bluuebunny/crossref_metadata_2025 huggingface dataset:
Ab initio study of the low-lying electronic states of Ag3−, Ag3, and Ag3+: A coupled-cluster approach
Authors: Yoon Jungjoo , Kim Kwang S. , Baeck Kyoung K.
Published: July 2002

The low-lying electronic states of Ag3−(1Σg+,3B2), Ag3(2B2,2A1,2B1,4B2,2Σu+,1 2Σg+,2 2Σg+,2Πu,4Σu+), and Ag3+(1A1,1Σg+,3Σu+,3A1) are studied by ab initio calculations with the Stuttgart effective core potentials and corresponding (8s7p6d)/[6s5p3d] and (8s7p5d3f )/[6s5p3d3f] basis sets. The geometries, vibrational frequencies, and energetic splittings are obtained by the coupled-cluster method including singles and doubles (CCSD) and those including up to the noniterative triples [CCSD(T)] correlation methods with additional frozen core molecular orbitals corresponding to 4s and 4p orbitals. The results for well-studied states (Ag3− 1Σg+;Ag3 2B2,2A1,2Σu+;Ag3+ 1A1) are in good agreement with previous experimental results, and therefore our results for other newly studied states are expected to be reliable. The vertical detachment energies of Ag3− are obtained by the electron excitation equation-of-motion coupled-cluster (EE-EOM-CCSD) method and the average deviation from the experimental results is small without any scaling correction of the obtained values. The effect of the f-functions in the basis sets and the noniterative triples in the CCSD(T) method is discussed; the bond lengths are reduced significantly and the vertical detachment energies and ionization potentials are in much better agreement with experiment.
Solvation of magnesium and singly ionized magnesium atoms in NH3 clusters: Theory and experiment
Authors: Elhanine Mohamed , Dukan Laure , Maı̂tre Philippe , Breckenridge W. H. , Massick Steve , Soep Benoit
Published: July 2002

The structure and energies of neutral Mg(NH3)nclusters have been investigated by experiment and theory, the ionization energy (IE) thresholds of these clusters being the probe of the differential solvation. Experimentally, the IE’s of the magnesium atoms solvated by ammonia have been investigated by tunable laser ionization of clusters prepared in a simple pick-up source. IE’s of clusters Mg(NH3)n have been measured for n=1 up to 37. The solvation of the magnesium ion is more efficient than that of the closed shell neutral Mg atom, resulting in a steep decrease of the ionization energy of ammonia clusters of increasing sizes (1.3 eV for n=1, 2.2 eV for n=2, and 2.9 eV for n=3). The stepwise decrease becomes smaller for higher order clusters (n>20) but the asymptotic value does not appear to be reached even at n=37, suggesting a still developing electrostatic stabilization of the ion clusters at these sizes. Quantum chemical calculations have been performed which reveal the unique features of the solvation of the neutral closed shell Mg atom. The formation of neutral clusters is dominated by singly coordinated cyclic subunits containing three ammonias, while the ion is best stabilized by triply coordinated magnesium. The experimental ionization energies are in excellent agreement with the calculated values, indicating a “locally adiabatic” process. The very low ionization energy limit or asymptote, 2.3 eV, measured for the largest clusters can be simply rationalized by electrostatic interactions in the ion cluster, without having to invoke charge separation in the neutral aggregate.
Theory and simulation of the swelling of polymer gels
Authors: Kenkare N. R. , Hall C. K. , Khan S. A.
Published: July 2002

A combined discontinuous molecular dynamics and Monte Carlo simulation technique is used to study the swelling of athermal, continuous-space, near-perfect, trifunctional polymer networks containing hard chains of lengths 20 and 35 immersed in an athermal hard-sphere solvent. The swelling simulations are conducted under conditions of constant pressure and chemical potential. A simple, analytical theory for gel swelling is presented in which the gel free energy is calculated as the sum of an elastic, affine-type term, and a liquidlike mixing term that is based on the generalized-Flory dimer equation of state. The theory shows good agreement with our simulation results for the gel properties at swelling equilibrium.
Photoelectron spectroscopy and ab initio study of mixed cluster anions of [(CO2)1–3(Pyridine)1–6]−: Formation of a covalently bonded anion core of (C5H5N–CO2)−
Authors: Han Sang Yun , Chu Inho , Kim Jeong Hyun , Song Jae Kyu , Kim Seong Keun
Published: July 2002

