bluuebunny/crossref_metadata_2025 huggingface dataset:
On some features of differentiable probabilities; a new viewpoint in physics
Authors: Collins R. Eugene
Published: July 2002

It is shown that imposition of the requirement of differentiability on a probability distribution imposes a structure on the probability formalism having the appearance of physical theory. Both the classical and quantum mechanical descriptions for the motion of a single point particle as consequences of describing the motion in terms of a differentiable probability density are exhibited. It is shown that the particle must appear as acted upon by a force having the form of the Lorentz force.
Dynamics and kinematics of reciprocal diffusions
Authors: Levy Bernard C. , Krener Arthur J.
Published: July 2002

This paper examines the dynamics and kinematics of reciprocal diffusions. Reciprocal processes were introduced by Bernstein in 1932, and were later studied in detail by Jamison. The reciprocal diffusions are constructed here by specifying their finite joint densities in terms of the Green’s function of a general heat operator, and an end-point density. A path integral interpretation of the heat operator Green’s function is provided, which is used to derive a stochastic form of Newton’s law, as well as a conditional distribution for the velocity of a diffusing particle given its position. These results are then employed to derive two conservation laws expressing the conservation of mass and momentum. The conservation laws do not form a closed system of equations, in general, except for two subclasses of reciprocal diffusions, the Markov and quantum diffusions.
A simple differential operator realization of the super-rotation algebra
Authors: Daumens Michel , Noirot Yves
Published: July 2002

The super-rotation algebra is realized as differential operators acting on functions defined on the E(1/2) superspace.
Zero curvature conditions and conformal covariance
Authors: Akemann G. , Grimm R.
Published: July 2002

Two-dimensional zero curvature conditions with special emphasis on conformal properties are investigated in detail and the appearance of covariant higher order differential operators constructed in terms of a projective connection is elucidated. The analysis is based on the Kostant decomposition of simple Lie algebras in terms of representations with respect to their ‘‘principal’’ SL(2) subalgebra.
The planar isosceles problem for Maneff’s gravitational law
Authors: Diacu Florin N.
Published: July 2002

Maneff’s gravitational law explains, with a very good approximation, the perihelion advance of the inner planets as well as the orbit of the Moon. Here the invariant set of planar isosceles solutions of the three-body problem for Maneff’s model is studied. The application of Maneff’s law in atomic physics provides, in the case of the isosceles problem, a model with relativistic correction for the helium atom. It is shown that every solution leads to a collision singularity and consequently has no periodic orbits. Using McGehee’s technique the triple-collision singularity is blown up and the binary-collision solutions are regularized. The flow on the collision manifold is shown to be nongradientlike and the set of collision/ejection solutions is described. The center manifold and the block-regularization problems are analyzed. The network of homoclinic and heteroclinic orbits is further discussed. Finally an anisotropic model having the property that the flow on the collision manifold changes drastically when the mass parameter is varied is studied, giving rise to a subcritical pitchfork bifurcation of the equilibria.
On Gürses’s symmetries of the Einstein equations
Authors: Ernst Frederick J. , Hauser Isidore
Published: July 2002

The symmetries of Gürses [Phys. Rev. Lett. 70, 367 (1993)] are reformulated in a more abstract, more geometrical manner. The type (b) transformation of Gürses is related to a diffeomorphism of the differentiable manifold onto itself. The type (c) symmetry is replaced by a more general type (c̄ ) symmetry that has the nice property that the commutator of a type (c̄ ) generator with a type (a) generator is itself of type (c̄). A differential constraint is identified that transformations of type (c) and (c̄ ) must satisfy, and which, in the opinion of the authors, may severely limit the usefulness of these transformations.
Electrically neutral Dirac particles in the presence of external fields: Exact solutions
Authors: Shishkin German V. , Villalba Víctor M.
Published: July 2002

In the present article exact solutions of the Dirac equation for electric neutral particles with anomalous electric and magnetic moments are presented. Using the algebraic method of separation of variables, the Dirac equation is separated in Cartesian, cylindrical, and spherical coordinates, and exact solutions are obtained in terms of special functions.
Multiparametric quantization of the special linear superalgebra
Authors: Karimipour V. , Aghamohammadi A.
Published: July 2002

It is shown how using the graded Faddeev–Reshetikhin–Takhtajan (FRT) formalism, one can multiparametrize the quantum superalgebra slq(n‖m). Since the naive Serre–Chevalley relations are not adequate for the presentation of this algebra, the quantization is carried out in the Cartan–Weyl basis. The final results can be generalized to any finite dimensional superalgebra with a symmetrizable Cartan matrix.
On hearing the shape of rectilinear regions
Authors: Zayed E. M. E. , Younis A. I.
Published: July 2002

From complete knowledge of the eigenvalues of the negative Laplacian on a bounded domain, one may extract information on the geometry and the boundary conditions by analyzing the asymptotic expansion of a spectral function. Explicit calculations are performed for an equilateral triangular domain with Dirichlet or Neumann boundary conditions, yielding in particular the corner angle terms. In three dimensions, some applications to eigenvalue problems for an equilateral triangular prism are dealt with, including the solid vertex terms.
Generalized supersymmetric quantum mechanics on Riemann surfaces with meromorphic superpotentials
Authors: Dolgallo A. D. , Ilinski K. N.
Published: July 2002

