bluuebunny/crossref_metadata_2025 huggingface dataset:
Similarity reduction of the one-Killing-vector vacuum equations in general relativity
Authors: Stephani H.
Published: July 2002

The one-Killing-vector vacuum equations are a set of partial differential equations in three independent variables. To make them tractable, one usually assumes the existence of a second commuting Killing vector field. In this paper, the full set of Lie-point symmetries of the equations and the related (other) possible reductions to differential equations in two independent variables are discussed.
On the absence of physical degrees of freedom in the Stephenson–Kilmister–Yang theory
Authors: Maluf José W.
Published: July 2002

Using Dirac’s prescription for constrained Hamiltonian systems, it will be shown that for the Stephenson–Kilmister–Yang theory of gravity the number of constraints is greater than the number of degrees of freedom when metric and connection are independent field variables.
The Riemann–Hilbert problem approach to a representation of the Virasoro group II
Authors: Li Wei , Hou Bo-yu
Published: July 2002

The development of a Riemann–Hilbert (RH) problem approach to the representation of the Virasoro group introduced in our earlier paper [W. Li and B. Y. Hou, J. Math. Phys. 30, 1198 (1989)] is continued. The Rouche theorem is employed to prove that there exists a set of scalar functions in the complex τ plane, in terms of which the structure of the Virasoro group can be decided. The general form of the RH problem will also be presented and the uniqueness of its solution will be proven. For future use, a standard form of a matrix Fredholm equation equivalent to our RH problem will be deduced. This may help to establish in a future paper the existence of a solution of the RH problem.
Schwinger terms from geometric quantization of field theories
Authors: Ewen H. , Schaller P. , Schwarz G.
Published: July 2002

Geometric quantization is applied to infinite (countable)-dimensional linear Kähler manifolds to obtain a closed expression for the anomalous commutator of arbitrary polynomial observables. Examples for the physical relevance of the result are given, including the polarization dependence of Schwinger terms in bilinear constraint algebras, the central terms of Virasoro and Kac–Moody algebras, and the determination of the critical dimension of the bosonic string.
Exact solutions for a soliton crystal
Authors: Dodd L. R. , Lohe M. A.
Published: July 2002

A model field theory in one space and one time dimension for a system of fermions interacting through a scalar field with the self-energy density of the linear sigma model is considered. Exact, periodic solutions of the mean field equations for N Nf fermions on a linear lattice of N cells with Nf fermions per cell are found for arbitrarily large N. The multisoliton solutions are expressed entirely in terms of Jacobi elliptic functions and explicit expressions for the fermion energy spectrum and the energy density of the system are given. In the low-density limit the solution in a single cell reduces to the shallow or deep bag solution previously found by Campbell and Liao. Conditions for the bifurcation of the periodic, crystal solutions from solutions with a constant sigma field at high densities are derived, and comparison is made with earlier numerical work.
The action principle revisited
Authors: Balasin H. , Stierle M.
Published: July 2002

The form of Schwinger’s action principle within the BPHZ method is investigated and some loopholes in the usual proofs are closed.
Infinite-dimensional generalizations of finite-dimensional symmetries
Authors: Fradkin E. S. , Linetsky V. Ya.
Published: July 2002

Infinite-dimensional algebras associated with simple finite-dimensional Lie algebra g are considered. Generalizations of sl2 are studied in details. A manifest expression for the Virasoro-like generalization of D=3 conformal algebra so(3,2) is also presented. Applications in higher spin theory and in conformal QFT are discussed.
Transformation properties of the Schrödinger equation with the momentum-dependent potential (x⋅∇)2ord
Authors: Papp E.
Published: July 2002

Using suitable coordinate transformations enables us to convert the Schrödinger equation with the momentum-dependent potential (x⋅∇)2ord into a pair of coupled s-wave Pöschl–Teller systems with zero energy. An equivalent zero-energy system with a related singular potential has also been derived, this time by using an appropriate wavefunction transformation.
Colliding wave solutions of the Einstein–Maxwell field equations
Authors: Li Wei , Hauser Isidore , Ernst Frederick J.
Published: July 2002

A large family of solutions of the vacuum Einstein equations [J. Math. Phys. 32, 723 (1991)] is generalized to the electrovac case. The new solutions are shown to possess Killing–Cauchy horizons when one of the parameters n is set equal to 3, 1, −1 or −3.
Spinor connections and geometrization of fermions
Authors: Liu Yufen
Published: July 2002

The basic principles of spinor gauge theories are presented. Spinor connections and their physical interpretations are studied in detail. The geometrization of right (or left)-handed fermions in higher-dimensional space is discussed.
Orthomodularity and quadratic transformations in probabilistic theories of physics
Authors: Lahti Pekka J. , Maczynski Maciej J.
Published: July 2002

A characterization of orthomodularity of a set of effects is given in terms of a triangle closedness of this set. This leads to a simple (probabilistic) characterization of observables with a Boolean range. Quadratic transformations on expectation functionals of observables are studied in order to investigate the derivability of the Heisenberg inequality and the form of the lower bound of such an inequality for a pair of observables.
On the motion of test particles in a fluctuating gravitational field
Authors: Modanese Giovanni
Published: July 2002

