bluuebunny/crossref_metadata_2025 huggingface dataset:
Representation of the five- and six-dimensional harmonic oscillators in a u(5)⊇so(5)⊇so(3) basis
Authors: Rowe D. J.
Published: July 2002

The duality that exists between the two subgroups SU(1,1) and O(5) of Sp(5,R) to construct basis states for the five-dimensional harmonic oscillator which simultaneously reduce the Sp(5,R)⊇U(5)⊇O(5)⊇SO(3) and Sp(5,R)⊇ SU(1,1)⊇U(1) subgroup chains is used. It is shown that the vector-coherent-state wave functions of the fundamental five-dimensional SO(5) irrep [1,0] realize the traceless bosons introduced by Lohe and Hurst to classify the irreps of the orthogonal groups and employed in Chacon, Moshinsky, and Sharp’s construction of a basis for the five-dimensional harmonic oscillator. Moreover, it is shown that VCS theory provides a simple mechanism for constructing matrix elements of the traceless boson operators. These matrix elements are used to extend the VCS representations of SO(5) in an SO(3) basis, given in a previous paper, to irreps of U(5) in an SO(5)⊇ SO(3) basis. The extension to U(6)⊇U(5)⊇SO(5)⊇SO(3) is also given.
Quantum electrodynamics in external fields from the spin representation
Authors: Gracia-Bondía José M. , Várilly Joseph C.
Published: July 2002

Systematic use of the infinite-dimensional spin representation simplifies and rigorizes several questions in quantum field theory. This representation permutes ‘‘Gaussian’’ elements in the fermion Fock space, and is necessarily projective: its cocycle at the group level is computed, and Schwinger terms and anomalies from infinitesimal versions of this cocycle are obtained. Quantization, in this framework, depends on the choice of the ‘‘right’’ complex structure on the space of solutions of the Dirac equation. We show how the spin representation allows one to compute exactly the S-matrix for fermions in an external field; the cocycle yields a causality condition needed to determine the phase.
Topological aspects of SU(2) Weyl fermion and global anomaly
Authors: Roy Ashim , Bandyopadhyay Pratul
Published: July 2002

It is argued here that the global anomaly of SU(2) Weyl fermions is related to the residual topological properties of massive Dirac fermions leading to the topological index corresponding to the fermion number. As in the case of the chiral anomaly with Dirac fermions, the SU(2) anomaly with a Weyl fermion vanishes when the effect of this topological property is taken into account in the Lagrangian formulation.
Exact solutions to the Dirac equation for neutrinos propagating in a particular Vaidya background
Authors: Christodoulakis T. , Grammenos T. , Korfiatis E. , Spanos V. C.
Published: July 2002

In this work the Dirac equation for massless left-handed neutrinos has been set up for the Vaidya background which describes the exterior of a spherically symmetric radiating source. With a particular Ansatz for the form of both the spinor and the background metric, analytical solutions of the Dirac equation are obtained. The coordinates in which the particular Vaidya metric assumes diagonal form are also found.
On the addition of quantum matrices
Authors: Majid S.
Published: July 2002

An addition law is introduced for the usual quantum matrices A(R) by means of a coaddition Δ_t=t⊗1+1⊗t. It supplements the usual comultiplication Δt=t⊗t and together they obey a codistributivity condition. The coaddition does not form a usual Hopf algebra but a braided one. The same remarks apply for rectangular m×n quantum matrices. As an application, left-invariant vector fields are constructed on A(R) and other quantum spaces. They close in the form of a braided Lie algebra. As another application, the wave functions in the lattice approximation of Kac–Moody algebras and other lattice fields can be added and functionally differentiated.
A unified description of null and non-null shear-free congruences
Authors: Benn I. M.
Published: July 2002

A simple tensor equation is given that is satisfied by null vectors if and only if they are proportional to shear-free geodesics. Non-null vectors satisfy this equation if and only if they can be normalized to shear-free unit vectors. Thus this equation unifies the treatment of the null and non-null cases. Conformal properties of the shear-free condition and this tensor equation are discussed.
Taub numbers extended to Einstein–Maxwell space–time
Authors: Glass E. N. , Naber Mark
Published: July 2002

Mass and angular momentum of asymptotically flat systems are computed by Taub number τ1. This work extends the Taub number method from a vacuum region outside the central source to a region with stationary electric and magnetic fields while preserving global mass and angular momentum. The Reissner–Nordström and Kerr–Newman solutions are treated. Function spaces for curves of solutions of the coupled Einstein–Maxwell equations are discussed, together with the linearized field equations which are directional derivatives of the field equations along the solution curves in the direction of the perturbation.
The abstract complex Lorentz transformation group with real metric. II. The invariance group of the form ‖t‖2−∥x∥2
Authors: Ungar Abraham A.
Published: July 2002

