraction at complex frequencies are presented. Sum rules based on known experimental points for which n (ω)−1 has zeros are indicated. An outline of a modified derivation of some recently presented sum rules for the optical constants is given.
Representations of the universal covering group of SU(1,1) and their bilinear and trilinear invariant forms
Authors: Rühl W. , Yunn B. C.
Published: March 2003

The unitary irreducible and many nonunitary representations of the universal covering group of SU(1,1) are given in a realization on certain spaces of functions. We discuss intertwining operators for these representations and their connection with the discrete series. The tensor product decomposition is performed by means of an integral transformation. A completeness relation for these integral kernels is derived.
Lagrange multipliers and gravitational theory
Authors: Safko J. L. , Elston F.
Published: March 2003

The Lagrange multiplier version of the Palatini variational principle is extended to nonlinear Lagrangians, where it is shown in the case of the quadratic Lagrangians, as expected, that this version of the Palatini approach is equivalent to the Hilbert variational method. The (nonvanishing) Lagrange multipliers for the quadratic Lagrangians are then explicitly obtained in covariant form. It is then pointed out how the Lagrange multiplier approach in the language of the (3+1) -formalism developed by Arnowitt, Deser, and Misner permits the recasting of the equations of motion for quadratic and general higher-order Lagrangians into the ADM canonical formalism. In general without the Lagrange multiplier approach, the higher order ADM problem could not be solved. This is done explicitly for the simplest quadratic Lagrangian (g1/2R2) as an example.
Quantum mechanics on topological networks
Authors: Budgor Aaron B.
Published: March 2003

A quantum mechanical model of electrons on a network which has been used to obtain the line spectra of conjugated organic molecules and the band structure for various solid state systems is shown to be intimately connected with the homology and cohomology sequences of the algebraic topology of 1-complexes. Thus, the remarkable qualitative agreement of these models to experiment implies that those calculated physical quantities are structural quantities. Quantum mechanical conservation laws analogous to Kirchhoff’s electrical conservation laws are derived by variational methods applied to the system’s Lagrangian. The topology is shown to enforce energy conservation on the network.
A ’’nonstandard’’ approach to the thermodynamic limit. II. Weakly tempered potentials and neutral Coulomb systems
Authors: Ostebee A. , Gambardella P. , Dresden M.
Published: March 2003

Nonstandard analysis is used to prove the existence and uniqueness of the thermodynamic limit for a number of physical systems. Included are neutral Coulomb systems and systems described by weakly tempered potentials. The basic feature of the method is the application of the transfer theorem of nonstandard analysis to the inequalities for the free energy for finite systems. Nonstandard transcriptions of packing theorems are also needed. The nonstandard procedure has the great advantage of providing an explicit separation of the physical and geometric elements in the proof. This allows a unified treatment of several distinct cases, so that the demonstrations—in spite of unavoidable technical details—become physically intuitive and mathematically straightforward.
Quantization from the algebraic viewpoint
Authors: Abellanas L. , Martinez Alonso L.
Published: March 2003

We use the Weyl quantization W in a general context valid for any finite-dimensional Lie algebra G, to derive an explicit formula for (P1,P2) ≡W−1([W (P1),W (P2)]), P1,P2 polynomials. In the particular case of the Heisenberg Lie algebra, this formula reduces to the familiar Moyal bracket.
Symmetry and invariance properties of the Boltzmann equation on different groups
Authors: Massot J. N. , Bacis R.
Published: March 2003

The introduction of the group theory in the treatment of the Boltzmann equation shows the reducibility of the collision integral operator on the invariant subspaces of Klein V or SO2 group. Especially we prove the equality of matrices representing the collision integral operator between inequivalent subspaces first in its linear form and then in its general form. These results are finally expanded to the full Boltzmann equation when we consider its properties as a whole in the phase space (ℰr×ℰv). This brings back Boltzmann equation following the Chapmann–Enskog process to the differential equation system depending solely on the variable ‖r‖. The examination of the Boltzmann equation symmetries allows us to obtain the selection rules which lead to an important simplification in theoretical as well as numerical calculations of the distribution function.
One-component plasma in 2+ε dimensions
Authors: Deutsch C.
Published: March 2003