Anions of mixed cluster between carbon dioxide (CO2) and pyridine (C5H5N, denoted by Py), each possessing a negative adiabatic electron affinity, were studied. The minimum size cluster anion was the 1:1 complex of [(CO2)1(Py)1]−, which displayed highest mass spectral intensity in the series. It was shown by photoelectron spectroscopy that [(CO2)1(Py)1]− is not a typically expected ion–molecule complex of the type (CO2)1−(Py)1 or (CO2)1(Py)1−. Ab initio calculation in the UHF/6-311++G** level revealed that [(CO2)1(Py)1]− is indeed a totally new anion of the type (C5H5N-CO2)− with a planar C2v structure, bound by an intermolecular bond of a strongly covalent character. The calculation predicted 1.24 eV for the vertical detachment energy of this anion, which is in reasonably good agreement with the measured value of 1.46 eV by photoelectron spectroscopy. A Mulliken analysis showed that the excess negative charge is fully delocalized throughout the entire molecular frame. Further calculation on intramolecular rotational barrier predicted a considerable barrier height of ∼0.68 eV, which could be due to an additional, weak π-bond character of the newly formed C–N σ-bond. Such extra π-bond network was suggested to provide a path for the charge delocalization and thus lead to the stability of the anion core.
Spectroscopy of the A 2Δ–X 2Π transition of CH/D–Ar
Authors: Komissarov Anatoly V. , Heaven Michael C.
Published: July 2002

The CH(A 2Δ)–Ar van der Waals molecule provides a prototypical example of a Δ2 state complex. The rovibronic structure of CH/D(A)–Ar has been examined by recording rotationally resolved spectra for the A–X transition. The spectra are dominated by vibrational progressions of the intermolecular stretch in combination with two bending states. Rotational energy level patterns were consistent with a linear equilibrium geometry for CH(A)–Ar. Parity splittings resulting from vibronic interactions were below the resolution of the present measurements. Spectra for the A–X transition of CD, recorded incidentally in this study, reveal an error in the previously accepted assignment of the 0–0 band R2(1/2) line.
Reaction dynamics of electronically state-specific CH2 with NO
Authors: Su Hongmei , Kong Fanao , Chen Bozhen , Huang Ming-Bao , Liu Yajun
Published: July 2002

With time-resolved Fourier transform infrared emission spectroscopy and DFT B3LYP quantum calculation, the reaction dynamics of CH2(X̃ 3B1) and CH2(ã 1A1) with NO have been investigated. It is found that both CH23+NO and CH21+NO reactions follow the same reaction pathways and produce same products arising from the same elementary channels. The primary products of vibrationally excited CO(v), HCO(v1), HOCN(v2), OH(v), and NH2(v3) were detected for the first time and four reaction channels have thus been identified. Theoretically, a doublet potential energy surface is characterized. On the potential energy surfaces, both the CH23+NO and CH21+NO systems reach a crucial intermediate OCHNH via a CNO ring-closure and ring-opening process. From this intermediate, the four reaction pathways proceed: C–N bond rupture in OCHNH simply leads to NH+HCO; OCHNH rearranges either to H2NCO producing CO+NH2, or to HOCHN generating HOCN+H and HCN+OH.
Gradients in valence bond theory
Authors: Dijkstra Fokke , van Lenthe Joop H.
Published: July 2002

A gradient method for general valence bond wave functions is presented. The electronic energy is used as a Lagrange multiplier. The derivatives of the normalization and of the first- and second-order cofactors present in the energy expression have to be evaluated, giving rise to first-, second-, and third-order cofactors. This evaluation is done using an extension of methods described previously. The use of gradients is illustrated with some calculations on organic molecules, viz. ethene, 1, 4-butadiene, and benzene.
Geometrical methods for the elasticity theory of membranes
Authors: Peterson Mark A.
Published: July 2002