Let TX=C×V∞ be equipped with the Hermitian form ‖t‖2−∥x∥2, where t∈C is a complex number and x∈V∞ is a vector in an abstract complex inner product space V∞. The abstract complex Lorentz group (with real metric) is the invariance group of this form. A novel formalism to deal with the abstract real Lorentz transformation group has recently been developed by Ungar [Am. J. Phys. 59, 824–834 (1991); Am. J. Phys. 60, 815–828 (1992)], allowing one to solve in an abstract context previously poorly understood problems in one time and three space dimensions. Intrigued by the success of the abstract real Lorentz group formalism, resulting in the understanding of Thomas gyration in its abstract context, a formalism to deal with the abstract complex Lorentz group is proposed in this article. The extension from the real to the complex Lorentz group is not trivial. Complex Lorentz groups involve two interacting gyrations, a complex-time gyration and a complex-space gyration, as opposed to the real case which involves a single gyration, that is, a real-space gyration called Thomas gyration. The proposed formalism allows one to manipulate the seemingly involved abstract complex Lorentz group in a way analogous to the way one commonly manipulates Galilei transformation groups. Thus, for instance, equipped with the proposed formalism, one can readily (i) compose abstract complex Lorentz transformations, and (ii) determine those which link any two given events by manipulations analogous to Galilei group manipulations. When the abstract complex inner product space V∞ associated with the underlying abstract complex Minkowski space is realized by a finite-dimensional complex Hilbert space of dimension n, the abstract complex Lorentz group studied in this article reduces to the group U(1,n) or SU(1,n), depending on whether unitary or special unitary transformations are being considered.
The m-function for Hamiltonians with Wigner–von Neumann potentials
Authors: Behncke H.
Published: July 2002

Hamiltonians with strong Wigner–von Neumann potentials are known to possess bound states in the continuous spectrum. For smaller couplings these bound states become resonances, which appear as singularities of the m-function. These singularities are intimately connected with the decay of the corresponding subordinate eigenfunction. For Coulomb-type potentials with Schrödinger operators this has recently be shown by Atkinson, the author, and Hinton, Klaus and Shaw. Here these results are extended to a general class of Wigner–von Neumann potentials for Dirac and Schrödinger operators.
Ground state energy for the Hartree–Fock equations with Dirichlet boundary conditions
Authors: Campbell Joel
Published: July 2002

The Hartree–Fock equations for 2 N fermions in a one-dimensional box are solved in terms of a power series in the coupling constant for various values of N and the quantum numbers. A general formula is found for the total energy and wave function for N=1, which is accurate to sixth order. Another formula for the total energy is conjectured for any N, which is accurate to second order. Using these results, the ground state energy, energy of interaction, and boundary energy are found to second-order accuracy for arbitrary N.
N-body quantum scattering theory in two Hilbert spaces. VII. Real-energy limits
Authors: Chandler Colston , Gibson Archie G.
Published: July 2002

A study is made of the real-energy limits of approximate solutions of the Chandler–Gibson equations, as well as the real-energy limits of the approximate equations themselves. It is proved that (1) the approximate time-independent transition operator Tπ(z) and an auxiliary operator Mπ(z), when restricted to finite energy intervals, are trace class operators and have limits in trace norm for almost all values of the real energy; (2) the basic dynamical equation that determines the operator Mπ(z), when restricted to the space of trace class operators, has a real-energy limit in trace norm for almost all values of the real energy; (3) the real-energy limit of Mπ(z) is a solution of the real-energy limit equation; (4) the diagonal (on-shell) elements of the kernels of the real-energy limit of Tπ(z) and of all solutions of the real-energy limit equation exactly equal the on-shell transition operator, implying that the real-energy limit equation uniquely determines the physical transition amplitude; and (5) a sequence of approximate on-shell transition operators converges strongly to the exact on-shell transition operator. These mathematically rigorous results are believed to be the most general of their type for nonrelativistic N-body quantum scattering theories.
Gauge potential decomposition, space-time defects, and Planck’s constant
Authors: Duan Yi-Shi , Zhang Sheng-Li , Feng Sze-Shiang
Published: July 2002

A new geometrization of Planck’s constant is proposed, which also bases on the torsion in the space-time. A quantity is introduced to describe the space-time dislocations that appear due to torsion. It will be pointed out that there is U(1)-like gauge invariance in this new geometrization. Using the gauge-potential decomposition, the quantity is quantized in units of the Planck length. The quantum number is determined by Hopf indices and Brouwer degrees.
Jump conditions for a radiating relativistic gas
Authors: Alì G. , Romano V.
Published: July 2002

Analytical solutions of the Rankine–Hugoniot conditions for a radiating gas are presented both for shocks and subshocks. The case of Synge gas is studied in detail. In order to study subshocks, radiation is described by the moment equations closed with a variable Eddington factor.
Multidimensional extension of a Wentzel–Kramers–Brillouin improvement for spherical quantum billiard zeta functions
Authors: Romeo August
Published: July 2002

Some insight is offered into the dimensional dependence of the Wentzel–Kramers–Brillouin (WKB) and improved-WKB approximations introduced by Steiner in connection with hyperspherical (originally circular) quantum billiards. The accuracy of every new D-dimensional picture is estimated by examining the residues of the spectral zeta-function poles.
The Riemann–Liouville integral and continuous KP hierarchy
Authors: Gawrylczyk Jarosl/aw
Published: July 2002