The one-component plasma (ocp) model with neutralizing background is extended to real dimensionality ν=2+ε with −2⩽ε⩽2. The equilibrium properties (pair correlation and thermodynamic functions) investigated within the Debye approximation, up to the second-order in the plasma parameter e2/kBTλεD, with the aid of the Wilson quadratures, interpolate between two- and three-dimensional results for 0<ε<1, and extend the ν=3 behavior to all ν⩽2. The dimensionality ν=2 is shown to play a special role. Quantum diffraction corrections are included in the high temperature limit through a temperature-dependent effective Coulomb interaction. As a by-product, the particle diffusion coefficient (Bohm) of the strongly magnetized two-component plasma taken in the fluid limit may be given a finite volume-independent expression in the thermodynamic limit when ν=2, provided due attention is paid to the Tauberian properties of the Coulomb potential for −2⩽ε⩽0.
Stability and instability conditions for nonlinear evolutional equations in Hilbert spaces
Authors: Wang P. K. C.
Published: March 2003

Sufficient conditions for stability, global asymptotic stability, and explosive instability are established for a class of nonlinear evolutional equations defined in Hilbert spaces by using certain relations between an abstract function and its Gateaux differential. These results are applied to specific forms of nonlinear evolutional equations arising from physics, in particular, a finite-dimensional system of complex ordinary differential equations, functional differential equations, and systems of complex partial differential equations describing nonlinear diffusion or wave phenomena.
Exact dynamics of a model for a three-level atom
Authors: Davidson Russell , Kozak John J.
Published: March 2003

In this paper we investigate the dynamics of a model for a three-level atom in interaction with a radiation field. The exact solution to the spontaneous-emission problem is derived using methods developed earlier by the authors, and expressions are obtained for the probabilities of the atom’s being in the first or second excited states at any time t. For the special case that the strengths of the coupling between each of the excited states and the λth mode of the field are proportional, detailed conclusions can be drawn concerning the effects of such factors as system size, coupling function, and level splitting on the temporal evolution of the system. The evolution of excited quantum systems having one versus two modes of decay to the ground state is also compared, and similarities and differences in the temporal behavior are noted. Finally the relevance of the theory presented in this paper to experimental problems in radiation chemistry and physics is indicated in our concluding remarks.
Derivation of an exact spectral density transport equation for a nonstationary scattering medium
Authors: Besieris Ioannis M.
Published: March 2003

Within the framework of the quasioptical description and the pure Markovian random process approximation, an exact kinetic equation is derived for the spectral density function in the case of wave propagation in a nondispersive medium characterized by large-scale space–time fluctuations. Also, a quantity, called the degree of coherence function, is defined as a quantitative measure of the irreversible effects of randomness.
Closed first- and second-order moment equations for stochastic nonlinear problems with applications to model hydrodynamic and Vlasov-plasma turbulence
Authors: Besieris Ioannis M. , Stasiak Wojciech B.
Published: March 2003

Working along the lines of a procedure outlined by Keller, a technique is developed for deriving closed first- and second-order moment equations for a general class of stochastic nonlinear equations by performing a renormalization at the level of the second moment. The work of Weinstock, as reformulated recently by Balescu and Misguich, is extended in order to obtain two equivalent representations for the second moment using an exact, nonperturbative, statistical approach. These general results, when specialized to the weak-coupling limit, lead to a complete set of closed equations for the first two moments within the framework of an approximation corresponding to Kraichnan’s direct-interaction approximation. Additional restrictions result in a self-consistent set of equations for the first two moments in the stochastic quasilinear approximation. Finally, the technique is illustrated by considering its application to two specific physical problems: (1) model hydrodynamic turbulence and (2) Vlasov-plasma turbulence in the presence of an external stochastic electric field.
A continuum theory of deformable ferrimagnetic bodies. I. Field equations
Authors: Maugin Gérard A.
Published: March 2003

The first part of this work concerns a thorough study of both global and local field equations that govern deformable (not necessarily linear elastic) ferrimagnets and antiferromagnets from a phenomenological viewpoint. The main tool used is a generalized version of d’Alembert’s principle, valid for both reversible and irreversible phenomena, simultaneously with the invariance requirement provided by the so-called objectivity and applied a priori to generalized internal forces which represent the various interactions. All interactions taking place in such media are thus given a phenomenological description and are introduced via the duality inherent in the method. The development follows a rational and deductive mathematical scheme in which the notion of topological linear space of velocities plays a predominant role, so that particular cases follow by selecting the appropriate member of this space. In the following companion paper the allied thermodynamics and a thorough discussion of the relevant constitutive equations that follow therefrom are given. The formulation so obtained will allow the consideration of slight perturbations superimposed on bias fields.
Inverse wave propagation in an inhomogeneous waveguide
Authors: DeSanto John A.
Published: March 2003