The elasticity theory of curved membranes is developed using geometrical methods. The strain tensor is shown to be the Lie derivative of the metric tensor with respect to a flow. This formulation is coordinate-free, and can be expressed in any convenient coordinate system. A useful fixed coordinate system for the neighborhood of any given membrane surface is constructed. The formalism is used to expand the curvature free energy of a membrane about its minimum and to find the induced flow which minimizes shear dissipation in a curved membrane when the membrane is deformed at constant density. The shear free energy is expanded about its minimum for deformations of the shape at constant density. The curvature free energy is explicitly expanded about its minimum for shape changes of a closed membrane which conserve area and interior volume.
Energy eigenvalues of d-dimensional quartic anharmonic oscillator
Authors: Seetharaman M. , Vasan S. S.
Published: July 2002

On the basis of a radial generalization of the JWKB quantization rule, which incorporates higher orders of the approximation, an explicit analytical formula is derived for the energy levels of the three-dimensional quartic anharmonic oscillator. The formula exhibits the scaling property of the exact eigenvalues, and is readily generalized to any dimension. Together with the Hellmann–Feynman theorem, it yields the values of the diagonal moments of r2k. The predicted energies and moments are in excellent agreement with known numerical results.
Explicit reduction of spl(1,2) to osp(1,2) as a simplified model for applications of supersymmetry to nuclear physics
Authors: Baake M. , Reinicke P.
Published: July 2002

The reduction of irreducible representations of the superalgebra spl(1,2) to the subsuperalgebra osp(1,2) is given explicitly. The oscillator representations are discussed in detail and their relevance for nuclear physics is outlined by a simple model containing three ground-state nuclei. The results have important implications on a recently suggested mechanism for the symmetry breaking of spl(6,2m) via osp(6,2m).
Classical particles with internal structure: General formalism and application to first-order internal spaces
Authors: Atre M. V. , Mukunda N.
Published: July 2002

Group theoretic methods are used to systematically classify all possible internal structures for an elementary classical relativistic particle in terms of coset spaces of SL(2,C) with respect to its continuous subgroups. The allowed internal spaces Q are separated into first- and second-order ones, depending on whether a canonical description can be given using Q itself or if it needs the cotangent bundle T*Q. Three of the former are found, one corresponding to the use of a Majorana spinor as the internal variable, the other two related to orbits in the Lie algebra of SO(3,1) under the adjoint action. For the latter two, a Lagrangian description of an elementary object with the corresponding internal space is set up, and the dynamics studied.
Canonoid transformations and constants of motion
Authors: Negri Luiz J. , Oliveira Luimar C. , Teixeira Julio M.
Published: July 2002

The necessary and sufficient conditions for a canonoid transformation with respect to a given Hamiltonian are obtained in terms of the Lagrange brackets of the transformation. The relation of these conditions with the constants of motion is discussed.
Decomposition of Lorentz transformations
Authors: Han D. , Kim Y. S. , Son D.
Published: July 2002

It is shown that every Lorentz transformation can be decomposed into a helicity-preserving transformation that changes the momentum of a free particle and a helicity-changing transformation that leaves the momentum invariant. Since momentum-preserving transformations constitute a subgroup of the Lorentz group, helicity-preserving transformations form a coset space. It is shown further that, for massive particles, every Lorentz transformation can be decomposed into the Wigner rotation and helicity-preserving transformations. For massless particles, every Lorentz transformation can be decomposed into the gauge transformation and helicity-preserving transformation. The gauge transformation in this case is a Lorentz-boosted Wigner rotation.
Inverse scattering for standing wave solutions of the Schrödinger equation
Authors: Somersalo Erkki
Published: July 2002

In this paper a reformulation of the inverse scattering theory for a three-dimensional Schrödinger equation is given in terms of the standing wave solutions and the reactance matrix. A counterpart of the generalized Marchenko equation is given as well as a trace-type formula for the potential. Derivations are based on the ∂̄ method in the complex k plane.
Debye potentials for Rarita–Schwinger fields in curved space-times
Authors: Torres del Castillo G. F.
Published: July 2002