Extension of the standard construction of the Kadomtsev–Petviashvili (KP) hierarchy by the use of Riemann–Liouville integral is given. In consequence we obtain the new classes of integer as well as fractional graded KP hierarchies, which are further investigated. The fractional calculus leads to the new generalization of the w∞ algebra.
Some rigorous results for Yang–Mills theories on a cylinder
Authors: Rajeev S. G. , Rossi L.
Published: July 2002

Using an approach based on the canonical formalism, the Yang–Mills theories on a cylinder are rigorously analyzed. In this way the moduli space 𝒜/𝒢, can be explicitly described with 𝒜 being the space of connections and 𝒢 the group of gauge transformations. In particular 𝒜/𝒢0, 𝒢0 being the group of the pointed gauge transformations, is diffeomorphic to the structure group of the theory G, whereas 𝒜/𝒢 is G modulo the group of inner automorphisms. It is also proven that 𝒜 → G is a principal fiber bundle with structure group 𝒢0.
On the question of singularity in higher-dimensional space–time
Authors: Banerjee A. , Panigrahi D. , Chatterjee S.
Published: July 2002

The problem of singularity is discussed in a (d+4)-dimensional space–time with d≥0. Some important relations are obtained, which may determine the conditions of occurrence of singularities in this more general situation.
Gravity without metric, torsion, and topological gravity
Authors: Mullick Lipika , Bandyopadhyay Pratul
Published: July 2002

The role of θ term in gravity without the metric formulation of Capovilla, Jacobson, and Dell has been investigated when the gauge group is taken to be SL(2,C) and it is shown that this corresponds to the introduction of torsion and as such represents the Einstein–Cartan action. Moreover, as this term is related to the chiral anomaly, this helps us to formulate the Einstein–Hilbert gravitational action as a symmetry-breaking effect in quantum field theory. In view of this one can consider this topological θ term as the fundamental entity. When the chiral nature of matter field is not manifested explicitly, the torsion term effectively gives rise to the cosmological constant. In case there is only the θ term in the action, one can have topological gravity which helps to realize physically Donaldson’s theory of four-dimensional space–time geometry.
Bound state variational principle employing a discontinuous trial function
Authors: Brownstein K. R.
Published: July 2002

A new variational principle for the bound state energy eigenvalues of a quantum system is presented. In it, not only ∇ψ(r) but also ψ(r) itself can be discontinuous across a surface. That is, the trial ψ(r) can have both a kink and a jump across a surface. This allows the use of different basis functions in different regions of space without having to impose any matching conditions across the surface. All parameters appearing in the principle can be variational parameters; none are needed to help invoke any continuity conditions on the trial function. Although the principle is not a definite (minimum) one, good results are obtained in several examples.
Exact calculation of the ground-state single-particle Green’s function for the 1/r2 quantum many-body system at integer coupling
Authors: Forrester P. J.
Published: July 2002

The ground-state single-particle Green’s function describing hole propagation is calculated exactly for the 1/r2 quantum many-body system at integer coupling. The result is in agreement with a recent conjecture of Haldane.
Analytical results for a class of sums involving Bessel functions and square arrays
Authors: Nicorovici N. A. , Poulton C. G. , McPhedran R. C.
Published: July 2002

We consider a class of sums involving Bessel functions summed over the square array. The sums involve the length (ξ) of an arbitrary vector lying within the central unit cell. We establish conditions under which the sums reduce to polynomial forms in ξ (possibly with a single logarithmic term in addition), and show how these polynomials may be conveniently evaluated.
The global flow of the Manev problem
Authors: Delgado Joaquín , Diacu Florin N. , Lacomba Ernesto A. , Mingarelli Angelo , Mioc Vasile , Perez Ernesto , Stoica Cristina
Published: July 2002

The Manev problem (a two-body problem given by a potential of the form A/r+B/r2, where r is the distance between particles and A,B are positive constants) comprises several important physical models, having its roots in research done by Isaac Newton. We provide its analytic solution, then completely describe its global flow using McGehee coordinates and topological methods, and offer the physical interpretation of all solutions. We prove that if the energy constant is negative, the orbits are, generically, precessional ellipses, except for a zero-measure set of initial data, for which they are ellipses. For zero energy, the orbits are precessional parabolas, and for positive energy they are precessional hyperbolas. In all these cases, the set of initial data leading to collisions has positive measure.
A manifestly reciprocal theory of scattering in the presence of elastic media
Authors: Wurmser Daniel
Published: July 2002

The role of elastic waves in the scattering problem is examined in the context of modern field theory. This effort builds upon a previously published, and since successfully applied formalism for solving the acoustic and electromagnetic scattering problems. It specifically addresses the scattering of acoustic waves from a fluid-solid interface, as well as the scattering of elastodynamic waves from surfaces satisfying the zero-displacement, stress-free, and solid–solid boundary conditions. Expressions for the change in the scattering amplitude due to a perturbation in the scattering surface are derived directly from the requirement of time reversal symmetry (also known as reciprocity). These results constitute formal statements of the composite (or two-scale) model. In a typical application, the perturbation usually corresponds to Bragg scattering and is treated statistically, while the reference surface provides tilt, shadowing, and multiple scattering, and is usually treated deterministically. Used in this way, the new formalism effectively allows existing numerical and operator expansion methods to be used to calculate the scattering from rougher and/or higher dimensional surfaces than would otherwise be possible. An alternate application of the formalism is illustrated using the fluid-solid boundary as an example. A new manifestly reciprocal expression for the scattering amplitude is presented, as are the small slope and ‘‘local’’ two-scale approximations for this problem. (By local, it is meant that only local phenomena such as the tilt of the reference surface are automatically included. However, since the result is manifestly reciprocal, it is fairly straightforward to incorporate a non-local effect such as shadowing.) During the course of the discussion, the classical scattering problem is reexamined from an entirely new perspective.
Cohomology and connections on fiber bundles and applications to field theories
Authors: Gross Christian
Published: July 2002