The structure of generalized supersymmetry with mutually commuting involutions for the meromorphic supersymmetric quantum mechanics on the compact Riemann surface is introduced. For this purpose a Riemann surface is considered as a self-conjugate complex manifold. On this basis the Witten index for the new involution is calculated.
Symplectic manifolds, coherent states, and semiclassical approximation
Authors: Rajeev S. G. , Kalyana Rama S. , Sen Siddhartha
Published: July 2002

The symplectic structure and Hamiltonian dynamics for a class of Grassmannian manifolds are described here. Using the two-dimensional sphere (S2) and disc (D2) as illustrative cases, we write their path integral representations using coherent state techniques. These path integrals can be evaluated exactly by semiclassical methods, thus providing examples of the localization formula. Along the way, we also give a local coordinate description for a class of Grassmannians.
An integrable three-particle system
Authors: Rañada Manuel F.
Published: July 2002

A study of the existence of some integrable systems with nonlinear constants of motion is presented using the approach of the theory of generalized (dynamical or hidden) symmetries. Two Lagrangians are considered, both obtained by modifying the Toda Lagrangian. First a two-particle system is studied and then the results are generalized to a three-particle system. It is shown that in both cases the Lagrangians possess nonlinear constants of motion in involution and, thus, they are integrable.
Stochastic renormalization group approach to random point processes. A fractal generalization of Poisson statistics
Authors: Vlad Marcel Ovidiu
Published: July 2002

A generalization of the Shlesinger–Hughes stochastic renormalization method is suggested for random point processes. A decimation procedure is introduced in terms of two parameters: the probability α that a decimation step takes place and the probability β that during a decimation step a random dot is removed from the process. At each step a random number of dots are removed; by this procedure a chain of point processes is generated. The renormalized point process is a superposition of the intermediate processes attached to the different steps. For a statistical ensemble the fraction Lq of systems for which q decimation steps occur is a power function of the fraction ρq of points which survive q decimation steps Lq = (ρq)1−df where df=1−ln α/ln(1−β) is a fractal exponent smaller than unity, df<1. If the random points are initially independent then a complete analysis is possible. In this case explicit expressions for the renormalized Janossy densities, the joint densities, and the generating functional of the process are derived. Even though the initial process is made up of independent random points the points in the renormalized process are correlated. The probability of the number of points is a superposition of Poissonians corresponding to the different steps; however, it is generally non-Poissonian. It may be considered as a fractal generalization of Poisson statistics. All positive moments of the number of points exist and are finite and thus the corresponding probability does not have a long tail; the fractal features are displayed by the dependence of the probability on the initial average number of points λ: for λ→∞ the probability has an inverse power tail in λ modulated by a periodic function in ln λ with a period −ln(1−β). The new formalism is of interest for describing the lacunary structures corresponding to the final stages of chemical processes in low dimensional systems and for the statistics of rare events.
Half-solitons as solutions to the Zakharov-Shabat eigenvalue problem for rational reflection coefficient. II. Potentials on infinite support
Authors: Rourke David E. , Saunders John K.
Published: July 2002

It is shown how to invert the Zakharov-Shabat eigenvalue problem for rational scattering coefficients, in order to produce potentials defined over the whole real line. The method reduces the problem to finding two semi-infinite potentials—which can be efficiently calculated using the soliton-lattice algorithm described in a previous paper. The inversion is usually unique for given rational scattering coefficients, since they usually specify the scattering data of the system uniquely. In the case of nonunique inversion, it is possible to obtain a family of potentials from the inversion. Each member of the family has the same scattering data, except for differing residues. Examples of the inversion include an ‘adiabatic’ inversion pulse for use in nuclear magnetic resonance, and a demonstration of how the cubic nonlinear Schrödinger equation may be integrated.
The N=2 super-Wess–Zumino–Novikov–Witten model valued in superdiffeomorphism (SDIFF) M2 is self-dual supergravity in four dimensions
Authors: Castro Carlos
Published: July 2002

It is shown that the pure topological term of the N=2 super-Wess–Zumino–Novikov–Witten (SWZNW) model, valued in the area-preserving diffeomorphisms group of a two-dimensional Euclidean surface, is self-dual supergravity (SDSG) in 3+1 dimensions. This is achieved by a suitable slicing and pasting procedure of the (2,0); (0,2) N=2 SWZNW models determined by the embedding of the (2,0); (0,2) superspace supercovariant derivatives into the (3+1) superspace ones. Preliminary steps are provided to show that the N=1 SWZNW model, valued in the area-preserving superdiffeomorphism group of a super Riemann surface (SRS) whose signature is (1+1), is self-dual supergravity in (2+2) dimensions: the so-called Atiyah–Ward space–times.
Stability of oscillators driven by ergodic processes
Authors: Nerurkar M. G. , Jauslin H. R.
Published: July 2002