Expressions for the complete solution of the Rarita–Schwinger equation in terms of complex scalar potentials are obtained by means of Wald’s method of adjoint operators. The background space-time is required to be an algebraically special solution of the Einstein vacuum field equations with cosmological constant or a solution of the Einstein–Maxwell equations such that one principal null direction of the electromagnetic field is geodetic and shear-free.
The geometry of gauge symmetry breaking in the superstring context
Authors: McInnes Brett
Published: July 2002

The Higgs mechanism has a very natural global formulation: given a principal fiber bundle (P,M,G), with structural group G, a subbundle with the unbroken subgroup as structural group (with the aid of the Higgs fields themselves) can be constructed. In superstring theory, the fundamental E8 symmetry, as well as the grand unification symmetry, are broken in a very different way. The principal purpose of this work is to construct a global formulation of the superstring gauge vacuum, without Higgs fields.
Membranes in string theory, trees, the Weil conjectures, and the Ramanujan numbers
Authors: Grossman Bernard
Published: July 2002

It is suggested that the factorization of the inverse partition function for 26-dimensional bosonic string theory can be interpreted as the existence of an 11-dimensional membrane. The geometry of diffusion on trees is found to be especially useful, with the p→1 limit corresponding to ordinary diffusion in the plane. Finally, the interpretation of the cohomological information in the Weil conjectures in terms of supersymmetric quantum mechanics and the arithmetic of the semiclassical limit is outlined.
Generalized Lie symmetries and complete integrability of certain nonlinear Hamiltonian systems with three degrees of freedom
Authors: Lakshmanan M. , Sahadevan R.
Published: July 2002

A systematic method for investigating the existence of nontrivial generalized Lie symmetries is presented and the associated integrals of motion for nonlinear oscillator systems with three-degrees of freedom defined in terms of the Lagrangian by L= (1)/(2) (ẋ2+ẏ2+ż2)−V(x,y,z) are constructed. Then the method is applied to study the integrability properties of quartically and cubically coupled nonlinear oscillators with three degrees of freedom. Compatibility with the Painlevé property is also investigated.
Linearization of novel nonlinear diffusion equations with the Hilbert kernel and their exact solutions
Authors: Matsuno Y.
Published: July 2002

Two novel nonlinear diffusion equations with the Hilbert kernel are proposed. The equations can be linearized by introducing appropriate dependent variable transformations. The initial value problems for the proposed equations are then solved exactly through the linearization and explicit nonperiodic and periodic solutions are constructed. The properties of solutions are investigated in detail. It is found that the blow up of solutions occurs at a finite time for both the nonperiodic and periodic cases due to the breakdown of certain analytic conditions imposed on the dependent variables.
Some important classes of quantum measurements and their information gain
Authors: Lahti Pekka J. , Busch Paul , Mittelstaedt Peter
Published: July 2002

The notions of ideal, first kind, and repeatable measurements are reformulated and their relations analyzed within a systematic theory of measurement in quantum mechanics. This allows one to investigate new information theoretical characterizations of such measurements.
Explicit canonical tensor operators and orthonormal coupling coefficients of SU(3)
Authors: Ališauskas Sigitas
Published: July 2002

The canonical unit SU(3) tensor operators are constructed by means of the stretched coupling of the auxiliary maximal and minimal null space tensor operators, with the renormalization factors expressed in terms of the denominator functions of Biedenharn, Gustafson, Lohe, Louck, and Milne. The matrix elements of the maximal null space tensor operators are expressed with the help of the modified projection operators of Asherova and Smirnov. The self-conjugate minimal null space tensor operators are expressed in terms of the group generators with the help of the weight lowering operator technique. The corresponding extreme isoscalar factors of the Clebsch–Gordan (Wigner) coefficients are used as constructive elements of the explicit recursive expression for the general orthonormal isoscalar factors of SU(3) with its considerable simplication for the boundary values of parameters. The general isofactors are also expanded in the different ways in terms of their boundary values. The new classes of the generalized hypergeometric series are used as constructive elements of the SU(3) and SU(2) representation theory functions and their properties are considered.
Analysis on the p-adic superspace. II. Differential equations on p-adic superspace
Authors: Khrennikov A. Yu.
Published: July 2002