Given any connection on a fiber bundle B(M,F,G), we discuss the question which closed differential forms on the fiber F can be extended to closed forms on the whole bundle B in a canonical way such that the horizontal parts of the extended forms are given in terms of the gauge fields. Such questions arise for many models in theoretical physics such as the skyrmion bundle and related theories with non-Abelian groups G. We introduce the notion of a G-transgressive form as a sufficient condition for the form to be extendable to any bundle which comes along with a given left action L:G×F→F. Using Lie algebra cohomology we prove that if the structure group G of the bundle is semisimple, then every closed n-form, n≤2, on the fiber which is invariant under L is G-transgressive and thus defines a unique de Rham cohomology class on any bundle which comes along with L.
On the ionization of a Keplerian binary system by periodic gravitational radiation
Authors: Chicone C. , Mashhoon B. , Retzloff D. G.
Published: July 2002

The gravitational ionization of a Keplerian binary system via normally incident periodic gravitational radiation of definite helicity is discussed. The periodic orbits of the planar tidal equation are investigated on the basis of degenerate continuation theory. The relevance of the Kolmogorov-Arnold-Moser theory to the question of gravitational ionization is elucidated, and it is conjectured that the process of ionization is closely related to the Arnold diffusion of the perturbed system.
Some rigorous results for the kinematic dynamo problem with general boundary conditions
Authors: Núñez Manuel
Published: July 2002

The main energy inequalities for the induction equation are studied for a variety of boundary conditions. The results are applied to the evolution of the magnetic field and the vector potential within a conducting fluid disregarding the influence of these upon the velocity (the kinematic dynamo problem). Emphasis is placed upon the behavior of these fields at the singular limit of zero magnetic diffusivity.
Dynamics of compact homogeneous universes
Authors: Tanimoto Masayuki , Koike Tatsuhiko , Hosoya Akio
Published: July 2002

A complete description of dynamics of compact locally homogeneous universes is given, which, in particular, includes explicit calculations of Teichmüller deformations and careful counting of dynamical degrees of freedom. We regard each of the universes as a simply connected four-dimensional space–time with identifications by the action of a discrete subgroup of the isometry group. We then reduce the identifications defined by the space–time isometries to ones in a homogeneous section, and find a condition that such spatial identifications must satisfy. This is essential for explicit construction of compact homogeneous universes. Some examples are demonstrated for Bianchi II, VI0, VII0, and I universal covers.
Electronic transport properties of quasicrystals
Authors: Roche S. , Trambly de Laissardière G. , Mayou D.
Published: July 2002

We present a review of some results concerning electronic transport properties of quasicrystals. After a short introduction to the basic concepts of quasiperiodicity, we consider the experimental transport properties of electrical conductivity with particular focus on the effect of temperature, magnetic field, and defects. Then, we present some heuristic approaches that tend to give a coherent view of different, and to some extent complementary, transport mechanisms in quasicrystals. Numerical results are also presented and in particular the evaluation of the linear response Kubo–Greenwood formula of conductivity in quasiperiodic systems in the presence of disorder.
The Feynman integral for time-dependent anharmonic oscillators
Authors: Grothaus Martin , Khandekar Dinkar C. , da Silva José L. , Streit Ludwig
Published: July 2002

We review some basic notions and results of white noise analysis that are used in the construction of the Feynman integrand as a generalized white noise functional. We show that the Feynman integrand for the time-dependent harmonic oscillator in an external potential is a Hida distribution.
SU(
N
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Quantum Yang–Mills theory in two dimensions: A complete solution
Authors: Ashtekar Abhay , Lewandowski Jerzy , Marolf Donald , Mourão José , Thiemann Thomas
Published: July 2002

A closed expression of the Euclidean Wilson-loop functionals is derived for pure Yang–Mills continuum theories with gauge groups SU(N) and U(1) and space-time topologies R1×R1 and R1×S1. (For the U(1) theory, we also consider the S1×S1 topology.) The treatment is rigorous, manifestly gauge invariant, manifestly invariant under area preserving diffeomorphisms and handles all (piecewise analytic) loops in one stroke. Equivalence between the resulting Euclidean theory and and the Hamiltonian framework is then established. Finally, an extension of the Osterwalder–Schrader axioms for gauge theories is proposed. These axioms are satisfied in the present model.
Hamiltonian structures for compact homogeneous universes
Authors: Tanimoto Masayuki , Koike Tatsuhiko , Hosoya Akio
Published: July 2002

