bluuebunny/crossref_metadata_2025 huggingface dataset:
Competitive charge transfer reactions in small [Mg(H2O)N]2+ clusters
Authors: Barran P. E. , Walker N. R. , Stace A. J.
Published: July 2002

Production of stable hydrated magnesium complexes of the general form [Mg(H2O)N]2+ (where 2⩽N⩽24) has been possible using the pick-up technique. Observations of ion intensities as a function of N together with data from collision induced dissociation processes (for ions in the range 3⩽N⩽10), indicates the existence of a closed solvation shell for N=6 to which additional water molecules are strongly bound. Collision-induced charge transfer in ions of all sizes yields solvated magnesium hydroxide ions Mg+OH(H2O)N−M−2 accompanied by the loss of a hydronium ion, H3O+, and M water molecules. For N=3, 4, and 5, the above process is seen to be in competition with charge transfer to unprotonated water, and clusters of the general form Mg(H2O)N−M+ are detected, where M now represents the total number of water molecules lost. These two separate loss channels are interpreted as being due to the presence of different structural (or transient) forms of those cluster ions where N⩽6. One structure corresponds to a highly symmetrical arrangement of the water molecules bonded directly to the magnesium dication, and is responsible for the formation of Mg(H2O)N−M+ ions by charge transfer. In the second type of structure, at least one water molecule moves to an outer solvation shell, but remains hydrogen bonded to a molecule in the first shell. In this latter configuration, it is suggested that the formation of a salt-bridge structure may lower the barrier to proton transfer and lead to the loss of a hydronium ion.
Vibrational overtone dephasing in liquids under the influence of non-Gaussian noise
Authors: Yamaguchi T.
Published: July 2002

We have calculated the vibrational overtone dephasing rates of an oscillator that is subject to uncorrelated, impulsive, and strong collisions. We have assumed the Poisson statistics for binary collisions, and not truncated the cumulant expansion at the second order. The decay of the response function is always exponential, and the dephasing rate shows subquadratic dependence on the vibrational quantum number (ν). The dephasing rate asymptotically converges to the collision frequency at the large-ν or strong collision limits. We have succeeded in reproducing the experimental results on chloroform [K. Tominaga and K. Yoshihara, J. Phys. Chem. A 102, 4222 (1998)] and those on methyl iodide [A. B. Myers and F. Markel, Chem. Phys. 149, 21 (1990)] by adjusting the collision frequency and the strength of the collision.
Synchronous helical pulse sequences in magic-angle spinning nuclear magnetic resonance: Double quantum recoupling of multiple-spin systems
Authors: Brinkmann Andreas , Edén Mattias , Levitt Malcolm H.
Published: July 2002

Some general principles of radio-frequency pulse sequence design in magic-angle spinning nuclear magnetic resonance are discussed. Sequences with favorable dipolar recoupling properties may be designed using synchronous helical modulations of the space and spin parts of the spin Hamiltonian. The selection rules for the average Hamiltonian may be written in terms of three symmetry numbers, two defining the winding numbers of the space and spin helices, and one indicating the number of phase rotation steps in the radio-frequency modulation. A diagrammatic technique is used to visualize the space-spin symmetry selection. A pulse sequence C1445 is designed which accomplishes double-quantum recoupling using a low ratio of radio frequency field to spinning frequency. The pulse sequence uses 14 radio frequency modulation steps with space and spin winding numbers of 4 and 5, respectively. The pulse sequence is applied to the double-quantum spectroscopy of C313-labeled L-alanine. Good agreement is obtained between the experimental peak intensities, analytical results, and numerically exact simulations based on the known molecular geometry. The general symmetry properties of double quantum peaks in recoupled multiple-spin systems are discussed. A supercycle scheme which compensates homonuclear recoupling sequences for chemical shifts is introduced. We show an experimental double-quantum C13 spectrum of [U–13C]–L-tyrosine at a spinning frequency of 20.000 kHz.
Comparison of charged sheets and corrected 3D Ewald calculations of long-range forces in slab geometry electrolyte systems with solvent molecules
Authors: Crozier Paul S. , Rowley Richard L. , Spohr Eckhard , Henderson Douglas
Published: July 2002

Two methods of calculating long-range intermolecular potentials are compared for an approximately 3 M aqueous electrolyte solution confined between two charged surfaces. We investigate the ionic density profiles using the charged-sheets method and the corrected three-dimensional (3D) Ewald method at two different system sizes and also compare the Coulomb forces directly. The corrected 3D Ewald method is recommended for the calculation of long-range potentials in systems of this nature because it is less system size dependent than the charged-sheets method and the resultant forces are more consistent with periodic boundaries. However, the charged-sheets method for estimating long-range potentials in Coulombic systems may be useful for certain applications, and the corrected 3D Ewald method also shows some system size dependence.
Dynamics of polarization relaxation in a dipolar mixture at a solid–liquid interface
Authors: Senapati Sanjib , Chandra Amalendu
Published: July 2002