The Cauchy problem for differential equations on the p-adic superspace is considered. The application of this mathematical theory to the model of the supersymmetric quantum mechanics on the p-adic Riemannian surface is proposed. The non-Archimedean superdiffusion is also considered.
Generalized Stephani universes
Authors: Jiang Sheng
Published: July 2002

Stephani universes are the conformally flat solutions of Einstein equations for perfect fluids. The rotation-free, shear-free, and conformally flat solutions of Einstein equations for fluids with heat flux are obtained. They are a natural generalization of Stephani universes.
A representation of solutions of the Helmholtz equation with application to crystal Green’s functions
Authors: Newton Roger G.
Published: July 2002

Functions that solve the Helmholtz equation in a bounded region are represented in the form of an integral on the unit sphere. The linear space needed for this, as well as the uniqueness of the representation, are investigated. A specific application of the technique to general spectral calculations for electrons in periodic crystals is included.
Generalized graph theory on Lie g and applications in conformal field theory
Authors: Halpern M. B. , Obers N. A.
Published: July 2002

Each magic basis of Lie g supports a generalized graph theory on Lie g, whose axioms include the graphs of order n as a special case on SO(n). Other examples include the sine-area graphs of SU(n) and the sine(⊕area) graphs of SU(Πini). The set of all (magic basis–generalized graph theory) pairs is not known, but each possible pair corresponds to a large set of new conformal field theories.
Riemannian twistors and Hermitian structures on low-dimensional space forms
Authors: Baird Paul
Published: July 2002

A Riemannian Kerr Theorem is described, which associates to an integrable Hermitian structure (with singularities) on S4 a complex analytic surface in CP3. To such a Hermitian structure can be associated a harmonic morphism defined on each of the four-dimensional space forms with values in a Riemann surface. This unifies the classifications for the three-dimensional space forms of Baird and Wood and the recent classifications for R4 and S4 by Wood, into one simple equation. As a consequence we derive the classification for harmonic morphisms defined on four-dimensional hyperbolic space with values in a Riemann surface and a new implicit form for harmonic morphisms defined on three-dimensional hyperbolic space. Unification of the Kerr Theorems for S4 and for compactified Minkowski space M is achieved at the complex level after suitably embedding the spaces in compactified, complexified Minkowski space.
On the quantum differential calculus and the quantum holomorphicity
Authors: Brzeziński T. , Da̢browski H. , Rembieliński J.
Published: July 2002

Under some natural assumptions [less restrictive than in the paper by Wess and Zumino (preprint CERN-TH-5697/90, LAPP-TH-284/90)] differential calculi on the quantum plane are found and investigated. Complex structure, complex derivatives, and holomorphic functions on the quantum plane are defined. Generalized Cauchy–Riemann equations are given and solved.
Low-velocity scattering of vortices in a modified Abelian Higgs model
Authors: Strachan I. A. B.
Published: July 2002

The moduli space metric for hyperbolic vortices is constructed, and their slow motion scattering is calculated in terms of geodesics in this space.
The braided Heisenberg group
Authors: Baskerville W. K. , Majid S.
Published: July 2002

The braided groups and braided matrices B(R) for the solution R of the Yang–Baxter equation associated to the quantum Heisenberg group are computed. It is also shown that a particular extension of the quantum Heisenberg group is dual to the Heisenberg universal enveloping algebra Uq(h), and this result is used to derive an action of Uq(h) on the braided groups. The various covariance properties are then demonstrated using the braided Heisenberg group as an explicit example. In addition, the braided Heisenberg group is found to be self-dual. Finally, a physical application to a system of n braided harmonic oscillators is discussed. An isomorphism is found between the n-fold braided and unbraided tensor products, and the usual ‘‘free’’ time evolution is shown to be equivalent to an action of a primitive generator of Uq(h) on the braided tensor product.
Critical exponents in the imperfect and the free Bose gas
Authors: Broidioi M.
Published: July 2002

The field fluctuations are studied for the free and imperfect Bose gas. In the phase where there is condensation, these field fluctuations are abnormal, with critical exponents depending on the way the symmetry-breaking external field tends to zero in the thermodynamic limit. On the critical line there is also abnormal behavior, but the dependence on the way the field disappears, is slightly different. For densities below the critical density, the fluctuations are normal and independent of the way the external field goes to zero.
Generalized multidimensional Epstein zeta functions
Authors: Kirsten Klaus
Published: July 2002