Hamiltonian structures for spatially compact locally homogeneous vacuum universes are investigated, provided that the set of dynamical variables contains the Teichmüller parameters, parameterizing the purely global geometry. One of the key ingredients of our arguments is a suitable mathematical expression for quotient manifolds, where the universal cover metric carries all the degrees of freedom of geometrical variations, i.e., the covering group is fixed. We discuss general problems concerned with the use of this expression in the context of general relativity, and demonstrate the reduction of the Hamiltonians for some examples. For our models, all the dynamical degrees of freedom in Hamiltonian view are unambiguously interpretable as geometrical deformations, in contrast to the conventional open models.
Tau-wavelets in the plane
Authors: Gazeau Jean Pierre , Patera Jiřı́ , Pelantová Edita
Published: July 2002

First an iterative process is described for subdivision and for scaling-up of the Penrose–Robinson tiles. Then we build the τ-wavelets of Haar (i.e., suitably normalized characteristic functions) on the tiles so that the orthogonality and multiresolution conditions are satisfied. Here τ=12(1+5).
Wavelets bases adapted to a self-similar quasicrystal
Authors: Bernuau Guillaume
Published: July 2002

Given any self-similar quasicrystal Λ in Rn with inflation θ>1, we construct bases of L2(Rn) having the following structure: θnj/2ψλ(θjx−λ), λ∈Λ\θΛ, j∈Z, where the mother wavelets ψλ, λ∈Λ\θΛ, are smooth and with exponential decay or compact support. We also show that wavelets ψλ constitute a relatively compact set in some Sobolev space and that they depend continuously on λ when Λ is equipped with an appropriate topology.
Square wave analysis
Authors: Wei Yuchuan , Chen Nanxian
Published: July 2002

This paper concerns square wave analysis, which is in no small part a generalization of the Fourier analysis based on sine and cosine functions. Following sine and cosine functions square waves become another frequently used and easily generated waveform in electronics, so it is an urgent practical problem to study the basic properties of square waves and the fundamental theory of square wave analysis. Like the sine-cosine function system, the square wave system, i.e., the function system of square waves with different frequencies (or periods), is linearly independent and complete in the real Hilbert spaces L2(−π,π), so square waves can approximate an arbitrary quadratically integrable function with a vanishing mean-square error. Since the square wave system is nonorthogonal, its biorthogonal functions are presented so that a function with a certain condition can be expanded as a square wave series easily. Meanwhile the orthogonalization of the square wave system is discussed so that a quadratically integrable function can be approximated best by a superposition of finite square waves. These results form the theory basis of the square wave analysis technique in modern electronics.
Quommutator deformations of spl(N,1)
Authors: Brihaye Y.
Published: July 2002

We analyze the Witten-Woronowicz’s type deformations of the Lie superalgebras spl(N,1) and obtain deformations parametrized by N(N−1)/2 independent parameters for N>2 and by three parameters for N=2. For some of these algebras, finite dimensional representations can be constructed in terms of finite difference operators, providing operators that are relevant for the classification of quasiexactly solvable, finite difference equations.
Algebraic characterization of gauge anomalies on a nontrivial bundle
Authors: John P. , Moritsch O. , Schweda M. , Sorella S. P.
Published: July 2002

We discuss the algebraic way of solving the descent equations corresponding to the BRST consistency condition for the gauge anomalies and the Chern–Simons terms on a nontrivial bundle. The method of decomposing the exterior space–time derivative as a BRST commutator is extended to the present case.
Lie-algebraic structure from inhomogeneous Hopf algebras
Authors: Lagraa M. , Touhami N.
Published: July 2002

We construct the vector space dual to the space of right-invariant differential forms constructed from a first-order differential calculus on inhomogeneous quantum groups. We show that this vector space is equipped with a structure of a Hopf algebra which closes on a noncommutative Lie algebra satisfying a Jacobi identity.
Realizations of su(1,1) and Uq(su(1,1)) and generating functions for orthogonal polynomials
Authors: Van der Jeugt J. , Jagannathan R.
Published: July 2002

Positive discrete series representations of the Lie algebra su(1,1) and the quantum algebra Uq(su(1,1)) are considered. The diagonalization of a self-adjoint operator (the Hamiltonian) in these representations and in tensor products of such representations is determined, and the generalized eigenvectors are constructed in terms of orthogonal polynomials. Using simple realizations of su(1,1), Uq(su(1,1)), and their representations, these generalized eigenvectors are shown to coincide with generating functions for orthogonal polynomials. The relations valid in the tensor product representations then give rise to new generating functions for orthogonal polynomials, or to Poisson kernels. In particular, a group theoretical derivation of the Poisson kernel for Meixner–Pollaczek and Al-Salam–Chihara polynomials is obtained.
Black hole thermodynamics and spectral analysis
Authors: Belgiorno F.
Published: July 2002