In this paper the ‘‘free fall’’ motion of a test tetrad in a weak gravitational field is studied. This is done with the intention of exploring the geometry locally through geodesics and parallel transport. By use of the so-called ‘‘radial gauge’’ the action of the field on the test tetrad just in terms of the Riemann tensor is expressed. The average effect of small quantized fluctuations of the field can thus be computed using the Feynman–De Witt propagator. Since the dimension L of the test particle must be finite, only fluctuations of wavelength λ≥L have to be considered. The corresponding corrections to the geometry are proportional to lPlanck/L. Such dependence on L spoils, in fact, a genuine geometrical description.
Distorted Riemannian space and technique of differential geometry
Authors: Rylov Yuri A.
Published: July 2002

A differential-geometric technique of non-Riemannian space description is considered. This n-dimensional distorted Riemannian space distinguishes from a Riemannian one by a substitution of one-dimensional geodesics by (n−1)-dimensional tubes. Such a space is of interest as a model of space-time, taking into account quantum effects.
Unified models from gauged supergroups. III. The ‘‘super-2-sphere’’ OSp(3‖2)/OSp(2‖2)
Authors: Jarvis P. D. , McAnally D. S.
Published: July 2002

The formalism of coset space dimensional reduction for internal supersymmetry [P. D. Jarvis, J. Math. Phys. 31, 1783 (1990); P. D. Jarvis and D. S. McAnally, J. Math. Phys. 33, 399 (1992)] is extended in the supersymmetric case, and the homogeneous superspace OSp(3‖2)/OSp(2‖2) is studied in detail, with gauge supergroup OSp(m+2‖2).
All universal coverings of two-dimensional gravity with torsion
Authors: Katanaev M. O.
Published: July 2002

Global solutions of two-dimensional gravity with torsion are found and elucidated. The model admits complete analysis of possible maximally continued space-times by means of Penrose’s diagrams. There are 13 types of orientable universal coverings. For zero cosmological constant there is flat two-dimensional Minkowskian space-time. For nonzero cosmological constant the universal covering of zero torsion covers one-sheet hyperboloid with Lorenzian metric of constant curvature. All other universal coverings are the surfaces of nonzero torsion and nonconstant curvature. The global solutions include surfaces of a black hole configuration.
Exact solutions of coupled-wave equations in piezoelectric solids
Authors: Ren Wei
Published: July 2002

The homogeneous coupled-wave equations under the quasistatic approximation are exactly solved by using the method of angular-spectrum expansions. And Weyl’s method of deriving the scalar Green’s functions in an isotropic media is generalized to the study of the tensor Green’s functions (solutions to inhomogeneous coupled-wave equations) in piezoelectric media. The series, integral representations, and addition theorems of the spherical wave functions of the first, second, third, and fourth kind for homogeneous piezoelectric solids are presented. The series representations of Green’s functions are of the form of separation variables. These representations are well suited to imposing the boundary conditions when dealing with fields and waves in spherically layered piezoelectric media.
The limiting dynamics of an imperfect Bose gas
Authors: Hertle Jochen
Published: July 2002

For an imperfect Bose gas consisting of massive particles and interacting through a long-range pair potential in a mean-field approximation, both in equilibrium and far from equilibrium, the dynamics are derived in the thermodynamic limit. This is done in the framework of the operator algebraic quantum theory. The limiting dynamics is formulated in the Schrödinger picture as a group of affine transformations of certain folia of physical states. Similar to the mean-field models for spin lattices, the algebra of quasilocal observables is not invariant under the Heisenberg dynamics in the GNS representation of general time invariant states. It is known that above critical density the infinite system exhibits condensation, and the condensate is characterized by the classical parameters density and phase. For these parameters a classical nonlinear equation of motion is derived.
Quantum Koszul complexes for Majid’s braided Lie algebras
Authors: Wambst Marc
Published: July 2002

A Yang–Baxter operator was canonically associated to any cocommutative braided Lie algebra as defined by Majid. Applying previous results, we construct quantum Koszul complexes for braided Lie algebras with respect to this operator. In the usual case, the complexes reduce to the Chevalley–Eilenberg complexes for classical Lie algebras.
Algebraic structure of the BRST symmetry
Authors: Tǎtar Liviu , Tǎtar Radu
Published: July 2002

An explicit construction of the BRST symmetry is presented in the Hamiltonian approach. The construction is based on the splitting homotopy and the transference problem.
Evolution hyperheavenly equations
Authors: Plebański J. F. , Przanowski M.
Published: July 2002

The Cauchy–Kovalevskaya and evolution forms of all hyperheavenly equations are presented. Some methods of integration of these equations are proposed.
Linear differential equations for a fractional spin field
Authors: Cortés J. L. , Plyushchay M. S.
Published: July 2002

The vector system of linear differential equations for a field with arbitrary fractional spin is proposed using infinite-dimensional half-bounded unitary representations of the SL(2,R) group. In the case of (2j+1)-dimensional nonunitary representations of that group, 0<2j∈Z, they are transformed into equations for spin-j fields. A local gauge symmetry associated to the vector system of equations is identified and the simplest gauge invariant field action, leading to these equations, is constructed.
On transformations preserving the basis conditions of a spin structure group in four-dimensional superstring theory in free fermionic formulation
Authors: Kholodnyi Valery A.
Published: July 2002