The evolution of a quantum harmonic oscillator, forced by a stationary ergodic process, is considered. Under suitable conditions on the ‘‘dynamics’’ of this process, it is shown that generically the spectrum of the associated quasienergy operator is continuous. These results also apply to kicked harmonic oscillators where the amplitudes of the kicks are governed by a stationary ergodic process.
A new integrable Toda-related three-particle system
Authors: Rañada Manuel F.
Published: July 2002

A study of a three-particle system that possesses, in addition to the energy function, two nonlinear constants of motion is presented herein. The system is obtained by modification of the Lagrangian of the Toda lattice. The explicit expression of the two integrals is obtained and it is proven that this new three-particle Lagrangian is integrable. Finally, the possible generalization to the case of n particles is discussed.
The orthogonality relations for SUq(2)
Authors: Finkelstein Robert J.
Published: July 2002

The orthogonality relations for SUq(2) are here formulated with the aid of the Woronowicz integral. The first part of this paper is devoted to a summary of the relevant parts of the Woronowicz theory and the second part to its implementation in terms of completely explicit representations of the irreducible unitary representations. The purpose of this presentation is to provide background for a separate study of the q deformation of the Coulomb problem.
Structural zeros of Racah coefficients and exceptional Lie algebras
Authors: Vanden Berghe G.
Published: July 2002

A new realization of F4 in terms of SO(3) tensor operators (boson realization) is given. For the first time the internal representation (or bosons) does not correspond to the lowest-dimensional representation of the algebra. Also for the exceptional Lie algebra E7 a new realization in terms of SO(3) tensors is presented, this time constructed out of the lowest-dimensional E7 representation. It is shown that those two particular realizations provide a basis in which certain structural zeros of Racah’s 6j symbol can be explained.
Generalized string-flip model for quantum cluster scattering
Authors: Kuperin Yu. A. , Levin S. B. , Melnikov Yu. B.
Published: July 2002

The generalized string-flip model for quantum scattering in a system of two N-body clusters is under consideration. The extra channel interpreted as the quark compound bag is considered which generates energy-dependent integral boundary conditions in the effective boundary problem. It is shown that the standard string-flip model can be generalized for N identical particles in a cluster. The effective Hamiltonian and effective integral equations for the partial s-wave S matrix are proven to be form invariant with respect to N. The effective configuration space is shown to be two-dimensional for every N and its geometry for different N is discussed. Results of the numerical calculations of s-wave scattering phases, inelasticity parameters, and scattering lengths for N=2 (meson–meson scattering) and N=3 (baryon–baryon scattering) are presented. The resonance influence of the extra channel is investigated. Generalizations including spin–spin interaction and quark color group SU(n) are also presented.
A non-Lagrangian approach to gauge symmetry in three dimensions
Authors: Gonera C.
Published: July 2002

A non-Lagrangian approach to three-dimensional field theory is discussed. The general classification and construction of Lorentz-covariant, local fields carrying massless and massive particles of arbitrary spin are presented. The ‘‘minimal’’ massive (massless) fields for (half) integer spin are explicitly constructed. Following Weinberg’s analysis in the 4D case it is shown that the gauge symmetry for massive fields results from the group theoretical considerations and the condition that there should exist a long-range interaction.
Supercritical bifurcation theory and stability of point attractors
Authors: Gumbs Godfrey , Kolář Miroslav
Published: July 2002

A novel approach is employed for studying a paramagnetic/ferromagnetic phase transition. Here, the Fokker–Planck transport equation is used to describe the time dependence of the spin distribution function (order parameter) for the XY model in mean-field theory. The evolution of the phase-space trajectories from initial nonequilibrium states is obtained. This is then applied in explaining the otherwise well-known behavior of the XY model using a fully dynamical-systems approach. The attractors of this infinite-dimensional dynamical system are determined and their stability for any value of a system parameter δ, that plays the role of the absolute temperature, is obtained. A supercritical bifurcation occurs for δ=1/2, and this bifurcation corresponds to the paramagnetic/ferromagnetic phase transition. For an arbitrary initial spin density, a unique equilibrium magnetization is shown as being due to a continuum of fixed points existing in the temperature range 0<δ<1/2. These fixed points attract all the phase-space trajectories, except those lying on the stable manifold of a trivial fixed point. The trivial fixed point at the origin is stable if δ≳1/2, otherwise it is a saddle point. These two types of fixed points determine the limit behavior of the dynamical system and therefore also the equilibrium state of the XY model in the approximation used here.
Regular solutions of the Einstein–Yang–Mills equations
Authors: Smoller J. A. , Wasserman A. G.
Published: July 2002

It is shown rigorously that any static symmetric solution of the Einstein–Yang–Mills (YM) equations with SU(2) gauge group that is well behaved in the far field is one of three types: black hole, particlelike, or Riessner–Nordström-like (RN) solution. (In particular, any solution with finite ADM mass is well behaved in the far field.) Black-hole solutions are proven to be analytic at the event horizon and thus coincides with Bartnik–McKinnon (BM) black holes. Furthermore, the singularity in the metric at the event horizon can be transformed away by a Kruskal-like change of coordinates in which the YM field remains well behaved. Particlelike solutions are shown to satisfy the same initial conditions as the BM solutions at r=0. RN-like solutions will be considered elsewhere.
Noncommutative integration calculus
Authors: Langmann Edwin
Published: July 2002