We deal with some problems concerning quantum matter fields thermodynamics on static spherosymmetric black hole backgrounds. By means of variable separation, we study the self-adjointness of the Euclidean wave operators relevant in the calculation of the partition function and of the thermal Green functions for the case of scalar quantum fields in thermal equilibrium with a Schwarzschild black hole. In this respect, the role of the horizon surface is analyzed. An approach to this topic, related to completeness of the Euclidean manifold, is also discussed. It is found that, if the horizon surface is not included in the Euclidean manifold (or if it cannot be included, as in the case of a temperature different from the black hole one), essential self-adjointness is missing and boundary conditions on the horizon are required. We also analyze some qualitative spectral properties of the given wave operators after introducing an infrared regularization by means of a spherical box. We find that in the standard Euclidean path integral approach the spectrum is purely discrete. The same analysis is carried out for the noncovariant choice of the functional measure in the Euclidean path integral. An analogous study is carried for an extremal Reissner–Nordström black hole and it is sketched in the nonextremal one. The latter is completely analogous to the Schwarzschild case, whereas in the extremal case it is found that the corresponding Riemannian manifold is complete for every choice of the temperature and that at finite four volume there is a nonvoid continuous spectrum. Physical implications of our results are discussed.
Group-theoretical quantization of 2+1 gravity in the metric-torus sector
Authors: Hájı́ček P.
Published: July 2002

A symmetry based quantization method of reparametrization invariant systems is described; it will work for all systems that possess complete sets of perennials whose Lie algebras close and those that generate sufficiently large symmetry groups. The construction leads to a quantum theory including a Hilbert space, a complete system of operator observables, and a unitary time evolution. The method is applied to the 2+1 gravity. The paper is restricted to the metric-torus sector, zero cosmological constant Λ and it makes strong use of the so-called homogeneous gauge; the chosen algebra of perennials is that of Martin. Two frequent problems are tackled. First, the Lie algebra of perennials does not generate a group of symmetries. The notion of group completion of a reparametrization invariant system is introduced so that the group does act; the group completion of the physical phase space of our model is shown to add only some limit points to it so that the ranges of observables are not unduly changed. Second, a relatively large number of relations between observables exists; they are transferred to the quantum theory by the well-known methods of Kostant and Kirillov. In this way, a uniqueness of the physical representation of some extension of Martin’s algebra is shown. The Hamiltonian is defined by a systematic procedure due to Dirac; for the torus sector, the result coincides with that by Moncrief. The construction may be extended to higher genera and nonzero Λ of the 2+1 gravity, because some complete sets of perennials are well-known and there are no obstructions to the closure of the algebra.
Integrable and solvable many-body problems in the plane via complexification
Authors: Calogero F.
Published: July 2002

A simple prescription allows us to transform, by appropriate complexification, any one-dimensional many-body problem (describing “motions on a line”) with Newtonian (“acceleration equals forces”) equations of motion featuring forces which depend analytically on the positions, and possibly on the velocities, of the particles, and which are moreover scaling- or translation-invariant, into a two-dimensional many-body problem (describing “motions in the plane”) with rotation-invariant equations of motion. If the original (one-dimensional) model is Hamiltonian, the two-dimensional model is also Hamiltonian (in fact, bi-Hamiltonian). In this manner, starting from known integrable or solvable one-dimensional many-body problems, integrable or solvable many-body problems in the plane, generally featuring much richer dynamics, are obtained. Several examples are exhibited. Finally another, more direct, prescription is outlined, to transform by complexification almost any one-dimensional many-body problem into a rotation-invariant many-body problem in the plane.
The Floquet analysis and noninteger higher harmonics generation
Authors: Cerveró José M. , Lejarreta Juan D.
Published: July 2002

We consider here the exact solution of a nonrelativistic quantum system composed of a two-level atom interacting with a laser with arbitrary large frequency and intensity. We use the analogy of this system and a ℏ/2-spin particle interacting with a time-dependent magnetic field. A systematic use of the dynamical symmetry underlying the physical system is made. Actually the Hamiltonian is a Hermitian element of the SU(2) Lie Algebra. The exact Temporal Evolution Operator in terms of a Generalized Displacement Operator of the group is constructed. It is possible to develop a nonperturbative method that allows us to solve exactly the model for any value of the relevant frequencies (Rabi, Laser, and Atom Frequencies) and in so doing the usual Rotating Wave and Small Interaction approximations are unnecessary. The properties of periodicity of this model and the phenomenon of harmonic generation are considered by using Floquet Analysis. We find that in addition to the so far well-known spectrum composed by odd harmonics, this model generates another type of noninteger harmonics whose frequencies and amplitudes are determined for any value of the relevant parameters of the system.
Resonances in a box
Authors: Hagedorn George A. , Meller Bernhard
Published: July 2002

We investigate a numerical method for studying resonances in quantum mechanics. We prove rigorously that this method yields accurate approximations to resonance energies and widths for shape resonances in the semiclassical limit.
Classification of finite dimensional modules of singly atypical type over the Lie superalgebras sl(m/n)
Authors: Su Yucai
Published: July 2002

We classify the finite dimensional indecomposable sl(m/n)-modules with at least a typical or singly atypical primitive weight. We do this classification not only for weight modules, but also for generalized weight modules. We obtain that such a generalized weight module is simply a module obtained by “linking” subquotient modules of generalized Kac-modules. By applying our results to sl(m/1), we have in fact completely classified all finite dimensional sl(m/1)-modules.
Neutral particles and super Schwinger terms
Authors: Ekstrand C.
Published: July 2002