Let Ξ stand for a finite Abelian spin structure group of 4-dimensional superstring theory in free fermionic formulation whose elements are 64-dimensional vectors (spin structure vectors) with rational entries belonging to ]−1,1] and the group operation is the mod 2 entry by entry summation ⊕ of these vectors. Let B={bi, i=1,...,k+1} be a set of spin structure vectors such that bi have only entries 0 and 1 for any i=1,...,k, while bk+1 is allowed to have any rational entries belonging to ]−1,1] with even Nk+1, where Nk+1 stands for the least positive integer such that Nk+1bk+1=0 mod 2. Let B be a basis of Ξ, i.e., let B generate Ξ, and let Λm,n stand for the transformation of B which replaces bn by bm⊕bn for any m ≠ k+1, n ≠ 1, m ≠ n. It is proven that if B satisfies the axioms for a basis of spin structure group Ξ, then B′=Λm,nB also satisfies the axioms. Since the transformations Λm,n for different m and n generate all nondegenerate transformations of the basis B that preserve the vector b1 and a single vector bk+1 with general rational entries, it can be concluded that the axioms are conditions for the whole group Ξ and not just conditions for a particular choice of its basis. Hence, these transformations generate the discrete symmetry group of four-dimensional superstring models in free fermionic formulation. This is the physical meaning of the obtained result. The practical impact is that in searching for a realistic model in four-dimensional superstring theory in free fermionic formulation it is enough to search only through different groups Ξ, which number dramatically less than the number of their different bases.
Hierarchical structures and asymmetric stochastic processes on p-adics and adeles
Authors: Karwowski Witold , Mendes R. Vilela
Published: July 2002

The space of states of some phenomena, in physics and other sciences, displays a hierarchical structure. When that is the case, it is natural to label the states by a p-adic number field. Both the classification of the states and their relationships are then based on a notion of distance with ultrametric properties. The dynamics of the phenomena, that is, the transition between different states, is also a function of the p-adic distance dp. However, because the distance is a symmetric function, probabilistic processes which depend only on dp have a uniform invariant probability measure, that is, all states are equally probable at large times. This being a severe limitation for cases of physical interest, processes with asymmetric transition functions have been studied. In addition to the dependence on the ultrametric distance, the asymmetric transition functions are allowed to depend also on the probability of the target state, leading to any desired invariant probability measure. When each state of a physical system is associated to several distinct hierarchical structures or parametrizations, an appropriate labeling set is the ring of adeles. Stochastic processes on the adeles are also constructed.
The Euclidean Hopf algebra U
q(e
N) and its fundamental Hilbert-space representations
Authors: Fiore Gaetano
Published: July 2002

The Euclidean Hopf algebra Uq(eN) dual of Fun(RNq■SOq−1(N)) is constructed by realizing it as a subalgebra of the differential algebra Diff(RNq) on the quantum Euclidean space RNq; in fact, the previous realization [G. Fiore, Commun. Math. Phys. 169, 475–500 (1995)] of Uq−1(so(N)) is extended within Diff(RNq) through the introduction of q derivatives as generators of q translations. The fundamental Hilbert-space representations of Uq(eN) turn out to be of highest weight type and rather simple ‘‘lattice-regularized’’ versions of the classical ones. The vectors of a basis of the singlet (i.e., zero-spin) irrep can be realized as normalizable functions on RNq, going to distributions in the limit q → 1.
Multivariable Grassmann integrals and the high temperature expansion of interacting fermionic models
Authors: Charret I. C. , Corrêa Silva E. V. , de Souza S. M. , Thomaz M. T.
Published: July 2002

Using the noncommuting nature of fermionic fields we obtain a nonperturbative method to calculate the high temperature limit of the grand canonical partition function of interacting fermionic models. This nonperturbative approach is applied to the Hubbard model in d=2(1+1) and we recover the known results in the limit T → ∞.
Focusing nonlinear Schrödinger equation with infinitely many solitons
Authors: Kamvissis Spyridon
Published: July 2002

We consider the long time behavior of the solutions of the focusing nonlinear Schrödinger equation, under particular initial data, giving rise to infinite soliton trains. We prove our results by using the Riemann–Hilbert factorization formulation of the inverse scattering problem. We extend the method of Potapov, Zakharov, and Shabat (originally introduced in the case of finitely many eigenvalues) by ‘‘factoring away’’ the ‘‘soliton’’ component of the solution in terms of infinite Blaschke-type products. Finally, we compare our approach with recent results that aim to construct infinite-soliton reflectionless potentials, by Gesztesy–Karwowski–Zhao and by Shabat.
A model for the continuous q-ultraspherical polynomials
Authors: Floreanini Roberto , Vinet Luc
Published: July 2002

An algebraic interpretation for two classes of continuous q-polynomials is provided. Rogers’ continuous q-Hermite polynomials and continuous q-ultraspherical polynomials are shown to realize, respectively, bases for representation spaces of the q-Heisenberg algebra and a q-deformation of the Euclidean algebra in these dimensions. A generating function for the continuous q-Hermite polynomials and a q-analog of the Fourier–Gegenbauer expansion are naturally obtained from these models.
Exact solutions of the Dirac equations in an anisotropic cosmological background
Authors: Portugal Renato
Published: July 2002