Dynamics of polarization relaxation in a dipolar mixture at solid–liquid interface is investigated theoretically by using time dependent density functional theory. The time dependence of the building up of polarization of different dipolar species next to a newly charged solid surface is calculated by solving both Markovian and non-Markovian equations of motion for density and momentum variables. The inhomogeneity of the interface is taken into account in the dynamical theory. The theory also includes the various intra- and interspecies molecular correlations and the surface–molecule interactions. Both the molecular size and the dipole moment of various species in the dipolar mixture can be unequal. The initial inhomogeneity of the interface is calculated by using a weighted density functional theory. Explicit numerical results are obtained for the polarization relaxation in a binary dipolar liquid at varying distances from the solid surface and the dynamics of interfacial relaxation of the two species are compared with that in the bulk phase. A slowing down of the rate of relaxation is found for interfacial molecules of both the species. However, the extent of slowing down is found to be different for different species. Also, the rate of relaxation is found to change nonmonotonically with distance from the surface due to the layering of solvent molecules at the interface. © 2000 American Institute of Physics.
Complete reflection in two-state crossing and noncrossing potential systems
Authors: Pichl Lukáš , Nakamura Hiroki , Horáček Jiřı́
Published: July 2002

A semiclassical study is made for the complete transmission and the complete reflection phenomena in two coupled molecular potential systems. The conditions for these phenomena to occur are expressed analytically in terms of nonadiabatic transition probabilities and phase integrals, which can be provided by the semiclassical theory. We also introduce an exactly solvable analytical model of diabatically avoided crossing, in which two diabatic potentials coupled by a constant coupling are close together in a certain spatial region. These models and phenomena may be useful in controlling various molecular processes in laser fields, since in the dressed or Floquet state formalism molecular potentials can be shifted up and down and are made to cross or avoid crossing with other potentials.
Three-body exchange energies in H3 and He3 calculated by the surface integral method
Authors: Kleinekathöfer U. , Sachse T. I. , Tang K. T. , Toennies J. P. , Yiu C. L.
Published: July 2002

Repulsive three-body exchange energies are calculated for H3 and He3 using a new method based on an extension of the surface integral method to three-body interactions. The dependence of the three-body exchange energies on the internuclear distances between 5 and 10 a0 is investigated for equilateral configurations. The angular dependence is also studied for geometries in which two distances are fixed at equal distances. Very good agreement with other calculations at the same level of approximation is obtained for H3 as well as for He3. The relative importance of the different electron permutations in He3 is discussed.
Relativistic superfluid in a rigid solid. Exact solutions
Authors: Papini G. , Weiss M.
Published: July 2002

Exact solutions of Einstein’s equations are obtained for a superfluid flowing in a rigid solid.
Solutions of the Einstein–Cartan–Dirac equations with vanishing energy-momentum tensor
Authors: Dimakis A. , Müller–Hoissen F.
Published: July 2002

It is shown that a frame can always be chosen with respect to which a Dirac spinor ψ has a particular simple form. This result is used to investigate the existence of solutions of the Einstein–Cartan–Dirac equations with vanishing energy-momentum tensor, but nonvanishing current (‘‘ghost solutions’’). We concentrate on solutions with a massive Dirac field, subject to the restriction (ψ̄ψ)2+(ψ̄γ5ψ)2>0. In this case, the field equations can be reduced to a set of (covariant) equations on the group SL(2, R). A family of new exact solutions is presented.
Integrals of some three Bessel functions and Legendre functions. II
Authors: Gervois A. , Navelet H.
Published: July 2002

Integrals of three Bessel functions of the form ∫∞0Jμ(at)Jν(bt) ×H(1)ρ(ct)dt are calculated when μ,ν,ρ,a,b, and c are arbitrary real numbers. For this, use is made of the factorization of the Appell function F4 in two hypergeometric functions. Further simplifications occur if μ=±ν or ρ=±1/2. New results are given, mainly when real a, b, and c satisfy the inequalities ‖a−b‖<c<a+b, which correspond to most physical situations.
Consistent superspace integration
Authors: Rogers Alice
Published: July 2002

The standard Berezin method for integration over odd variables is combined in a new way with De Witt’s contour method for integration over even Grassmann variables to give a new method of superspace integration. It is shown that this integral, unlike the standard superspace integral, is invariant under coordinate transformations in superspace. The relation between the new method and the standard method is discussed.
The geometrical setting of Utiyama’s interaction theory
Authors: Grassini Renato
Published: July 2002

A mathematical deduction of the fiber bundle theory of interaction from Utiyama’s theory is drawn, in order to get some deeper insights into the geometry of classical gauge theories.
Unbounded representations of symmetry groups in gauge quantum field theory. I. Confinement and differentiation
Authors: Völkel A. H.
Published: July 2002

Symmetry groups and especially the covariance (substitution rules) of the basic fields in a gauge quantum field theory of the Wightman–Gårding type are investigated. By means of the continuity properties hidden in the substitution rules it is shown that every unbounded form–isometric representation U of a Lie group has a form-skew-symmetric differential ∂U with dense domain in the unphysical Hilbert space. Necessary and sufficient conditions for the existence of the closures of U and ∂U as well as for the isometry of U are derived. It is proved that a class of representations of the translation group enforces a relativistic confinement mechanism, by which some or all basic fields are confined but certain mixed products of them are not.
Classical SU(2) Yang–Mills–Higgs system: Time-dependent solutions by similarity method
Authors: Babu Joseph K. , Baby B. V.
Published: July 2002

A similarity analysis of the Wu–Yang–’t Hooft–Julia–Zee-ansatz-reduced system of nonlinear differential equations of classical SU(2) Yang–Mills–Higgs theory is presented. This yields the similarity group 𝒢 of the equations. Considering 𝒢 and one of its subgroups denoted 𝒢1, some previously known time-dependent solutions in the Prasad–Sommerfield limit are generated. Two new time-dependent solutions are also reported.
On nonlocal point interactions in one, two, and three dimensions
Authors: Dabrowski L. , Grosse H.
Published: July 2002