A solution is given for the problem of inverse propagation of a scalar wave in inhomogeneous rectangular two-dimensional waveguide. The sound speed is assumed to vary in depth and inverse propagation means the calculation of the field at range x1 in terms of the field at range x2 where x2≳x1. The method is analogous to that used by Wolf, Shewell, and Lalor for the inverse diffraction problem in a homogeneous half-space. It is found that the field at x1 can be expressed in terms of two integrals over the field at x2. The kernel of the first integral is bounded and expresses physically the result at x1 of the waves at x2 reversing their direction of propagation and decay, i.e., they now propagate and decay in the direction of x1. A reciprocity relation for this term is possible. The kernel of the second integral is singular and expresses the mathematical fact of the residual effect of the evanescent waves at x1 as they reverse their direction at x2 and now grow exponentially. Consequences of the neglect of this singular term are discussed.
Off-shell Jost function and T matrix for the Woods–Saxon potential
Authors: Roy M. N. Sinha , Talukdar B. , Chattarji D.
Published: March 2003

The s-wave van Leeuwan and Reiner equation for the Woods–Saxon potential is solved. Analytical expressions for the off-shell Jost solution and Jost function are derived. The results are used to obtain the T matrix.
Bifurcation properties of Dicke Hamiltonians
Authors: Gilmore R. , Bowden C. M.
Published: March 2003

A variation in the coupled order parameter treatment of Dicke Hamiltonians in thermodynamic equilibrium is presented. The Hamiltonian is linearized by introducing disposable c-number parameters. These parameters are chosen to minimize the resulting free energy. This requirement leads to a system of coupled nonlinear equations whose bifurcation properties are studied. The solution branches are labelled by the inertia of the free energy stability matrix. We prove that the parameters on the solution branch which provide the global minimum free energy also produce a linearized Hamiltonian thermodynamically equivalent to the original Hamiltonian provided only a finite number of field modes are present. This method is used to discuss the bifurcation and stability properties of the Dicke Hamiltonian with A2 and counterrotating terms. We also discuss why the phase transition disappears in the presence of external currents or fields. We show how an internal gauge destroying mechanism may lead to the persistence of the phase transition even in the presence of external coupling. The method is used to discuss the phase transitions and multiplicity of ordered state phases in multilevel molecular systems. We also present a simple method for determining whether an external source will or will not destroy a second order phase transition and discuss the conditions under which such models may exhibit first order phase transitions.
Classification of all simple graded Lie algebras whose Lie algebra is reductive. I
Authors: Scheunert M. , Nahm W. , Rittenberg V.
Published: March 2003

All simple graded Lie algebras whose Lie algebra is reductive are presented, and the classification theorem is proved. Several theorems which may show up to be useful in a different context are also included.
How to calculate the grand partition function in the uncorrelated jet model
Authors: Gasser J.
Published: March 2003

We present a new technique for calculating the grand partition function and all quantities of physical interest in the uncorrelated jet model. The method, which is also valid in the large-pT region, consists of the numerical evaluation of the appropriate integral representation in the complex plane. We analyze in detail the difficulties associated with this approach and show how to overcome them. The numerical results are checked with a new high energy expansion for the grand partition function.
On the implementability of local gauge transformations in a theory with localized states
Authors: Leveille J. P. , Roman P.
Published: March 2003

A conflict between unitary implementability of local gauge transformations (kind one) on the one hand and certain properties of sets of localized states on the other is deduced in the axiomatic framework of relativistic local quantum field theory.
On the existence of localized solutions in nonlinear chiral theories
Authors: Hietarinta Jarmo
Published: March 2003

We study the existence of localized solutions to theories based on Weinberg’s nonlinear realization of chiral SU(2) ⊗SU(2). The analysis is done by using specific variations of the action integral and then checking the ensuing global conditions. The following cases are studied: (i) π fields only and without time dependence, (ii) π fields with simple time dependence, (iii) π fields coupled to gauge fields, (iv) the above with certain chiral symmetry breaking potentials. We find that only in certain special cases could there be localized solutions. In most cases the intrinsic nonlinearity of the system does not seem to be enough to guarantee their existence.
Subgroups of the Euclidean group and symmetry breaking in nonrelativistic quantum mechanics
Authors: Beckers J. , Patera J. , Perroud M. , Winternitz P.
Published: March 2003