Exact solutions of the Dirac equations are given for an anisotropic Bianchi VI0 background. The direction of propagation of the spinor obeys the geometrical symmetries of the cosmological model.
Representations of 𝒰h
(𝔰𝔲(N)
) derived from quantum flag manifolds
Authors: Šťovı́ček Pavel , Twarock Reidun
Published: July 2002

A relationship between quantum flag and Grassmann manifolds is revealed. This enables a formal diagonalization of quantum positive matrices. The requirement that this diagonalization defines a homomorphism leads to a left 𝒰h(𝔰𝔲(N))-module structure on the algebra generated by quantum antiholomorphic coordinate functions living on the flag manifold. The module is defined by prescribing the action on the unit and then extending it to all polynomials using a quantum version of the Leibniz rule. The Leibniz rule is shown to be induced by the dressing transformation. For discrete values of parameters occurring in the diagonalization one can extract finite-dimensional irreducible representations of 𝒰h(𝔰𝔲(N)) as cyclic submodules.
Octonionic representations of GL(8,ℛ) and GL(4,𝒞)
Authors: De Leo Stefano , Abdel-Khalek Khaled
Published: July 2002

Octonionic algebra being nonassociative is difficult to manipulate. We introduce left/right octonionic barred operators which enable us to reproduce the associative GL(8,ℛ) group. Extracting the basis of GL(4,𝒞), we establish an interesting connection between the structure of left/right octonionic barred operators and generic 4×4 complex matrices. As an application we give an octonionic representation of the four-dimensional Clifford algebra.
Dia- and paramagnetism for nonhomogeneous magnetic fields
Authors: Erdős László
Published: July 2002

Diamagnetism of the magnetic Schrödinger operator and paramagnetism of the Pauli operator are rigorously proven for nonhomogeneous magnetic fields in the large field, in the large temperature and in the semiclassical asymptotic regimes. New counterexamples are presented which show that neither dia- nor paramagnetism is true in a robust sense (without asymptotics). In particular, we demonstrate that the recent diamagnetic comparison result by Loss and Thaller [M. Loss and B. Thaller, Commun. Math. Phys. (submitted)] is essentially the best one can hope for.
Higher level WZW sectors from free fermions
Authors: Böckenhauer Jens , Fuchs Jürgen
Published: July 2002

We introduce a gauge group of internal symmetries of an ambient algebra as a new tool for investigating the superselection structure of WZW theories and the representation theory of the corresponding affine Lie algebras. The relevant ambient algebra arises from the description of these conformal field theories in terms of free fermions. As an illustration we analyze in detail the so(N) WZW theories at level two, which allows us in particular to construct explicit bases for the level-two irreducible highest weight modules. In this case there is actually a homomorphism from the representation ring of the gauge group to the subring of the WZW fusion ring that corresponds to the Neveu–Schwarz sector, even though the level-two observable algebra is smaller than the gauge invariant subalgebra of the field algebra.
Splitting in large dimension and infrared estimates. II. Moment inequalities
Authors: Helffer B.
Published: July 2002

This is the continuation of notes written for the NATO-ASI conference in Il Ciocco (September 96) consisting of the analysis of the links between estimating the splitting between the two first eigenvalues for the Schrödinger operator H and the proof of infrared estimates for quantities attached to Gaussian-type measures. These notes were mainly reporting on the “old” contributions of Dyson, Fröhlich, Glimm, Jaffe, Lieb, Simon, and Spencer (in the 1970s) in connection with more recent contributions of Pastur, Khoruzhenko, Barbulyak, and Kondrat’ev which treat in general more sophisticated models. Here we concentrate on the simplest model related to field theory and extend the results of Barbulyak and Kondrat’ev by mixing ideas coming from Pastur and Khozurenko related to the use of Bogolyubov’s inequality with classical inequalities due to Ginibre, Lebowitz, Sokal, and others, or, in the case when the temperature T is zero, by applying rather elementary estimates on Schrödinger operators, in order to find lower bounds for second-order moments attached to the measure φ⟼Trφ exp−βH/Tr exp−βH with β=1/T. This question was “left to the reader” in lectures given by J. Fröhlich in 1976 [Acta Phys. Austriaca, Suppl. XV, 133–269 (1976)], but we think that it is worthwhile to do this “homework” carefully.
Fixed points due to gravitational lenses
Authors: Petters A. O. , Wicklin F. J.
Published: July 2002

A fixed point of a gravitational lensing map represents those positions from which a pointlike light source has a lensed image that, despite gravitational lensing, corresponds to the original position of the source. In this paper we study fixed points of lensing maps due to a generic gravitational lens with applications to nonsingular isolated lenses, and to point-mass lenses with continuous matter and shear. Counting formulas and bounds on the number of fixed points are determined. The results include an odd-number fixed-point theorem for nonsingular isolated deflectors. Information on the positions of fixed points are found for the case of point masses on a lens plane with and without shear. The methods of the paper are based on Morse theory, complex variables, and resultants.
Shadow of noncommutativity
Authors: Dubois-Violette Michel , Madore John , Kerner Richard
Published: July 2002

We analyze the structure of the κ=0 limit of a family of algebras Aκ describing noncommutative versions of space–time, with κ a parameter of noncommutativity. Assuming the Poincaré covariance of the κ=0 limit, we show that, besides the algebra of functions on Minkowski space, A0 must contain a nontrivial extra factor A0I which is Lorentz covariant and which does not commute with the functions whenever it is not commutative. We give a general description of the possibilities and analyze some representative examples.
Deriving the Hamilton equations of motion for a nonconservative system using a variational principle
Authors: Tveter Frank Thomas
Published: July 2002