Z 2 -graded Schwinger terms for neutral particles in 1 and 3 space dimensions are considered.
Reconstruction of a charged helium film on a metallic substrate
Authors: Shikin V. , Leiderer P.
Published: July 2002

Peculiarities of the reconstruction of a charged helium film surface on a metallic substrate are considered. Instability evolution in this case resembles the generation of a solitary wave in hydrodynamics of a free liquid surface and leads to the formation of charged solitons under certain conditions. Basic characteristics of such solitons are obtained in the one-dimensional approximation under the conditions of weak nonlinearity of the problem.
Mechanisms of critical current limitation in YBCO thin film structures
Authors: Beňačka Š. , Štrbik V. , Chromik Š. , Adam R. , Darula M. , Gaži Š.
Published: July 2002

The limitation of critical current in high Tc superconducting YBCO thin films has a varied nature according to the quality of YBCO films. Our results showed that in strips from granular films the weak links of superconductor–normal metal–superconductor and superconductor–constriction–superconductor types were responsible for critical current limitation. In the YBCO strips with improved (preferential) crystallographic orientation a flux-creep critical current limitation was found and in the highly oriented YBCO strips the Ginzburg–Landau depairing mechanism approximated the critical current limitation for temperature close to Tc.
Vortex momentum density and invariants of the hydrodynamic equations of superfluidity and superconductivity
Authors: Kuz’min G. A.
Published: July 2002

The gauge transformation of the hydrodynamic equations of superfluidity and superconductivity is considered. The vortex and heat momentum densities are defined and their evolution equations are derived. The physical meaning of these quantities is analyzed. The Lagrangian invariants of the new set of equations, which are similar to those obtained by Hollman for classical hydrodynamics, are derived.
High-Tc rf SQUIDs for operation in magnetic fields. Effect of thermal fluctuations
Authors: Shnyrkov V. I. , Timofeev V. P. , Garbuz A. S. , Kim Cheol Gi
Published: July 2002

Optimization of bulk high-Tc rf SQUID characteristics is carried out in the limit of strong thermal fluctuations. It is shown that such fluctuations affect the impedance of interferometers so that they operate only in quasi-nonhysteretic mode. Textured ceramics can be used to produce SQUIDs capable of stable operation in unshielded environment and/or in strong magnetic fields (H=150–200 A/m) with a sensitivity about 2×10−13 T/Hz1/2. These SQUIDs form the basis of a portable susceptometer designed and tested in constant (up to 150 A/m) and varying (up to 4 A/m) magnetic fields with a magnetic moment sensitivity not lower than 1.6×10−10 A⋅m2.
Sequence of structural phase transitions induced by an external magnetic field in the Jahn–Teller elastic KTm(MoO4)2
Authors: Kobets M. I.
Published: July 2002

Electron paramagnetic resonance and ac magnetic susceptibility studies in the compound KTm(MoO4)2 have revealed a number of features in the microwave absorption and magnetic susceptibility. It is conjectured that there is a sequence of magnetic-field-induced structural phase transitions involving the formation of a superstructure of the crystal lattice in KTm(MoO4)2. Experimental studies are carried out at a temperature of 1.7 K.
The theory of equilibrium magnetic properties of granulated magnetic materials
Authors: Stefanovskii E.
Published: July 2002

The present-day analysis of the theoretical adaptation status of the experimental curves of the magnetization and the static magnetic susceptibility as functions of the external parameters H and T (H is an applied external magnetic field and T is a temperature) is made for granulated ferromagnetic systems. Once more it is pointed that the consideration of the energy of magnetic anisotropy of a ferromagnetic material (as against the methods of the adapt used everywhere) play an essential role for the understanding of the magnetic behavior of the systems mentioned above and allow us to investigate the magnetoanisotropic behavior of granulated magnetic systems [at certain granule distribution functions (by their volume and orientation) as regards the external magnetic field]. It is shown that the use of the “blocking” concept is not necessary for the investigations of the thermodynamically equilibrium magnetic properties of the above systems.
A new boundary condition in the flow of rarefied gases at surfaces
Authors: Goodman Frank O.
Published: July 2002

A new boundary condition in the flow of rarefied gases at surfaces, based on the idea of completely diffuse scattering with respect to the local surface, is proposed. With the example of free-molecule-flow transmission probabilities in capillaries, results from the new boundary condition are compared with experimental data and with results, obtained here analytically, from the ‘‘backscattering’’ model of Berman and Maegley [Phys. Fluids 15, 772, 780 (1972)]. The effective backscattering with the new boundary condition is related to the distribution of slopes of the local surface relative to the corresponding average geometrical surface. The analysis, in its present form, is restricted to the case of small local surface slopes.
The evolution of axisymmetric rectangular second-sound (heat) pulses in superfluid helium
Authors: Fiszdon W. , Peradzynski Z. , Stamm G.
Published: July 2002

Very little attention has been given, so far, to the problem of the propagation of axisymmetric second-sound shock waves, although they may occur in practical applications. In this paper, research on the propagation of moderate cylindrical heat pulses in superfluid helium is reported. A theoretical model is built based on the experimental observation of the evolution of the structure of rectangular heat pulses. The agreement between the experimental measurements and the theoretical calculations of the evolution of the main parameters is very satisfactory.
Magnetohydrodynamic stability in the electromagnetic levitation of horizontal molten-metal sheets
Authors: Hull John R. , Wiencek Tom , Rote Donald M.
Published: July 2002