A noncommutative integration calculus arising in the mathematical description of Schwinger terms of fermion–Yang–Mills systems is discussed. The differential complexes of forms u0[ε,u1]...[ε,un] with ε a grading operator on a Hilbert space ℋ and ui bounded operators on ℋ which naturally contains the compactly supported de Rham forms on Rd (i.e., ε is the sign of the free Dirac operator on Rd and ℋ is a L2-space on Rd) are considered. An elementary proof is presented in which the integral of d-forms ∫RdtrN(X0dX1...dXd) for Xi∈C0∞(Rd;glN) is equal, up to a constant, to the conditional Hilbert space trace of ΓX0[ε,X1]...[ε,Xd] where Γ=1 for d odd and Γ=γd+1 (‘γ5-matrix’) a spin matrix anticommuting with ε for d even. This result provides a natural generalization of integration of de Rham forms to the setting of Connes’ noncommutative geometry which involves the ordinary Hilbert space trace rather than the Dixmier trace.
Topological Yang–Mills theory from non-commutative geometry
Authors: Hwang Dae Sung , Lee Chang-Yeong
Published: July 2002

It will be shown that the topological Yang–Mills theory of Witten can be induced from the usual Yang–Mills theory of the second rank antisymmetric tensor field when the matrix derivative of non-commutative geometry proposed by Connes is incorporated in the superconnection framework. It is done by identifying consistently the antisymmetric tensor field B with the usual field strength F by B=−F.
Polylogarithmic analysis of chemical potential and fluctuations in a D-dimensional free Fermi gas at low temperatures
Authors: Lee M. Howard
Published: July 2002

The chemical potential and fluctuations in number of particles in a D-dimensional free Fermi gas at low temperatures are obtained by means of polylogarithms. This idea is extended to show that the density of any ideal gas, whether Fermi, Bose, or classical, can be expressed in polylogarithms. The densities of different statistics correspond to different domains of polylogarithms in such a way that there emerges a unifying picture. The density of the classical ideal gas represents a fixed point of polylogarithms. Inequalities for polylogarithms are used to provide a precise bound on errors in the fermion chemical potential at low temperatures.
Low-energy dynamics of a C
P1 lump on the sphere
Authors: Speight J. M.
Published: July 2002

Low-energy dynamics in the unit-charge sector of the CP1 model on spherical space (space-time S2×R) is treated in the approximation of geodesic motion on the moduli space of static solutions, a six-dimensional manifold with nontrivial topology and metric. The structure of the induced metric is restricted by consideration of the isometry group inherited from global symmetries of the full field theory. Evaluation of the metric is then reduced to finding five functions of one coordinate, which may be done explicitly. Some totally geodesic submanifolds are found, and the qualitative features of motion on these described.
Modified symmetry generators related to solvable scattering problems
Authors: Lévay Péter , Apagyi Barnabás
Published: July 2002

By employing the noncompact groups SO(n,1) we show how matrix valued differential operators for the realization of the so(n,1) algebra can be used to obtain multichannel scattering via the occurrence of LS-type interaction terms. These realizations are in terms of coordinates on the hyperboloids Hn regarded as cosets SO(n,1)/SO(n). The matrix-valued nature of such realizations is connected with a finite dimensional unitary irreducible representation of the compact subgroup SO(n). The associated scattering problems are solvable one dimensional ones. The interaction terms are of LS-type multiplied by Pöschl–Teller potentials, with S playing the role of the SO(n) spin. We also show that scattering Hamiltonians based on such realizations can be related to some effective Hamiltonian coming from a coupled system of slow and fast degrees of freedom after decoupling adiabatically the fast variables. The SO(n) symmetry in this picture can be identified as the residual symmetry group of the fast subsystem surviving the adiabatic decoupling. The SO(n) spin, manifesting itself through the appearance of the aforementioned irreducible representation, also originates from the fast dynamics.
Auto-Bäcklund transformation as a gauge transformation preserving the form of Lax connection
Authors: Yang Huan-xiong , Li Kang , Chen Yi-xin
Published: July 2002

In this article, the auto-Bäcklund transformation of the sine-Gordon equation is formulated as a gauge transformation acting on the Lax connection and preserving its form. This gauge transformation contains the known Darboux transformation as a special case. Therefore the auto-Bäcklund transformation is a dressinglike symmetry but of a different kind in general than the dressing transformation. Only in the case of the transformation between the vacuum and one-soliton solution are these two kinds of transformations equivalent.
Modified nonlinear Schrödinger equation: Spectral transform and N-soliton solution
Authors: Doktorov E. V. , Shchesnovich V. S.
Published: July 2002

It is shown in the framework of the ∂̄-formalism that the modified nonlinear Schrödinger (MNLS) equation is gauge equivalent to one which is canonical in the class of nonlinear equations associated with the quadratic bundle. Such a viewpoint permits us to obtain a simple expression for the N-soliton solution of the MNLS equation. The spectral transform matrix R for both continuous and discrete spectral data is derived and its gauge invariance is demonstrated.
Construction of a transformation operator
Authors: Boumenir Amin
Published: July 2002