The classical derivation of the canonical transformation theory [H. Goldstein, Classical Mechanics, 2nd ed. (Addison–Wesley, Reading, 1981)] is based on Hamilton’s principle which is only valid for conservative systems. This paper avoids this principle by using an approach that is basically reversed compared to the classical derivation. The Lagrange equations of motion are formulated in the undefined and general variable set {Q,P}, and the general Hamilton equations of motion are derived from the Lagrange equations by using a variational principle. The undefined general variables {Q,P} are defined through a transformation to a special (defined) variable set {q,p}. The transformation equations connecting the two sets are derived by using the invariants property of the value of the Lagrangian. This approach results in a more general interpretation of the generator function.
A classical large N hierarchical vector model in three dimensions: A nonzero fixed point and canonical decay of correlation functions
Authors: Faria da Veiga P. A. , O’Carroll M. , Schor R.
Published: July 2002

We consider a hierarchical N-component classical vector model on a three-dimensional lattice Z3, for large N. The model differs from the usual one in that the kernel of the inverse Laplace operator is nontranslational invariant but has matrix elements which are positive and exhibit the same falloff as the inverse Laplacian in Z3. We introduce a renormalization group transformation and for N=∞, corresponding to the leading order of the 1/N expansion, we construct explicitly a nonzero fixed point for this transformation and also obtain some correlation functions. The two-point function has canonical decay. For 1≪N<∞, we obtain the fixed point and the two-point function in the first 1/N approximation. Canonical decay is still verified, in contrast to what is reported for the full model.
Stochastic quantum geometry within a (1+1) manifold: A basic construction
Authors: Miller Steven D.
Published: July 2002

A bounded, globally hyperbolic, space–time manifold M2 with topology I(t)⊗R is presented as a simple classical, deterministic, geometry, with ADM (1+1) slicing via a lapse function and shift vectors. The Cauchy development is then equivalent to the evolution of a spatial Riemann 1-metric β(x,0)→β(x,t) for a bounded spatial interval I(t)=[0,l] such that x−x′<=l for all x,x′∈(t) for all t∈R. The 1-metric is considered a parametrized, stochastically fluctuating variable {β(x,t)}∈Riemm(I) for some critical (microscopic) correlation scale l, where Riemm(I) is the space of all 1-metrics on I. If the metric fluctuations are constrained by a scale-dependent probability kernel or density distribution on [0,1], then a Fokker–Planck equation can be developed for the Cauchy evolution of the kernel. The stationary (Cauchy invariant) equilibrium limit solution is obtained. The equilibrium limit correlations 〈β(x,t)β(x′,t)〉 at second order derived from the stochastic model, can be directly identified with the general, well-known form of the metric two-point (equal time) correlations obtained from linearized general relativity treated as a quantum field theory. The metric diffusion coefficients of the stochastic model are then correctly identified. The uncertainty relation lδβ>=l* for nonzero metric fluctuations δβ, emerges from the solution and is a necessary condition for the kernel to be constrained on [0,1]. The 1-metric fluctuations are exponentially damped or amplified as the spatial interval I=[0,l] is expanded or contracted with respect to the Planck length l*.
Similarity reduction for a class of algebraically special perfect fluids
Authors: Rainer A. , Stephani H.
Published: July 2002

For a class of perfect fluids first considered by Wainwright [Int. J. Theor. Phys. 10, 39 (1974)], a complete symmetry analysis of the field equations is performed. The results are used for a symmetry reduction of the field equations and the construction of (new) similarity solutions.
The geometry of coherent states
Authors: Field Timothy R. , Hughston Lane P.
Published: July 2002

We examine the geometry of the state space of a relativistic quantum field. The mathematical tools used involve complex algebraic geometry and Hilbert space theory. We consider the Kähler geometry of the state space of any quantum field theory based on a linear classical field equation. The state space is viewed as an infinite-dimensional complex projective space. In the case of boson fields, a special role is played by the coherent states, the totality of which constitutes a nonlinear submanifold 𝒞 of the projective Fock space PF. We derive the metric on 𝒞 induced from the ambient Fubini–Study metric on PF. Arguments from differential geometric, algebraic, and Kählerian points of view are presented, leading to the result that the induced metric is flat, and that the intrinsic geometry of 𝒞 is Euclidean. The coordinates for the single-particle Hilbert space of solutions are shown to be complex Euclidean coordinates for 𝒞. A transversal intersection property of complex projective lines in PF with 𝒞 is derived, and it is shown that the intrinsic geodesic distance between any two coherent states is strictly greater than the corresponding geodesic distance in the ambient Fubini–Study geometry. The functional metric norm of a difference field is shown to give the intrinsic geodesic distance between two coherent states, and the metric overlap expression is shown to measure the angle subtended by two coherent states at the vacuum, which acts as a preferred origin in the Euclidean geometry of 𝒞. Using the flatness of 𝒞 we demonstrate the relationship between the manifold complex structure on PF and the quantum complex structure viewed as an active transformation on the single-particle Hilbert space. These properties of 𝒞 hold independently of the specific details of the single-particle Hilbert space. We show how 𝒞 arises as the affine part of its compactification obtained by setting the vacuum part of the state vector to zero. We discuss the relationship between unitary orbits and geodesics on 𝒞 and on PF. We show that for a Fock space in which the expectation of the total number operator is bounded above, the coherent state submanifold is Kähler and has finite conformal curvature.
Zero curvature formalism of the four-dimensional Yang–Mills theory in superspace
Authors: Vilar L. C. Q. , Sorella S. P. , Sasaki C. A. G.
Published: July 2002