Three characterizations of all self-adjoint extensions of the Laplacian in one, two, and three dimensions are discussed.
Nonexistence of static conformally flat solutions in a new scalar–tensor theory
Authors: Singh Tarkeshwar
Published: July 2002

For the special case when the scalar field is massless and conformally invariant, it is shown that there do not exist spherically symmetric conformally flat solutions in a new scalar–tensor theory proposed by Schmidt et al. [Phys. Rev. D 24, 1484 (1981)] representing disordered radiation and in the presence of a source-free electromagnetic field except for the trivial empty flat space-time of Einstein’s theory. The solution in the vacuum case is also only a flat space-time of Einstein’s theory.
Stable thermodynamic states
Authors: Cohen J. S. , Winnink M.
Published: July 2002

A general class of perturbations of the dynamics for thermodynamic quantum systems is discussed. Without making use of weak asymptotic Abelianess, stability of a state for these perturbations is shown to lead to the φ-KMS condition and to the KMS condition in particular cases. Conversely, φ-KMS states satisfy the stability property introduced here.
Do trilinear commutation relations in quantum mechanics admit coordinate space realization in three dimensions?
Authors: Bhattacharya Ranjan , Bhowmick Siddhartha
Published: July 2002

The trilinear commutation relations involving coordinates and momenta introduced by Wigner [E. P. Wigner, Phys. Rev. 77, 711 (1950)] are generalized to three dimensions. It is shown that the only realizable coordinate space representation of the momenta implies the usual bilinear commutation relations.
Algebraic structures of degenerate systems and the indefinite metric
Authors: Grundling Hendrik , Hurst C. A.
Published: July 2002

It is shown that the indefinite metric structures of degenerate systems as given by Strocchi and Wightman [F. Strocchi and A. S. Wightman, J. Math. Phys. 15, 2198 (1974); 17, 1930 (1976)] arise in a natural fashion from the algebraic structure of such systems, where the latter has been developed in a C*-context by Grundling and Hurst [H. B. G. S Grundling and C. A. Hurst, Commun. Math. Phys. 98, 369 (1985)]. Auxiliary concepts like gauge equivalence are examined, and the preceding general theory is specialized to the situation of linear boson fields with linear Hermitian constraints. Two examples of this situation are given—a one-dimensional scalar boson in a periodic universe and Landau gauge electromagnetism.
Efficient integration of the one-dimensional time independent wave equation for bound states and for wave propagation
Authors: Skorupski Andrzej A.
Published: July 2002

The wave equation is solved with the phase-integral approximation in the asymptotic regions, and integrated numerically elsewhere. In this application the phase-integral approximation is relatively simple in higher orders, and its accuracy can be precisely controlled with the derived error estimates. For the bound states the analytical formulas defining the termination error in the wave function are derived. For the wave propagation an efficient formalism is given for calculating the reflection, transmission, and absorption coefficients.
Exact solutions of the Schrödinger equation for nonseparable anharmonic oscillator potentials in two dimensions
Authors: Taylor D. R. , Leach P. G. L.
Published: July 2002

An explicit procedure is given to construct exact closed-form solutions to the time-independent Schrödinger equation in two dimensions [∇2+λ−w(x,y)]ψ=0, where w(x,y) is a polynomial potential of degree greater than two not separable in Cartesian coordinates. Several examples are discussed for which w(x,y) is a sextic polynomial. As has already been seen in studies of the corresponding one-dimensional problem, a complete set of eigenvalues and wave functions is not found. However, these closed-form solutions can be used to check the accuracy and efficiency of numerical algorithms.
Particle symmetry and antisymmetry in approximately relativistic Lagrangians
Authors: Woodcock Harry W. , Herman Warren N.
Published: July 2002

For a single-time approximation of the type discussed by Woodcock and Havas [Phys. Rev. D 6, 3422 (1972)] applied to particle-asymmetric Poincaré-invariant variational principles (VPs) of the Fokker type, a method is presented for expressing approximately relativistic Lagrangians (ARLs) to any order in c−1 in a form such that coefficients of functions of the instantaneous three-separation rij are either particle symmetric or antisymmetric. These functions of rij are determined solely by the corresponding particle symmetric or antisymmetric parts of the exactly relativistic kernel of the VP describing two-body interactions of N classical point particles. While the exact kernel involving the particles’ four-separations and four-velocities is particle asymmetric, the built-in static Newtonian limit is particle symmetric. Using this method to reformulate previously published ARLs to order c−3 makes it obvious that a sufficient condition for acceleration-free ARLs to order c−3 is that the kernel of the exact non-time-reversal-invariant interaction be particle symmetric.
Solutions of an equation that lead to solutions of a modified Emden equation and a coupled Korteweg–deVries equation
Authors: Basu Ashis , Ray Dipankar
Published: July 2002