We shall be concerned with the explicit construction of the kernel of transformation operator used in the scattering theory associated with the Gelfand–Levitan–Marchenko equations. The kernel of the transmutation is well known to play an important role in the inverse scattering theory, and nonlinear integrable systems such as KdV equations. Our method shall use operational calculus.
Lorentz transformations as Lie–Poisson symmetries
Authors: Simoni A. , Stern A. , Yakushin I.
Published: July 2002

We write down the Poisson structure for a relativistic particle where the Lorentz group does not act canonically, but instead as a Poisson–Lie group. In so doing we obtain the classical limit of a particle moving on a noncommutative space possessing SLq(2, C) invariance. We show that if the standard mass shell constraint is chosen for the Hamiltonian function, then the particle interacts with the space–time. We solve for the particle trajectory and find that it originates and terminates at singularities.
Statistical mechanics of conducting phase transitions
Authors: Golden K. M.
Published: July 2002

The critical behavior of the effective conductivity σ* of the random resistor network in Zd, near its percolation threshold, is considered. The network has bonds assigned the conductivities 1 and ε ≥ 0 in the volume fractions p and 1−p. Motivated by the statistical mechanics of an Ising ferromagnet at temperature T in a field H, we introduce a partition function and free energy for the resistor network, which establishes a direct correspondence between the two problems. In particular, we show that the free energies for the resistor network and the Ising model both have the same type of integral representation, which has the interpretation of the complex potential due to a charge distribution on [0, 1] in the s=1/(1−ε) plane for the resistor network, and on the unit circle in the z=exp(−2βH) plane for the ferromagnet. Based on this correspondence, we develop a Yang–Lee picture of the onset of nonanalytic behavior of the effective conductivity σ*, so that the percolation threshold p=pc is characterized as an accumulation point of zeros of the partition function in the complex p-plane as ε → 0. A scheme is developed to find the locations of a certain sequence of zeros in the p-plane, which is based on Padé approximation of a perturbation expansion of σ*(p,ε) around a homogeneous medium (ε=1). Furthermore, for ε ≳ 0, we construct a domain 𝒟ε containing [0, 1] in the p-plane in which σ*(p,ε) is analytic, and which collapses as ε → 0. The explicit construction of this domain allows us to obtain a lower bound on the size of the gap in zeros of the partition function around the percolation threshold p=pc, which leads to the gap exponent inequality Δ≤1.
Representation of the propagator and Schwinger functions of Dirac fields in terms of Brownian motions
Authors: Albeverio S. , Wang Zheng-dong
Published: July 2002

A mathematical path integral representation of the propagator and Schwinger functions of the Dirac fields on R4 interacting with a smooth non-Abelian gauge field is presented. The representation is essentially in terms of expectations with respect to the Brownian motion on R4.
Nonstandard quantum groups and superization
Authors: Majid Shahn , Rodríguez-Plaza M. J.
Published: July 2002

We obtain the universal R-matrix of the nonstandard quantum group associated to the Alexander–Conway knot polynomial. We show further that this nonstandard quantum group is related to the super-quantum group Uq gl(1‖1) by a general process of superization, which we describe. We also study a twisted variant of this nonstandard quantum group and obtain, as a result, a twisted version of Uq gl(1‖1) as a q supersymmetry of the exterior differential calculus of any quantum plane of Hecke type, acting by mixing the bosonic xi coordinates and the forms dxi.
Quantized Neumann problem, separable potentials on S
n and the Lamè equation
Authors: Gurarie David
Published: July 2002

The paper studies spectral theory of Schrödinger operators H=ℏ2Δ+V on the sphere from the standpoint of integrability and separation. Our goal is to uncover the fine structure of spec H, i.e., asymptotics of eigenvalues and spectral clusters, determine their relation to the underlying geometry and classical dynamics and apply this data to the inverse spectral problem on the sphere. The prototype model is the celebrated Neumann Hamiltonian p2+V with quadratic potential V on Sn. We show that the quantum Neumann Hamiltonian (Schrödinger operator H) remains an integrable and find an explicit set of commuting integrals. We also exhibit large classes of separable potentials {V} based on ellipsoidal coordinates on Sn. Several approaches to spectral theory of such Hamiltonians are outlined. The semiclassical problem (small ℏ) involves the EKB(M)-quantization of the classical Neumann flow along with its invariant tori, Maslov indices, etc., all made explicit via separation of variables. Another approach exploits Stäckel–Robertson separation of the quantum Hamiltonian and reduction to certain ODE problems: the Hill’s and the generalized Lamè equations. The detailed analysis is carried out for S2, where the ODE becomes the perturbed classical Lamè equation and the Schrödinger eigenvalues are expressed through the Lamè eigendata.
Vortex solutions in a class of 2-d symmetry breaking Skyrme-like models
Authors: Arthur K. , Tchrakian D. H.
Published: July 2002