A systematic study of explicit symmetry breaking in the nonrelativistic quantum mechanics of a scalar and a spinor particle is presented. The free Schrödinger (or Pauli) equation is invariant under the Euclidean group E(3); an external field will break this symmetry to a lower one. We first find all continuous subgroups of E(3) and then for each subgroup construct the most general (within certain restrictions) external field that breaks the symmetry from E(3) to the corresponding subgroup. For a scalar particle the interaction term is assumed to be of the form V (r)+A(r)P, where P is the momentum, i.e., it involves an arbitrary scalar and vector potential. For a spinor particle it is of the form V (r)+A(r)P +B(r) σ+Mik(r) σiPk (σi are the Pauli matrices). A one-to-one correspondence between subgroups of E(3) and classes of ’’symmetry breaking potentials’’ is established. The remaining subgroup symmetry is then used to solve or at least simplify the obtained Schrödinger equation. The existence of a one-dimensional invariance group (for a particle in a field) leads to the partial separation of variables and determines the functional dependence of the wavefunction on one variable. A two-dimensional group implies the complete separation of variables and the functional dependence on two variables. A higher dimensional invariance group implies the separation of variables in one or more systems of coordinates and in some cases specifies the wavefunction completely.
Clebsch potentials in the theory of electromagnetic fields admitting electric and magnetic charge distributions
Authors: Rund Hanno
Published: March 2003

Any skew-symmetric tensor field on a four-dimensional pseudo-Riemannian space V4 admits a representation in terms of Clebsch potentials and their derivatives. Since the usual 4−potential representation of the electromagnetic field tensor of classical electrodynamics breaks down in the presence of magnetic charges, these Clebsch potentials are treated as the field variables of an invariant variational principle. The resulting Euler–Lagrange equations determine not only a useful representation of the electromagnetic field tensor (in the presence of magnetic charges), but also give rise to Maxwell-type field equations. The associated Lagrange density defines a unique energy–momentum tensor entirely on the basis of invariance consideration. A generalized variational principle is postulated, whose Euler–Lagrange equations specify the behavior of both the electromagnetic field tensor and the metric tensor of V4. These are generalized Einstein–Maxwell equations. For the case of a spherically symmetric line-element and a static electromagnetic field an explicit solution of these equations is found which generalizes the well known Reissner–Nordström metric. In the course of the construction of this solution the magnetic charge of the central mass appears naturally as a constant of integration of the associated differential equations for the Clebsch potentials. The equations of motion of a test particle in an external electromagnetic field are also deduced from a variational principle; subject to fairly weak restrictions, the expected generalization of the classical Lorentz force emerges from this analysis.
Is the Wick square infinitely divisible?
Authors: Baumann Klaus , Hegerfeldt Gerhard C.
Published: March 2003

We derive a sort of Lévy–Khintchine formula for the Wick square of the Euclidean free field in two and three dimensions and use it to show that the Euclidean Wick square is infinitely divisible. On the other hand, by analyzing the truncated four-point function we prove that the relativistic Wick square is not infinitely divisible in any space–time dimension.
Structural stability of the phase transition in Dicke-like models
Authors: Gilmore R.
Published: March 2003

The free energy for a general class of Dicke models is computed and expressed simply as the minimum value of a potential function Φ = (E−TS)/N. The function E/N is the image of the Hamiltonian under the quantum–classical correspondence effected by the atomic and field coherent state representations, and the function S is the logarithm of an SU(2) multiplicity factor. The structural stability of the second order phase transition under changes in the functional form of the Hamiltonian is determined by searching for stability changeovers along the thermal critical branch of Φ. The necessary condition for the presence of a second order phase transition is completely determined by the canonical kernel of the Hamiltonian. The sufficient condition is that a first order phase transition not occur at higher temperature. The critical temperature for a second order phase transition is given by a gap equation of Hepp–Lieb type.
On integral relations for invariants constructed from three Riemann tensors and their applications in quantum gravity
Authors: van Nieuwenhuizen P. , Wu C. C.
Published: March 2003

The lowest order quantum corrections to pure gravitation are finite because there exists an integral relation between products of two Riemann tensors (the Gauss–Bonnet theorem). In this article several algebraic and integral relations are determined between products of three Riemann tensors in four- and six-dimensional spacetime. In both cases, one is left with only one invariant when Rμν=0, viz., ℱ (−g)1/2(RαβμνRμνρσRρσ  αβ).It is explicitly shown that this invariant does not vanish, even when Rμν=0. Consequently, the two-loop quantum corrections to pure gravitation will only be finite if, due to miraculous cancellation, the coefficient of this invariant vanishes.
Metastability and the analytic continuation of eigenvalues
Authors: Newman C. M. , Schulman L. S.
Published: March 2003