In a recent paper, Moreira [Res. Rep. IF/UFRJ/83/25, Universidade Federal do Rio de Janeiro Inst. de Fisica, Cidade Univ., Ilha do Fundao, Rio de Janeiro, Brazil] obtained a nonlinear second-order differential equation that leads to the first integral of a modified Emden equation. He also obtained two particular solutions of his equation. This paper completely integrates Moreira’s equation and uses it to get a class of solutions of a coupled Korteweg–deVries (KdV) equation, recently studied by Guha Ray, Bagchi, and Sinha [J. Math. Phys. 27, 2558 (1986)].
Ground-state energy of H=P2+ 2X2+ 2(2λ)1/2X3+λX4 for λ<<<1
Authors: Rath Biswanath
Published: July 2002

A self-consistent perturbation theory is developed to compute the ground-state energy for the Hamiltonian H=P2+2X2+2(2λ)1/2X3+λX4 in the weak coupling regime λ<<<1. Energy corrections up to third order are given. Reasonably good agreement is obtained with previous computations.
Evaluations of distribution functions for flexible macromolecules by the saddle-point method
Authors: Wei Gaoyuan , Eichinger B. E.
Published: July 2002

The method of steepest descents has been applied to the evaluation of distribution functions for flexible macromolecules of arbitrary complexity with the effective potential of the mean force being a quadratic form. Approximate evaluations of the distribution functions of the radius of gyration and the two-dimensional shape distribution functions over the entire variable domains are shown to be both feasible and effective. The asymptotics of the distribution functions are also studied, and a simple asymptotic formula is obtained that is valid for flexible macromolecules confined to a plane and of any structure such that the smallest eigenvalue of the Kirchhoff matrix has odd degeneracy.
The problem of gravity-gyroscopic waves, which are excited by the oscillations of a curve
Authors: Kharik V. M. , Pletner U. D.
Published: July 2002

The problem of the oscillations of an ideal stratified rotating fluid, which are excited by a curve in the case where the distribution of pressure on both sides of the curve is prescribed, is considered. The solution to the problem is obtained, as well as results about symmetry properties of the operators used for the solution of such problems. The question of the uniqueness of the solution is also considered.
Some examples of the algebra of flows
Authors: Bose S. K.
Published: July 2002

The algebra of the group of smooth maps from a manifold M to a compact simple Lie group G is studied for two cases. The first is when M is the double coset SO (d,R)/SO(d+1,R)/SO (d,R), the corresponding maps are those from a d sphere to G that are invariant under left translations by elements from SO (d, R). In the second example, M is a two-dimensional torus. The problem of central extension of these algebras is solved. For the first example, no central extension is possible. For the second, the number of independent central extensions is infinite.
The Jordan–Schwinger representations of Cayley–Klein groups. III. The symplectic groups
Authors: Gromov N. A. , Man’ko V. I.
Published: July 2002

The symplectic Cayley–Klein groups are defined as the groups that are obtained by the contractions and analytical continuations of the classical symplectic groups. The Jordan–Schwinger representations of the groups under consideration are discussed based on the mixed sets of creation and annihilation operators of boson or fermion type. The matrix elements of finite group transformations are obtained in the bases of coherent states.
A triangular property of the associated Legendre functions
Authors: Fineschi S. , Degl’Innocenti E. Landi
Published: July 2002

The property of the associated Legendre functions with non-negative integer indices, Pmn(z), described by the formula: Pmn (cos β)=(−1)m(a/c)n ∑n−mk=0 (n+mk) (−b/a)n−k ×Pmn−k(cos γ), where a,b,c are the sides of an assigned triangle and α,β,γ the respective opposite angles, is introduced. A useful application of this series in simplifying the calculation of collisional electron–atom cross sections higher than the dipole is mentioned. A proof of the stated identity by use of the Gegenbauer polynomials and of their generating function is given.
Hidden variables in quantum logic approach reexamined
Authors: Pykacz Jarosl/aw , Santos Emilio
Published: July 2002

Various impossibility proofs for hidden variables theories produced within the quantum logic approach are analyzed. A very general form of n-term Bell-type inequalities is given. From these inequalities a new impossibly proof for hidden variables theories able to reproduce all numerical results of quantum mechanics follows.
Methods of holonomy theory for Ricci-flat Riemannian manifolds
Authors: McInnes Brett
Published: July 2002

Compact, Ricci-flat Riemannian manifolds often arise in physical applications, either as a technical device or as models of ‘‘internal’’ space. The idea of extending the holonomy group of such a manifold to a larger gauge group (‘‘embedding the connection in the gauge group’’) plays a fundamental role in the ‘‘manifold compactification’’ approach to superstring phenomenology, and the work of Gepner suggests that this idea may have equally fundamental analogs in other approaches. The holonomy theory of simply connected Ricci-flat manifolds has recently been the subject of much mathematical work, but physicists are mainly interested in the case of multiply connected manifolds. The purpose of this paper is to present some techniques for understanding the holonomy theory of compact, multiply connected Ricci-flat manifolds. These lead to a general classification theorem.
Para-squeezed states
Authors: Saxena G. M. , Mehta C. L.
Published: July 2002

In this paper the squeezed states for a one mode para-bose system is considered and it will be shown that a recently published contradictory assertion that no such states exist is based on an erroneous consideration. It is found that the squeeze operator is identical for both the ordinary and para-bose systems. The uncertainties in the canonical variables q (position) and p (momentum) in the para-squeezed state are obtained. The normal ordered form of the para-squeeze operator is also obtained and is then used to write the number and the coordinate representation of the para-bose vacuum.
Bell inequalities on quantum logics
Authors: Pulmannová Sylvia , Majernik Vladimir
Published: July 2002