We find vortex solutions in 2+1 dimensions belonging to a class of Skyrme-like models, defined in terms of a global O(2) invariant unconstrained field and featuring a symmetry breaking potential. In the static limit all these models support finite-energy topologically stable vortices characterized by a nonvanishing value of the field at infinity, but they do not support nontopological vortices characterized by vanishing value of the field at infinity. We have introduced a modified version of one of our models, which in a stationary field configuration supports a nontopological solution.
Semilocal Chern–Simons defects
Authors: Fuertes Wifredo García , Guilarte Juan Mateos
Published: July 2002

We find both radially symmetric and more general solutions in a Chern–Simons–Higgs model with a Higgs doublet. They are of the kind of the so-called semilocal defects, and show richer properties than those previously known in another type of Higgs models.
Spectral properties of a charged particle in antidot array: A limiting case of quantum billiard
Authors: Geyler V. A. , Pavlov B. S. , Popov I. Yu.
Published: July 2002

A model of the periodic array of quantum antidots in the presence of a uniform magnetic field is suggested. The model can be conceived as a periodic lattice of resonators(curvilinear triangles)connected through ‘‘infinitely small’’ openings at the vertices of the triangles. The model Hamiltonian is obtained by means of operator extension theory in indefinite metric spaces. In the case of rational magnetic flux through an elementary cell of the lattice, the dispersion equation is found in an explicit form with the help of harmonic analysis on the magnetic translation group. It is proved, at least in the case of integer flux, that the spectrum of the model Hamiltonian consists of three parts: (1) Landau levels (they correspond to the classical orbits lying between antidots); (2) extended states that correspond to the classical propagation trajectories; and (3) bound states satisfying the dispersion equation; they correspond to the classical chaotic orbits rotating around single antidots. Among other things, methods of finding the Green’s function for some planar domains with curvilinear boundaries are derived.
Singularities in the spectra of random matrices
Authors: Walker Paul N. , Sánchez María José , Wilkinson Michael
Published: July 2002

We consider singularities of the set of energy levels En(X) of a quantum Hamiltonian, obtained by varying a set of d parameters X=(X1,..,Xd). Singularities such as minima, degeneracies, branch points, and avoided crossings can play an important role in physical applications. We discuss a general method for counting these singularities, and apply it to a random matrix model for the parameter dependence of energy levels. We also show how the density of avoided crossing singularities is related to a non-analyticity of a correlation function describing the energy levels.
On Green–Cusson Ansätze and deformed supersymmetric quantum mechanics
Authors: Beckers J. , Debergh N.
Published: July 2002

Supersymmetric quantum mechanics cannot be deformed when the superposition of only a pair of usual bosons and fermions is considered, but it can if nontrivial parabosons and parafermions of the same order p of paraquantization are superposed. We take the simplest case p=2 and exhibit reducibility problems in that context by using Green–Cusson Ansätze following Macfarlane methods. Specific representations of the Lie superalgebra osp (2|2, R) play an interesting role in connection with possible deformations.
The time harmonic electromagnetic field in a disturbed half-space: An existence theorem and a computational method
Authors: Piccolo Santa , Recchioni Maria Cristina , Zirilli Francesco
Published: July 2002

The scattering of time harmonic electromagnetic waves by a perfectly conducting surface that is the boundary of a ‘‘disturbed half-space’’ is considered. This problem is translated in a boundary value problem for an elliptic system of partial differential equations. Under appropriate hypotheses an existence theorem and an integral representation formula for the solution of this boundary value problem is given. Based on this integral representation formula a new method to compute the solution of the boundary value problem is proposed. This method involves only quadratures and is fully parallelizable. Finally some numerical examples of the results obtained on test problems with this computational method are shown.
Group quantization on configuration space: Gauge symmetries and linear fields
Authors: Navarro Miguel , Aldaya Victor , Calixto Manuel
Published: July 2002

A new, configuration-space picture of a formalism of group quantization, the GAQ formalism, is presented in the context of a previous algebraic generalization. This presentation serves to make a comprehensive discussion in which other extensions of the formalism, principally to incorporate gauge symmetries, are developed as well. Both images are combined in order to analyze, in a systematic manner and with complete generality, the case of linear fields (Abelian current groups). To illustrate these developments we particularize them for several fields and, in particular, we carry out the quantization of the Abelian Chern–Simons models over an arbitrary closed surface in detail.
Nonlinear operators and their propagators
Authors: Schwartz Charles
Published: July 2002

Mathematical physicists are familiar with a large set of tools designed for dealing with linear operators, which are so common in both the classical and quantum theories; but many of those tools are useless with nonlinear equations of motion. In this work a general algebra and calculus is developed for working with nonlinear operators: The basic new tool being the “slash product,” defined by A(1+εB) =A+εA/B+O(ε2). For a generic time development equation, the propagator is constructed and then there follows the formal version of time dependent perturbation theory, in remarkable similarity to the linear situation. A nonperturbative approximation scheme capable of producing high accuracy computations, previously developed for linear operators, is shown to be applicable as well in the nonlinear domain. A number of auxiliary mathematical properties and examples are given.
Reissner–Nordström-like solutions of the SU(2) Einstein–Yang/Mills equations
Authors: Smoller J. A. , Wasserman A. G.
Published: July 2002