The supersymmetric descent equations in N=1 superspace are discussed by means of the introduction of two operators ζα,ζ̄α̇, which allow to decompose the supersymmetric covariant derivatives Dα,D̄α̇ as BRS commutators.
A new first integral for a binary rigid body collision of arbitrarily short duration
Authors: Nash Patrick L.
Published: July 2002

A standard classical model of a so-called rigid two-body collision that employs the dynamic Coulomb friction law to model friction is studied. For arbitrary object geometries and initial conditions it is known that the direction of the relative sliding velocity continuously changes during the impact. A (new) exact analytical solution for the relative sliding speed utr of the two objects in terms of initial conditions and sliding direction is derived. This solution is formulated in terms of a first integral, which is used to rigorously prove that the dynamic Coulomb friction law does not allow either instantaneous sticking or stable sticking to evolve from an initially nonzero utr, except for certain very special cases. The first integral also yields a new procedure for accurately and efficiently computing the final center of mass velocity and the final angular velocity of each of the objects in the model two-body collision. Accurate solutions such as these are essential for analyzing and controlling impacts, which is important, for example, in robot manipulation. Efficient solutions are critically important for producing real-time simulations of rigid two-body collisions.
Curvature conditions for the occurrence of a class of spacetime singularities
Authors: Rudnicki Wiesław , Ziȩba Paweł
Published: July 2002

It has recently been shown [W. Rudnicki, Phys. Lett. A 224, 45–50 (1996)] that a generic gravitational collapse cannot result in a naked singularity accompanied by closed timelike curves. An important role in this result plays the so-called inextendibility condition, which is required to hold for certain incomplete null geodesics. In this paper, a theorem is proved that establishes some relations between the inextendibility condition and the rate of growth of the Ricci curvature along incomplete null geodesics. This theorem shows that the inextendibility condition may hold for a much more general class of singularities than only those of the strong curvature type. It is also argued that some earlier cosmic censorship results obtained for strong curvature singularities can be extended to singularities corresponding to the inextendibility condition.
Two-parametric extension of h-deformation of Gr(1|1)
Authors: Çelik Sultan A. , Hizel Emanullah , Çelik Salih
Published: July 2002

The two-parametric quantum deformation of the algebra of coordinate functions on the (dual) supergroup Gr(1|1) via a contraction of Grp,q(1|1) is presented. Although the quantum superdeterminant of any element of Grp,q(1|1) is not central, in the two parametric Jordanian deformation of Gr(1|1) the quantum superdeterminant belongs to the center. The Hopf algebra structure of Grh1,h2(1|1) is discussed.
On phase transitions in a Fermi liquid. I. The transition associated with rotational symmetry breaking in momentum space
Authors: Peletminsky A. S. , Peletminsky S. V. , Slyusarenko Yu. V.
Published: July 2002

A phase transition associated with the rotational symmetry breaking in momentum space in a Fermi liquid is considered. It is shown that the phase transition is connected with the violation of one of the Pomeranchuk conditions, viz., the criterion of normal state stability. The structure of flux densities of the additive integrals of motion is determined in the vicinity of the phase transition point, and a physical interpretation of the phase under investigation is also given.
Some turbulence quantities and energy spectra in the wall region in bubble flows
Authors: Souhar M.
Published: July 2002

The data relating to turbulence in bubble flows are few, and quite nonexistent when referring to wall turbulence. The purpose of this paper is to fill in such a gap. The first experimental data dealing with turbulence scales are presented and give an order of magnitude for some important turbulent quantities near the wall. These quantities are different from those known in turbulent single-phase flows. Then, the results of the spectral analysis show evidence of decreasing laws, such as k−1 for large eddies and k−7/3 for small eddies, differing from those usually met. A convenient simple model is proposed to point out these decreases.
A kinetic model for a multicomponent gas
Authors: Garzó V. , Santos A. , Brey J. J.
Published: July 2002

A kinetic model for a dilute multicomponent gas system is proposed. It is constructed by replacing the Boltzmann collision operator with a relaxation-time term, in the same manner as in the Bhatnagar–Gross–Krook (BGK) model for a single gas. The model contains several parameters that are determined by keeping some of the main properties of the Boltzmann description. In contrast to previous works, the BGK equation is recovered when mechanically identical particles are considered. Thus the model can be expected to apply to systems in which masses are comparable. The transport properties to the Navier–Stokes level are studied and Onsager’s reciprocal relations are found to hold.
Instantaneous supersonic velocity profiles in an underexpanded sonic air jet by oxygen flow tagging
Authors: Miles Richard B. , Connors John , Markovitz Edward , Howard Philip , Roth Gregory
Published: July 2002