Three types of Bell inequalities, expressed in terms of quantum logics (orthomodular lattices) and states on them, are studied. It is shown that the two first types are equivalent to the subadditivity of the corresponding state. The third type is equivalent to the existence of a Boolean quotient B of the orthomodular lattice L and a state s̄ on B, such that s̄⋅φ=s, where s is the state on L and φ:L→B is the quotient mapping.
Mixtures of potentials in quantum mechanics
Authors: Hall Richard L.
Published: July 2002

A global geometrical approximation theory for the spectra of Schrödinger operators H =− D2 + vf(x) is discussed. The potential f(x) is composed either of sums, or of continuous mixtures, of soluble potentials. In both cases it is proved that the kinetic-potential formalism [J. Math. Phys. 24, 324 (1983); 25, 2078 (1984)] automatically yields optimal energy lower bounds. The examples f(x)=‖x‖+x2 and f(x)=−∫basech2(tx)dt are treated in detail.
Matrix nonlinear Schrödinger equations and moment maps into loop algebras
Authors: Harnad J. , Wisse M.-A.
Published: July 2002

It is shown how Darboux coordinates on a reduced symplectic vector space may be used to parametrize the phase space on which the finite gap solutions of matrix nonlinear Schrödinger equations are realized as isospectral Hamiltonian flows. The parametrization follows from a moment map embedding of the symplectic vector space, reduced by suitable group actions, into the dual ■g̃+*̃ of the algebra ■g̃+ of positive frequency loops in a Lie algebra 𝔤 . The resulting phase space is identified with a Poisson subspace of ■g̃+* consisting of elements that are rational in the loop parameter. Reduced coordinates associated to the various Hermitian symmetric Lie algebras (𝔤 ,𝔨) corresponding to the classical Lie algebras are obtained.
Tensor operators for quantum groups and applications
Authors: Rittenberg V. , Scheunert M.
Published: July 2002

Tensor operators are defined for Hopf algebras. If the Hopf algebra is quasitriangular, the properly defined tensor product of tensor operators is a tensor operator. In one application, the problem of defining invariant correlation functions for the Uq (sl(2))-symmetric spin 1/2 Heisenberg chain is considered. In another application, it is shown that suitably modified bosonic and fermionic q-creation and annihilation operators are tensor operators of Uq (sl(n)).
On a zero curvature problem related to the ZS–AKNS operator
Authors: Zubelli Jorge P.
Published: July 2002

All the ZS–AKNS operators, L = i[∂x−g(x)r(x)−∂x], which admit two linearly independent families of eigenfunctions, satisfying a differential equation in the spectral parameter λ of the form a(λ)∂λV+B(λ)V=Θ(x)V, are characterized. Here, a(λ)∈C, B, and Θ take values in the space of 2×2 complex matrices.
Kink metrics in (2+1)-dimensional space-time
Authors: Williams J. G. , Zvengrowski P.
Published: July 2002

A homotopy classification scheme is developed for Lorentz metrics that are defined on (2+1)-dimensional space-times of various topologies. The ‘‘kink number,’’ in the sense of the Finkelstein–Misner kink number in higher dimensions, is discussed, and examples are presented of kink metrics that satisfy the Einstein field equations in 2+1 dimensions.
A new class of exact solutions in general relativity representing perfect fluid balls
Authors: Pant D. N. , Pant Neeraj
Published: July 2002

In this paper is presented a new class of spherically symmetric analytic solutions in canonical coordinates in general relativity which corresponds to causal models of perfect fluid balls. Tolman’s IV solution is a member of this class. Two new solutions belonging to this class have been studied here in detail. These correspond to positive, monotonically decreasing expressions for pressure and density and realistic equations of state within causal fluid balls.
Symplectic analysis of a Dirac constrained theory
Authors: Barcelos-Neto J. , Braga N. R. F.
Published: July 2002

The symplectic formalism is applied to a system recently analyzed by the Dirac method. It is shown that this procedure is quite straightforward and elegant for the two versions of the model.
Representations of the q-deformed algebras U
q(so2,1) and U
q(so3,1)
Authors: Gavrilik A. M. , Klimyk A. U.
Published: July 2002

Representations of the algebra Uq(so2,1) are studied. This algebra is a q-deformation of the universal enveloping algebra U(so2,1) of the Lie algebra of the group SO0(2,1) and differs from the quantum algebra Uq(su1,1). Classifications of irreducible representations and of infinitesimally unitary irreducible representations of Uq(so2,1), with simple and discrete spectrum of one of generators are derived. The set of infinitesimally unitary representations of Uq(so2,1) does not coincide with that for the algebra Uq(su1,1). The sets of irreducible representations and of infinitesimally unitary irreducible representations of the algebra Uq(so3,1) are given. We also consider representations of Uq(son,1) which are of class 1 with respect to the subalgebra Uq(son).
An algorithm to calculate the invariants of any Lie algebra
Authors: Pecina-Cruz J. N.
Published: July 2002