We introduce a new class of spherically symmetric solutions of the SU(2) Einstein–Yang/Mills equations. These solutions have a Reissner–Nordström-type essential singularity at the origin, and are well behaved in the far field. These solutions are needed to classify all spherically symmetric solutions which are smooth, asymptotically flat in the far field, and have finite (ADM) mass.
Feynman integral in regularized nonrelativistic quantum electrodynamics
Authors: Haba Z.
Published: July 2002

We express the unitary time evolution in nonrelativistic regularized quantum electrodynamics at zero and positive temperature by a Feynman integral defined in terms of a complex Brownian motion. An average over the quantum electromagnetic field determines the form of the quantum mechanics in an environment of a quantum black body radiation. In this nonperturbative formulation of quantum electrodynamics we prove the existence of the classical limit ℏ→0. We estimate an error to some approximations commonly applied in quantum radiation theory.
Couple coefficients for the two-block AKNS system
Authors: Corona Gulmaro Corona
Published: July 2002

A model for the 2×2 AKNS system is extended for the two-block AKNS system. Zeroes of the determinant of the J-diagonal scattering matrix blocks give the bound states of such a system. The couple coefficients are now matrices.
Foliation of a dynamically homogeneous neutral manifold
Authors: Blažić Novica , Bokan Neda , Rakić Zoran
Published: July 2002

It is known that Riemannian and Lorentzian four-dimensional dynamically homogeneous manifolds are two-point homogeneous spaces. This is not true for signature (−−++) (neutral or Kleinian signature). In order to better understand their rich structure we study the geometry of nonsymmetric dynamically homogeneous spaces (types II and III): they admit autoparallel distributions and they are locally foliated by totally geodesic, flat, isotropic two-dimensional submanifolds. Moreover we characterize them locally in terms of the existence of an appropriate coordinate system (in the sense of A. G. Walker [Q. J. Math. 1, 69–79 (1950)]).
Equivalence classes of perturbations in cosmologies of Bianchi types I and V: Formulation
Authors: Banach Zbigniew
Published: July 2002

In this paper we deal for the first time with gauge-invariant perturbations of anisotropic cosmological models of Bianchi types I and V from a unified point of view. Motivated by Ehlers’ pioneering concepts, the key idea is to identify the gauge-invariant perturbations with the equivalence classes of tangents to one-parameter families of exact solutions to Einstein’s field equations. For cases where these models are filled with a nonbarotropic perfect fluid, we show that a set of 26 “geometrically” independent, not identically vanishing gauge-invariant variables, denoted collectively by D and referred to as the complete set of basic variables, can be used to extract the equivalence classes of tangents from D in a unique way. The set D is complete because it has the following property: any gauge-invariant quantity is obtainable linearly from the basic variables through purely algebraic and differential operations. Mathematically, this approach to the gauge problem is a nontrivial example of the general scheme that we have described in our two previous papers [Int. J. Theor. Phys. 36, 1787, 1817 (1997)], and the new concepts developed were also applied to the construction of a complete set of basic gauge-invariant variables for the cases of a fixed background de Sitter space–time and an almost-Robertson–Walker universe model. Arguments are given that there are a number of advantages to be gained by replacing the coordinate-based method of Bardeen or the covariant formalism of Ellis and Bruni by the present one.
Time dependence of operators in anharmonic quantum oscillators: Explicit perturbative analysis
Authors: Kahn Peter B. , Zarmi Yair
Published: July 2002

An explicit, order-by-order perturbative solution, valid over extended time scales, for the time dependence of operators of anharmonic oscillators, is developed within the framework of the method of normal forms. The freedom of choice of the zeroth-order term and, concurrently in the higher-order corrections, is exploited to develop a minimal normal form (MNF). The expansion for the eigenvalues of the perturbed Hamiltonian in a standard form is independent of the choice. However, the simple form obtained for the time dependence of the perturbative solution is more suitable than any other choice for application to high-lying excited states, as it offers a renormalized form for the propagator.
Jacobi’s principle for magnetic interactions
Authors: Torres del Castillo G. F.
Published: July 2002

It is shown that the trajectories of a charged particle in a static magnetic field and a velocity-independent potential in a three-dimensional space are (the projection of) the geodesics of a suitably defined metric in a four-dimensional space. It is shown that each one-parameter group of isometries of the original configuration space that leaves the magnetic field invariant gives rise to a one-parameter group of isometries of the metric defined on the four-dimensional space and, hence, to a constant of the motion. It is also shown, similarly, that the Schrödinger equation for a charged particle in a static magnetic field is equivalent to the Schrödinger equation for a free particle in the four-dimensional space mentioned above.
The stationary KdV hierarchy and so(2,1) as a spectrum generating algebra
Authors: Doebner H.-D. , Zhdanov R. Z.
Published: July 2002