The statistics and structure of velocity profiles across the free shear layer of a sonic free jet are examined using oxygen tagging by Raman excitation plus laser-induced electronic fluorescence. The flow is observed both before and after the Mach disk at centerline Mach numbers of 3.6 and 0.4, respectively. Instantaneous images of the displaced line of tagged molecules show a clear picture of the turbulent structure including large-scale coherent features.
Stabilization of Taylor–Couette flow due to time-periodic outer cylinder oscillation
Authors: Murray B. T. , McFadden G. B. , Coriell S. R.
Published: July 2002

The linear stability of circular Couette flow between concentric infinite cylinders is considered for the case when the inner cylinder is rotated at a constant angular velocity and the outer cylinder is driven sinusoidally in time with zero mean rotation. This configuration was studied experimentally by Walsh and Donnelly [Phys. Rev. Lett. 60, 700 (1988)]. The critical Reynolds numbers calculated from linear stability theory agree with the experimental values, except at large modulation amplitudes and small frequencies. The theoretical values are obtained using Floquet theory implemented in two distinct approaches: (1) a truncated Fourier series representation in time and (2) a fundamental solution matrix based on a Chebyshev-pseudospectral representation in space. For large-amplitude, low-frequency modulation, the linear eigenfunctions are temporally complex, consisting of a quiescent interval followed by rapid change in the perturbed flow velocities.
Does deterministic chaos imply intermittency in fully developed turbulence?
Authors: Eggers Jens , Grossmann Siegfried
Published: July 2002

A Fourier–Weierstrass decomposition of the velocity field is introduced. The admitted number of real amplitudes is 572 or 836. They are determined numerically from the Navier–Stokes equation including viscosity, driven by constant energy input stirring the largest eddies only. In another calculation, the energy input is provided by an external shear. The Reynolds number Re is about 106, the inertial range comprises about 2 decades, and there are 11 levels of successively decaying eddies. The hierarchical mode ansatz thus allows for a state of high turbulence, which usually is inaccessible numerically. Deterministic chaos is found on all scales. The mean values of the amplitudes scale with the eddy size r as rζ with ζ very near 1/3. Expected deviations δζ=ζ−1/3, as one typical signature of intermittency, are very small only, well compatible with none at all. So, despite stochasticity (chaos) in the Fourier–Weierstrass decomposition with a tractably restricted set of plane waves, intermittency in the velocity scaling cannot be found. This changes if, in addition to temporal chaos, a spatial branching of the eddy decay process is also admitted.
The role of mixing in traveling-wave convection
Authors: Ohlsen D. R. , Yamamoto S. Y. , Surko C. M. , Kolodner Paul
Published: July 2002

In binary fluid mixtures with negative separation ratio, the conduction state has a vertical concentration gradient, due to the Soret effect, which opposes the destabilizing effect of the vertical temperature gradient. The first convective states are traveling waves (TW) with a phase velocity which is much lower than that of the linear instability. Recent perturbation theory calculations and numerical simulations of this nonlinear, traveling-wave state predict that the linear concentration gradient in the conduction state is eliminated in the interior of the fluid by convective mixing, and the concentration gradient remains only in the boundary layers. It is the persistence of the concentration gradient in these boundary layers which leads to the small but nonzero wave speed. As the Rayleigh number R is increased, convective stirring of the mixture decreases the concentration boundary layers, and the TW phase speed goes continuously to zero. We report experimental studies of these nonlinear, traveling-wave states in ethanol/water mixtures in an annular geometry. The measured TW phase speed as a function of R is in excellent agreement with the theoretical predictions over the entire TW branch. The experiments also confirm that this transition to stationary convection is not hysteretic. The role of mixing and the transport of concentration in the dynamics of nonlinear fronts and pulses observed in this system will also be discussed. [Work supported by DARPA URI Contract No. N00014-86-K-0758.]
Anomalous diffusion of momentum in a dilute gas–solid suspension
Authors: Koch Donald L.
Published: July 2002

The velocity variations in a monodisperse suspension of solid particles settling in a gas are studied in the limit 1≪St≪φ−3/4, where φ is the volume fraction, St=mU/(6πμfa2) is the Stokes number, m is the mass of particles, a is their radius, U is their terminal velocity, and μf is the viscosity of the suspending gas. In this limit, the particles’ viscous relaxation time is small compared to a time scale for interparticle fluid dynamic interactions. Thus the particles act to enhance the effective density of the suspension. The velocity fluctuations induced by the body forces acting on the particles lead to a Reynolds stress that is described by a wave-number-dependent effective viscosity. This nonlocal viscosity causes a screening of the velocity disturbance of a particle at an O(a St−1/2φ−3/4) radial separation; the screening yields finite O(U2 St−2/3) variances of the velocities of the gas and particles.
Thermocapillary convection in two immiscible liquid layers with free surface
Authors: Doi Takao , Koster Jean N.
Published: July 2002

Thermocapillary convection is studied in two immiscible liquid layers with one free surface, one liquid/liquid interface, and differential heating applied parallel to the interfaces. An analytical solution is introduced for infinite horizontal layers. The defining parameter for the flow pattern is λ, the ratio of the temperature coefficient of the interfacial tension to that of the surface tension. Four different flow patterns exist under zero gravity conditions. ‘‘Halt’’ conditions which halt the fluid motion in the lower encapsulated liquid layer have been found. A numerical experiment is carried out to study effects of vertical end walls on the double layer convection in a two-dimensional cavity. The halt condition obtained from the analytical study is found to be valid in the limit of small Reynolds numbers. The flow in the encapsulated liquid layer can be suppressed substantially.
Measurement of the electron–ion-hose instability growth rate
Authors: Lipinski R. J. , Smith J. R. , Shokair I. R. , Struve K. W. , Werner P. , Armistead D. J. , Kiekel P. D. , Molina I. , Hogeland S.
Published: July 2002