An analytical method to calculate invariants is developed, based on the theory of complete systems of simultaneous linear first order partial differential equations. The application of this algorithm to the general case, in which the invariants are not polynomials is included. For the case of Lie algebras with one invariant the procedure of finding the invariant can be computerized. As an example of this procedure, the algorithm is applied in the calculation of the invariants of the group SA(n,R). The explicit construction of its invariants for n=2, 3, 4 is given. A theorem determining the order of a polynomial invariant of a Lie group is proven allowing us to show that the invariant of SA(n,R) is a homogeneous polynomial of order 1/2n(n+1) in the generators. From this fact an immediate consequence is that the order in the generators of translations is n. The method is also applied in the calculation of invariants of the dimension six solvable Lie algebras, and dimension seven nilpotent.
The Lorentz–Dirac equation in Minkowski space
Authors: Gaftoi Violeta , López-Bonilla José L. , Morales Jesús , Rosales Marco A.
Published: July 2002

The Lorentz–Dirac equation is obtained by means of a modification imposed on Maxwell’s tensor for the Liénard–Wiechert field. This procedure avoids the mass renormalization of the point charge.
Bicovariant 3D calculus for SLq(2) from Poisson–Lie structures
Authors: Aref’eva I. Ya , Arutyunov G. E. , Medvedev P. B.
Published: July 2002

All possible graded Poisson–Lie structures on the external algebra of SL(2) are described. We prove that differential Poisson–Lie structures prolonging the Sklyanin brackets do not exist on SL(2). There are two and only two graded Poisson–Lie structures on SL(2) and neither of them can be obtained by a reduction of graded Poisson–Lie structures on the external algebra of GL(2). Both of them can be quantized and as a result we get new graded algebras of quantum right-invariant forms on SLq(2) with three generators.
Topology change in (2+1)-dimensional gravity
Authors: Carlip S. , Cosgrove R.
Published: July 2002

In (2+1)-dimensional general relativity, the path integral for a manifold M can be expressed in terms of a topological invariant, the Ray–Singer torsion of a flat bundle over M. For some manifolds, this makes an explicit computation of transition amplitudes possible. In this paper, the amplitude for a simple topology-changing process is evaluated. It is shown that certain amplitudes for spatial topology change are nonvanishing—in fact, they can be infrared divergent—but that they are infinitely suppressed relative to similar topology-preserving amplitudes.
A Z2 structure in the configuration space of Yang–Mills theories
Authors: Axenides Minos , Johansen Andrei , Mo/ller Jesper
Published: July 2002

We argue for the presence of a Z2 topological structure in the space of static gauge–Higgs field configurations of SU(2n) and SO(2n) Yang–Mills theories. We rigorously prove the existence of a Z2 homotopy group of mappings from the two-dimensional projective sphere RP2 into SU(2n)/Z2 and SO(2n)/Z2 Lie groups, respectively. Consequently the symmetric phase of these theories admits infinite surfaces of odd-parity static and unstable gauge field configurations which divide into two disconnected sectors with integer Chern–Simons numbers n and n+1/2, respectively. Such a Z2 structure persists in the Higgs phase of the above theories and accounts for the existence of CS=1/2 odd-parity saddle point solutions to the field equations which correspond to spontaneous symmetry breaking mass scales.
Quantum chains with a Catalan tree pattern of conserved charges: The Δ=−1 XXZ model and the isotropic octonionic chain
Authors: Grabowski M. P. , Mathieu P.
Published: July 2002

A class of quantum chains possessing a family of local conserved charges with a Catalan tree pattern is studied. Recently, we have identified such a structure in the integrable SU(N)-invariant chains. In the present work we find sufficient conditions for the existence of a family of charges with this structure in terms of the underlying algebra. Two additional systems with a Catalan tree structure of conserved charges are found. One is the spin 1/2 XXZ model with Δ=−1. The other is a new octonionic isotropic chain, generalizing the Heisenberg model. This system provides an interesting example of an infinite family of noncommuting local conserved quantities.
Algebraic structure of diffusion and scattering in one dimension
Authors: Miyazawa Toru
Published: July 2002

The one-variable Fokker–Planck equation is studied from an algebraic point of view. Diffusion in an external potential can be interpreted as a multiple scattering process. A description of the one-dimensional scattering in terms of boson operators is introduced, and it is generalized to a form that does not depend on representation. An expression for the Green’s function is derived in terms of generators of the OSp(1/2) superalgebra. It is shown that many seemingly different descriptions of the diffusion problem are just different representations of this general expression.
Inlaying vertex function and scattering amplitude
Authors: Naito Seichi
Published: July 2002

Scattering processes among strings are analyzed by using fundamental equations of three types, which divide the whole complex z-plane into various types of N punctured ring domains plus various unpunctured ring domains, where internal strings freely propagate. In order to calculate scattering amplitudes (among physical particles) in Witten’s quantum string field theory, we derive and apply the “Gluing theorem,’’ mathematical proof of which is given (in operator forms) by constructing various (inlint) conformal mapping operators.
Scattering theory for finitely many sphere interactions supported by concentric spheres
Authors: Hounkonnou M. N. , Hounkpe M. , Shabani J.
Published: July 2002

We study stationary scattering theory for finitely many sphere interactions formally given by the Hamiltonian H=−Δ+∑j=1Nαjδ(|x|−Rj) and its generalizations to the case of interactions of the second type and interactions with nonseparated boundary conditions. In a previous publication [J. Math. Phys. 29, 660–664 (1988)], it was shown that the self-adjoint Hamiltonian H{αl},{R} corresponding to H may be defined as a limit in norm resolvent convergence of a family Hε of local scaled short-range Hamiltonians. In this paper we also study scattering theory corresponding to Hε and show that the scattering quantities associated with Hε converge to those of H{αl},{R} as ε→0.
Continuum limit of lattice approximation schemes
Authors: Bender Carl M. , Tovbis Alexander
Published: July 2002