The family FLκ of all potentials V(x) for which the Hamiltonian H=−d2/dx2+V(x) in one space dimension possesses a high-order Lie symmetry is determined. A subfamily FSGA(2) of FLκ, which contains a class of potentials allowing a realization of so(2,1) as spectrum generating algebra of H through differential operators of finite order, is identified. Furthermore and surprisingly, the families FSGA(2) and FLκ are shown to be related to the stationary KdV hierarchy. Hence, the “harmless” Hamiltonian H connects different mathematical objects: high-order Lie symmetry, the realization of so(2,1)-spectrum generating algebra and families of nonlinear differential equations. We describe in a physical context the interplay between these objects.
The effective σ-model of multidimensional gravity
Authors: Rainer Martin
Published: July 2002

The properties of the effective σ-model for D-dimensional Einstein gravity based on multidimensional geometries is analyzed. Besides pure geometry additional minimally coupled scalars and (p+2)-forms are considered which yield an extended target space after reduction to the effective D0-dimensional geometry. The target space is always a homogeneous space. Exact solutions exist provided an orthobrane condition is satisfied which geometrically makes the target space a locally symmetric one. New solutions with scalar fields are found which may inflate not only in time-like but in also in additional spatial directions of the effective geometry. Static spherically symmetric solutions with a particular configuration of intersecting electric and magnetic branes are investigated both, for the orthobrane case and for degenerated charges. In both cases TH depends critically on the intersection dimension of the branes. Finally, the role of the Einstein frame for 4-geometries is addressed, and the physical frame transformation for cosmological geometries is given.
Hypergeometric functions and moduli spaces of null-correlation bundles
Authors: Nitta Takashi , Taniguchi Tadashi
Published: July 2002

The moduli space Nn of null-correlation bundles over CP2n+1 has a natural L2-Kähler metric. We explicitly describe that metric in terms of Appell–Lauricella hypergeometric functions. The proof uses a Penrose twistor correspondence.
Group theoretical quantization and the example of a phase space S1×R+
Authors: Bojowald Martin , Strobl Thomas
Published: July 2002

The group theoretical quantization scheme is reconsidered by means of elementary systems. Already the quantization of a particle on a circle shows that the standard procedure has to be supplemented by an additional condition on the admissibility of group actions. A systematic strategy for finding admissible group actions for particular subbundles of cotangent spaces is developed, two-dimensional prototypes of which are T*R+ and S=S1×R+ (interpreted as restrictions of T*R and T*S1 to positive coordinate and momentum, respectively). In this framework (and under an additional, natural condition) an SO↑(1,2)-action on S results as the unique admissible group action. Furthermore, for symplectic manifolds which are (specific) parts of phase spaces with known quantum theory a simple “projection method” of quantization is formulated. For T*R+ and S equivalent results to those of more established (but more involved) quantization schemes are obtained. The approach may be of interest, e.g., in attempts to quantize gravity theories where demanding nondegenerate metrics of a fixed signature imposes similar constraints.
A novel method to promote parallel vortex shedding in the wake of circular cylinders
Authors: Hammache M. , Gharib M.
Published: July 2002

Slanted vortex shedding dominates the wake of circular cylinders of finite aspect ratio in the Reynolds number range of 72–158. Parallel vortex shedding can be induced in the wake of a circular cylinder by imposing a symmetric pressure boundary condition at the two ends of the cylinder. This condition can be achieved by positioning two upstream circular cylinders of larger diameter normal to it. The resulting Strouhal–Reynolds number curve shows no discontinuity. Also, the turbulent transition in the wake of a circular cylinder could be delayed by using this technique.
The stability of two superposed viscous fluids in a channel
Authors: Hooper Alison P.
Published: July 2002

The Couette/Poiseuille flow of two superposed viscous fluids in a channel is studied. There are two mechanisms for instability of this flow: one mechanism is associated with the presence of the interface, the other with the presence of the boundary walls. Analytical results are presented based on the short wave perturbation scheme of Hooper and Boyd [J. Fluid Mech. 179, 201 (1987)] and the long wave perturbation scheme of Yih [J. Fluid Mech. 27, 337 (1967)], together with numerical results. Similarities between the stability of plane Poiseuille flow and one fluid and two-layer Couette/Poiseuille flow are discussed.
Effect of stepheight on the separated flow past a backward facing step
Authors: Thangam S. , Knight Doyle D.
Published: July 2002

This Brief Communication presents a numerical study of planar laminar flow over a backward facing step. The principal parameters are the expansion ratio (defined as the ratio of stepheight to channel height) and the Reynolds number (based on the maximum inflow velocity and the hydraulic diameter of the channel inlet). Results are presented for expansion ratios of 0.25–0.75 and Reynolds numbers from 50–900. The computed results are in close agreement with previous experimental and numerical results for expansion ratios of 0.5. The effect of the expansion ratio on the reattachment length is summarized as a function of the Reynolds number.
Space-time correlations in turbulence: Kinematical versus dynamical effects
Authors: Yakhot Victor , Orszag Steven A. , She Zhen-Su
Published: July 2002

Space and time correlation functions in a randomly stirred turbulent fluid are evaluated to lowest order of the ε expansion in the renormalization group theory of turbulence. It is shown that wavenumber and frequency energy spectra differ substantially since random sweeping effects on the small eddies by large-scale eddies do not contribute to the decorrelation in the RNG theory.