A metastable analytic continuation of the Ising model free energy is conjectured to follow from certain analyticity properties of the eigenvalues of the transfer matrix. The resulting description of metastability is applicable to any system whose phase transition is associated with eigenvalue degeneracy. Motivation for the conjectures concerning the Ising model is provided by the study of eigenvalue continuation in several simpler systems.
Factored irreducible symmetry operators
Authors: Folland N. O.
Published: March 2003

Irreducible symmetry operators (ISO’s) are defined and their properties are displayed. A method for the systematic construction of ISO’s in the form of products of interchangeable factors is described. The key to the method is a set of conditions for directly testing for the irreducibility of induced symmetry operators formulated in terms of the operators themselves. Detailed examples are presented for the tetrahedral group and double group. The tetrahedral double group provides an example in which the induction process in its simplest form fails, but which does yield to a modification of the induction techniques.
Nonexistence theorem for spherically asymmetric solutions of the Fermi–Thomas model of atoms and ions
Authors: Eimerl David
Published: March 2003

It is proved that there are no spherically asymmetric solutions of the Fermi–Thomas equation ∇2(u/r) = (u/r)3/2ξ, where ξ is unity inside the surface u=0, and zero otherwise. This is proved by showing that the boundary conditions on u at the origin and on the surface at infinity necessarily lead to unphysical discontinuities in u at the surface u=0, except for the case where u is spherically symmetric. A simple, only approximately statistical model is presented, which may replace the Fermi–Thomas model for asymmetric systems.
Nonstationary multiple scattering
Authors: Wang A. P.
Published: March 2003

This paper is devoted to the abstract formulation of the general nonstationary multiple scattering problem in radiative transfer. We consider the linear operators on curved surfaces. Therefore, the problem is attacked from the unified and general point of view. Special geometric considered are spherical shells and slabs. Special cases lead to stationary, instantaneous, and time invariant cases. The extension from stationary to nonstationary involves the distribution theory and the concept of nonpredictive operators. Many well−known physical problems in astrophysics are solved in the unified way.
Gleason measures on infinite tensor products of Hilbert spaces
Authors: Christensen Mark J.
Published: March 2003

Nowak [Bull. Acad. Pol. Sci. Ser. Sci. Math. Astron. Phys. 22, 393–5 (1974)] has given an example of a consistent (in the sense of Kolmogorov) family of Gleason measures [A. M. Gleason, J. Math. Mech. 6, 885–94 (1957)] {mn} defined over ⊗ni=1Hi which do not extend to a Gleason measure on ⊙∞i=1 ΦHi for a given construction of the infinite tensor product. In this paper we show: (1) In the example of Nowak it is not necessary to assume, as is done, that the Hi are infinite dimensional. (2) That every consistent family developed from pure states, which is the type considered by Nowak, extends over the complete infinite tensor product of von Neumann [Compositio. Math. 6, 1–77 (1938)]. (3) Even if each Hi is two-dimensional and the complete infinite tensor product of von Neumann is used, it is possible to give a simple counterexample to the conjecture that every consistent family of Gleason measures extends by the use of nonpure states.
Hamiltonian dynamics in symplectic phase space and Nambu’s formulation of mechanics
Authors: Oliveira Colber G.
Published: March 2003

Starting from the formulation of the Hamiltonian dynamics in phase spaces with a symplectic structure, we show that it is possible to formulate the mechanics recently proposed by Nambu by means of a mapping from the even-dimensional Hamiltonian phase space to a ’’phase space’’ which displays all properties of Nambu’s theory. The difficulties concerning the process of quantization of Nambu’s theory can be presently discussed at classical level by means of a suitable interpretation of the meaning of the several Hamiltonians of the theory. Some examples are given.
Graded Lie algebras: Generalization of Hermitian representations
Authors: Scheunert M. , Nahm W. , Rittenberg V.
Published: March 2003

Hermitian representations play a fundamental role in the study of the representations of simple Lie algebras. We show how this concept generalizes for classical simple graded Lie algebras. Star and grade star representations are defined through adjoint and grade adjoint operations. Each algebra admits at most two adjoint and two grade adjoint operations (we list the various possibilities for all classical simple graded Lie algebras). To each adjoint (grade adjoint) operation corresponds a class of star (grade star) representations. The tensor product of two star representations belonging to one class is completely reducible into irreducible representations belonging to the same class. This property is very useful since in general the finite-dimensional representations of classical simple graded Lie algebras are not completely reducible.