Boundary-layer perturbation theory problems are inherently singular. However, it is known that discretizing the problem by introducing a lattice may convert such problems into regular perturbation problems. The singular nature of boundary-layer problems is then relegated to and hidden in the continuum limit, the subtle limit in which the lattice spacing tends to zero. If the lattice is introduced cavalierly, then extrapolating to zero lattice spacing gives a sequence of extrapolants that at first approaches the correct limit and then veers off, thereby revealing the asymptotic nature of such problems. However, discretizing the problem following the procedures described here yields lattice approximations that have a smooth and regular continuum limit. These ideas are illustrated by three nonlinear ordinary differential equations: the cubic equation that describes instantons, an oscillator equation having a quadratic nonlinearity, and the Blasius equation.
Finite coherence length for equilibrium states of generalized adiabatic Holstein models
Authors: Baesens C. , MacKay R. S.
Published: July 2002

We prove that the equilibrium states of the adiabatic Holstein model, and a wide range of generalizations, have finite coherence length as long as they have electronic gap and phonon gap.
L
operators and Drinfeld’s generators
Authors: Hayaishi Norifumi , Miki Kei
Published: July 2002

Utilizing the multiplicative formula of universal R matrices, the correspondence between the L operators and Drinfeld’s generators is explicitly calculated for quantum group Uq(g) with g=Al(1),Bl(1),Cl(1),Dl(1).
On a class of distributions of interest in quantum field theory
Authors: Thomas Launey J. , Wichmann Eyvind H.
Published: July 2002

A class of tempered distributions studied by Araki is considered. These distributions are of interest in quantum field theory since they include certain matrix elements of commutators or anticommutators of local quantum field operators. A number of results concerning the null regions in spacetime of such distributions are presented, for the cases when the null regions are causal complements of closed, convex, causally complete subsets of spacetime. Applications to quantum field theory are discussed, and some immediate applications to the theory of the Klein–Gordon equation and the wave equation are noted.
On the Coulomb Sturmian matrix elements of relativistic Coulomb Green’s operators
Authors: Kónya B. , Papp Z.
Published: July 2002

The Hamiltonian of the radial Coulomb Klein–Gordon and second order Dirac equations are shown to possess an infinite symmetric tridiagonal matrix structure on the relativistic Coulomb Sturmian basis. This allows us to give an analytic representation for the corresponding Coulomb Green’s operators in terms of continued fractions. The poles of the Green’s matrix reproduce the exact relativistic hydrogen spectrum.
Quantum geometry of field extensions
Authors: Majid Shahn
Published: July 2002

We introduce a new kind of topological gauge configuration or “soliton” associated to the extension C⊇R of the real numbers to the complex ones. These configurations describe zero-curvature gauge fields and nontrivial cohomology over the real line, but with a quantum choice of differential calculus. In general, the quantum differential 1-forms on the line with coordinate algebra k[x] are in correspondence with field extensions of k, and the quantum cohomology detects the nontriviality of the extension.
Percolation and number of phases in the two-dimensional Ising model
Authors: Georgii Hans-Otto , Higuchi Yasunari
Published: July 2002

We reconsider the percolation approach of Russo, Aizenman, and Higuchi for showing that there exist only two phases in the Ising model on the square lattice. We give a fairly short alternative proof which is only based on stochastic monotonicity and avoids the use of symmetry inequalities originally needed for some background results. Our proof extends to the Ising model on other planar lattices such as the triangular and honeycomb lattice. We can also treat the Ising antiferromagnet in a homogeneous field and the hard-core lattice gas model on Z2.
Gibbs states of graphical representations of the Potts model with external fields
Authors: Biskup M. , Borgs C. , Chayes J. T. , Kotecký R.
Published: July 2002

We consider the ferromagnetic q-state Potts model, with each of the q spin values coupled to an external field. We also introduce a generalized random cluster model, which includes both the Potts model in arbitrary homogeneous external fields and the noninteger q random cluster model as special cases. We establish the FKG property, the finite energy condition, uniqueness of the infinite cluster, and Gibbsianness of limit states for this generalized model. Furthermore, we develop the theory of Gibbs states for the Edwards–Sokal representation of the Potts model in a field, and relate the phase structure in this representation to those in the spin and random cluster representations. Finally, we characterize the possible color(s) of the infinite cluster(s) and show that the correspondence between Edwards–Sokal Gibbs states and their random cluster marginals is bijective, once the color of the infinite cluster is fixed.
Exactly solvable models of δ′-sphere interactions in relativistic quantum mechanics
Authors: Hounkonnou M. N. , Avossevou G. Y. H.
Published: July 2002

We introduce and develop a systematic theory of δ′-sphere interactions formally given by the Hamiltonian H{R}=HD+Σm=1Nα̃mδ′(|x_|−Rm); α̃m∈R,x_∈R3,Rm>0,1⩽m⩽N with boundary conditions of the second type, as a logical continuation of the work performed [J. Math. Phys. 40, 4255 (1999)]. First, we give the mathematical definition of the model, self-adjointness of the Hamiltonian, the indicial equation, and the useful scattering elements. Next, we extend the model by adding a Coulomb potential and provide useful mathematical definitions and corresponding stationary scattering elements.
Relativistic scattering theory for finitely many δ-sphere interactions supported by concentric spheres
Authors: Hounkonnou M. N. , Avossevou G. Y. H.
Published: July 2002