The growth rate of the ion-hose instability has been measured for a 2.5 MeV, 1 kA, 1 μsec electron beam following plasma channels of O2, N2, and H2 (in the ion-focused regime). The amplitude of transverse oscillations of a given beam segment was seen to grow, saturate, and damp as the segment traveled. The offset amplitude at saturation (dm) was seen to be an exponential function of the beam pulse duration (t): dm=dm,0 exp(2πGLt/tc), where tc is the time required for one channel oscillation and GL is the growth rate (for beam oscillations less than the channel radius). With beam radius equal to channel radius (rb=rc), and channel density equal to half the beam density, GL=0.75±0.15. Here GL was seen to scale with the square root of channel ion mass when data from channels of O2, N2, and H2 were compared. Also, GL was seen to increase as rb was increased (with the initial beam emittance kept the same). A fivefold decrease in growth rate was observed for t>tc and dm>rc. The decrease in growth rate may be due to the strongly anharmonic potential outside the channel or detuning from radial oscillations. Agreement was obtained between the data and models.
Resistive tearing mode instability with shear flow and viscosity
Authors: Ofman L. , Chen X. L. , Morrison P. J. , Steinolfson R. S.
Published: July 2002

The linear theory of the resistive tearing mode instability in slab geometry, has been recently extended by introducing the effect of equilibrium shear flow and viscosity [Phys. Fluids 29, 2563 (1986); Phys. Fluids B 1, 2224 (1989); ibid. 2, 495 (1990); ibid. 2, 2575 (1990)]. In the present analysis, numerical solutions of the time-dependent resistive equations are generalized to this problem and growth rate scaling is obtained. The results of the computations are compared to previous work, and the computed growth rate scalings agree with analytical predictions. Namely, the ‘‘constant-ψ’’ growth rate scales as S−1/2 and the ‘‘nonconstant-ψ’’ growth rate scales as S−1/3, where S is the magnetic Reynolds number. The Furth–Killeen–Rosenbluth (FKR) scaling of S−3/5 is reproduced for small values of shear flow. The presence of flow introduces a new peak in the eigenfunction, which is outside of the peak that occurs in the case without flow. The introduction of viscosity and small shear alters the growth rate scaling to S−2/3(Sv/S)1/6 where Sv is the ratio of the viscous time to the Alfvén time. When the shear flow is large, the growth rate behaves in a more complex way, and Kelvin–Helmholtz instability effects are present.
Core instability of elliptic drift vortices
Authors: Rath S. , Sridhar S.
Published: July 2002

It is shown that two-dimensional drift vortices with elliptic cores are unstable to certain short-wavelength three-dimensional perturbations. Circular vortices are stable to those modes. At short wavelengths, the growth rate is independent of the wavelength and, for small ellipticity, it is proportional to the ellipticity.
A trapped-passing fluid model for tokamak neoclassical transport
Authors: Harvey R. W. , Dendy R. O.
Published: July 2002

In the low collisionality banana regime, the response of the passing and trapped particles to toroidal forces is essentially distinct: Passing particles accelerate, whereas trapped particles drift radially. In order to model current drive and particle transport in a physically intuitive manner, a four-fluid model for a simple electron–ion plasma involving separate momentum equations for each of the trapped and passing species has been formulated. Because of relative drifts, the four fluids undergo collisional friction with each other and with neutrals; a radial electric field arises with the inclusion of momentum sources, particle sources, and the collisions with neutrals. Radial plasma transport, which conserves canonical angular momentum, is modeled by scattering the configurational component of trapped particle momentum into translational momentum of the passing particles at a rate related to the density and temperature gradients by standard neoclassical theory. For given radial temperature profile, the neoclassical differential equation for the density is obtained. This equation is integrated numerically to obtain the radial density profile. Over a broad range of parameters, the volume average density is close to the empirical Hugill–Murakami–Greenwald [Nucl. Fusion 28, 2199 (1988)] density limit n̄ (1020 m−3)=J̄ (MA m−2); although most plasmas operate below this density, the results suggest that near the density limit, plasma particle confinement may be neoclassical. In this case, it is shown explicitly, in the steady state, that Ohm’s law can be expressed very simply in terms of the classical Spitzer conductivity with no trapped particle correction, a fact first noted by Ware [Nucl. Fusion 13, 793 (1973)]. Alternately, the effect of the trapped particle correction on conductivity cancels the bootstrap current. Concomitantly, deposition of rf wave momentum on thermal, trapped particles in the direction so as to drive plasma current, will pinch the particles inward and result in toroidal current independent of the trapping effect.
Influence of the Hall effect on convection in plasmas
Authors: dos Santos C. A. M. , Galvão R. M. O.
Published: July 2002

The influence of the Hall effect on stationary convection in shearless current-carrying plasma columns is considered. It is shown that the Hall effect can inhibit the formation of convection cells generated by viscosity and resistivity.