High-frequency electromagnetic (EM) fields are investigated for the levitation of thin horizontal sheets of liquid metal. A magnetic configuration is analyzed in which inductance stabilization provides global stability and magnetic flux compression provides local stability. Stability analysis indicates that frequencies greater than about 24 kHz are desirable to stably levitate 6 mm thick steel. For stability in systems without active feedback, a conducting screen is required below the metal, with a gap between the screen and the molten metal of no more than twice the metal thickness. Experiments in which 10 kHz EM fields were used to statically levitate sheets of molten tin indicate that dominant magnetohydrodynamic instabilities are of the Rayleigh–Taylor type and correspond to theory.
Nonlinear kink modes for supersonic vortex sheets
Authors: Artola Miguel , Majda Andrew J.
Published: July 2002

Both recent large-scale numerical simulations and time-dependent asymptotic nonlinear wave theories reveal the prominence of kink modes in the nonlinear instability of supersonic vortex sheets. These kink modes are nonlinear traveling waves that move along the vortex sheet at various speeds and have a wave structure consisting of a kink in the slip stream bracketed by shocks and rarefactions emanating from each side of the kink. Here an explicit construction is developed for calculating all the nonlinear kink modes that bifurcate from a given unperturbed contact discontinuity. This construction is applied at small amplitudes to provide a completely independent confirmation of the asymptotic nonlinear wave theories through a static bifurcation analysis. For the unperturbed vortex sheet, bifurcation diagrams at large amplitudes are also computed for several interesting density ratios and Mach numbers. These results are applied at large amplitude to explain some of the phenomena observed in numerical simulations.
Free expansion of a gas against a rigid wall
Authors: Diez J. A. , Thomas L. P.
Published: July 2002

The flow behind the shock wave produced when a freely expanding gas strikes a rigid wall is studied. The shock speed is known within an early stage after the shock onset, when the flow is self-similar and, also, as is pointed out, when the shock decays into a sonic disturbance, propagating in an almost uniform gas. On this basis, an approximate differential equation can be written for the shock position, whose solution is analytic, and therefore, the flow magnitudes are given by simple relationships. Comparison with numerical simulations shows that the flow is well described by this approximation. This work also includes a brief review of the equations for the self-similar regime, because corrections to previously published results were found necessary.
Choice of the threshold level in a velocity-based conditional sampling procedure
Authors: Tabatabai M. , Kawall J. G. , Keffer J. F.
Published: July 2002

Analysis of velocity traces obtained in the intermittent region of a wake by means of a rake of hot-wire probes has clearly shown that many of the weak fluctuations observed in the outer, very low-intermittency-factor region of the flow are associated with the turbulent bulges and are not potential flow fluctuations, as might be concluded from single probe measurements. Since most velocity-based conditional sampling techniques rely, to some extent, on a visual comparison of the intermittent signal and its indicator function, the choice of the threshold level associated with these techniques is rather subjective and, consequently, identification of these weak turbulent-zone fluctuations is often not made. A relatively objective and robust method of obtaining the threshold level for a velocity-based turbulent detector function is presented and discussed.
Deformation of some biological particles
Authors: Nir Avinoam
Published: July 2002

The deformation of biological particles in a quiescent fluid medium is considered by simulating the particle as a viscous droplet surrounded by a thin surface layer in which the forces rendering the motion arise. The dynamics is studied using the boundary integral equation developed by Rallison and Acrivos [J. Fluid Mech. 89, 191 (1978)] in conjunction with various formulations for the surface tractions depending on the availability of biological information. The cases of vesicle coalescence, cell division, and embryo development are simulated by regarding the interfacial forces as constant surface tension, variable surface tension, and nonhomogeneous anisotropic tension, respectively.
Sedimentation of axisymmetric particles in shear flows
Authors: Davis Robert H.
Published: July 2002

Axisymmetric particles possessing fore-and-aft symmetry undergo tumbling motions, known as Jeffery orbits, when suspended in shear flows. The sedimentation velocity of such a particle depends on its instantaneous orientation and, hence, varies during an orbit. Closed-form analytical expressions are derived for the time-averaged sedimentation velocity of a particle as it tumbles through one full orbit, with the gravity vector being oriented arbitrarily with respect to the flow direction. This orbit velocity is then integrated numerically over the distribution of orbits in order to obtain the average sedimentation velocity in dilute suspensions, for several different orbit distributions corresponding to the short-time limit with random initial orientations, the long-time limit for dilute suspensions with weak Brownian motion, measured steady distributions for dilute suspensions of non-Brownian particles with particle–particle interactions, and singular distributions of particles aligning such that viscous dissipation is minimized. Specific calculations are made for prolate and oblate ellipsoids, cylindrical rods and disks, and a pair of touching spheres. The average sedimentation velocity depends strongly on the aspect ratio of the particles, and on the orientation of the gravity vector relative to the flow field, but only weakly on the assumed form of the distribution of orbits.