For the model formally expressed as H{R}=HD+∑m=1Nαmδ(|x¯|−Rm); x¯∈R3,αm∈R, Rm>0, we give a precise mathematical definition, provide basic properties and main scattering elements.
The Reeh–Schlieder property for thermal field theories
Authors: Jäkel Christian D.
Published: July 2002

We show that the Reeh–Schlieder property w.r.t. KMS states is a direct consequence of locality, additivity, and the relativistic KMS condition. The latter characterizes the thermal equilibrium states of a relativistic quantum field theory. The statement remains valid even if the given equilibrium state breaks spatial translation invariance.
On the K-property of quantized Arnold cat maps
Authors: Neshveyev S. V.
Published: July 2002

We prove that some quantized Arnold cat maps are entropic K-systems. This result was formulated by H. Narnhofer [J. Math. Phys. 33, 1502–1510 (1992)], but the fact that the optimal decomposition for the multi-channel entropy constructed there is not strictly local was not appropriately taken care of. We propose a strictly local decomposition based on a construction of Voiculescu.
W-algebras from canonical transformations
Authors: Bandelloni G. , Lazzarini S.
Published: July 2002

It is shown how W-algebras emerge from very peculiar canonical transformations with respect to the canonical symplectic structure on a compact Riemann surface. The action of smooth diffeomorphisms of the cotangent bundle on suitable generating functions is written in the BRS framework while a W-symmetry is exhibited. Subsequently, the complex structure of the symmetry spaces is studied and the related BRS properties are discussed. The specific example of the so-called W3-algebra is treated in relation to some other different approaches.
Vortex-in-cell simulations of buoyant bubbles in three dimensions
Authors: Brecht Stephen H. , Ferrante John R.
Published: July 2002

The three-dimensional evolution of one and two inviscid buoyant bubbles is studied. The study considers evolution of the buoyant bubble from the initial spherical state to the point where the bubble has formed into a vortex ring. The effect of the nonlinear interaction between two bubbles upon this evolution is also considered. This research considered a variety of density jumps across the interface with Atwood numbers ranging from 0.5 to nearly 1.0. The studies were performed with the three-dimensional vortex-in-cell code, VINCE3D. The results indicate that the evolution of either one or two bubbles follows scaling predicted from the equations being solved. This scaling holds until the bubbles become nonlinearly involved.
The effect of an axial electric field on the stability of a rotating dielectric cylindrical liquid bridge
Authors: González H. , Castellanos A.
Published: July 2002

The branching points of the shape families bifurcating from a cylindrical liquid bridge anchored on two plane-parallel electrodes, when subjected to rotation and an electric potential difference, are determined. It is shown that the cylindrical shape may be destabilized through either an axisymmetric mode or a C mode. The stable region in the parameter space is always enlarged as the electric field is increased.
Transition to hard turbulence in thermal convection at infinite Prandtl number
Authors: Hansen Ulrich , Yuen David A. , Kroening Sherri E.
Published: July 2002

Direct numerical simulations of two-dimensional high Rayleigh (Ra) number, base-heated thermal convection in large aspect-ratio boxes are presented for infinite Prandtl number fluids, as applied to the Earth’s mantle. A transition is characterized in the flow structures in the neighborhood of Ra between 107 and 108. These high Ra flows consist of large-scale cells with strong intermittent, boundary-layer instabilities. For Ra exceeding 107 it is found that the heat-transfer mechanism changes from one characterized by mushroom-like plumes to one consisting of disconnected ascending instabilities, which do not carry with them all the thermal anomaly from the bottom boundary layer. Plume–plume collisions become much more prominent in high Ra situations and have a tendency of generating a pulse-like behavior in the fixed plume. This type of instability represents a distinct mode of heat transfer in the hard turbulent regime. Predictions of this model can be used to address certain issues concerning the mode of time-dependent convection in the Earth’s mantle.
On the nonlinear stability of a high-speed, axisymmetric boundary layer
Authors: Pruett C. David , Ng Lian L. , Erlebacher Gordon
Published: July 2002

The stability of a high-speed, axisymmetric boundary-layer flow is investigated by means of secondary instability theory and direct numerical simulation. Parametric studies based on temporal secondary instability theory identify subharmonic secondary instability as a likely path to transition on a hollow cylinder at Mach 4.5. The theoretical predictions are validated by direct numerical solution of the compressible Navier–Stokes equations. Initial perturbations for the temporal direct numerical simulation consist of an axisymmetric ‘‘second-mode’’ primary disturbance and a subharmonic secondary disturbance comprised of four oblique wave components. At small initial amplitudes of the secondary disturbance, growth rates obtained from the spectrally accurate numerical simulation agree to several significant digits with linear growth rates predicted by secondary instability theory. Qualitative agreement persists to relatively large amplitudes of the secondary disturbance. Moderate transverse curvature is shown to significantly affect the growth rate of axisymmetric ‘‘second-mode’’ disturbances, the likely candidates of primary instability. The influence of curvature on secondary instability is largely indirect, but most probably significant, through modulation of the primary disturbance amplitude. Subharmonic secondary instability is shown to be predominantly inviscid in nature, and to account for peaks in the Reynolds stress components near the critical layer.