Explicit formulas are given for the expression of multiple-sum zeta functions of the type ∑l1,...,lN=−∞∞[a1(l1 − c1)2 +... + aN(lN − cN)2 + M2]−s, where ai≳0, M2≥0, i=1,...,N, in terms of Riemann and Hurwitz zeta functions and in terms of Kelvin functions. Using different analytical continuation methods several formulas, especially useful for different values of the involved parameters, are obtained.
Spatial entropy of central potentials and strong asymptotics of orthogonal polynomials
Authors: Aptekarev A. I. , Dehesa J. S. , Yáñez R. J.
Published: July 2002

The Boltzmann–Shannon information entropy of quantum-mechanical systems in central potentials can be expressed in terms of the entropy Sn of the classical orthogonal polynomials. Here, an asymptotic formula for the entropy of general orthogonal polynomials on finite intervals is obtained. It is shown that this entropy is intimately related to the relative entropy I (ρ0,ρ) of the equilibrium measure ρ0(x) and the weight function ρ(x) of the polynomials. To do so, the theory of strong asymptotics of orthogonal polynomials on compact sets is used.
Reformulation of QCD in the language of general relativity
Authors: Lunev F. A.
Published: July 2002

It is shown that there exists such a collection of variables that the standard QCD Lagrangian can be represented as the sum of usual Palatini Lagrangian for Einstein general relativity and the Lagrangian of matter and some other fields where the tetrad fields and the metric are constructed from initial SU(3) Yang–Mills fields.
Green functions of higher-order differential operators
Authors: Avramidi Ivan G.
Published: July 2002

The Green functions of the partial differential operators of even order acting on smooth sections of a vector bundle over a Riemannian manifold are investigated via the heat kernel methods. We study the resolvent of a special class of higher-order operators formed by the products of second-order operators of Laplace type defined with the help of a unique Riemannian metric but with different bundle connections and potential terms. The asymptotic expansion of the Green functions near the diagonal is studied in detail in any dimension. As a by-product a simple criterion for the validity of the Huygens principle is obtained. It is shown that all the singularities as well as the non-analytic regular parts of the Green functions of such high-order operators are expressed in terms of the usual heat kernel coefficients ak for a special Laplace type second-order operator.
A Lie algebra for closed strings, spin chains, and gauge theories
Authors: Lee C.-W. H. , Rajeev S. G.
Published: July 2002

We consider quantum dynamical systems whose degrees of freedom are described by N×N matrices, in the planar limit N→∞. Examples are gauge theories and the M(atrix)-theory of strings. States invariant under U(N) are “closed strings,” modeled by traces of products of matrices. We have discovered that the U(N)-invariant operators acting on both open and closed string states form a remarkable new Lie algebra which we will call the heterix algebra. (The simplest special case, with one degree of freedom, is an extension of the Virasoro algebra by the infinite-dimensional general linear algebra.) Furthermore, these operators acting on closed string states only form a quotient algebra of the heterix algebra. We will call this quotient algebra the cyclix algebra. We express the Hamiltonian of some gauge field theories (like those with adjoint matter fields and dimensionally reduced pure QCD models) as elements of this Lie algebra. Finally, we apply this cyclix algebra to establish an isomorphism between certain planar matrix models and quantum spin chain systems. Thus we obtain some matrix models solvable in the planar limit; e.g., matrix models associated with the Ising model, the XYZ model, models satisfying the Dolan–Grady condition and the chiral Potts model. Thus our cyclix Lie algebra describes the dynamical symmetries of quantum spin chain systems, large-N gauge field theories, and the M(atrix)-theory of strings.
Contractions of Lie algebras and separation of variables. The n-dimensional sphere
Authors: Izmest’ev A. A. , Pogosyan G. S. , Sissakian A. N. , Winternitz P.
Published: July 2002

Inönü–Wigner contractions from the rotation group O(n+1) to the Euclidean group E(n) are used to relate the separation of variables in Laplace–Beltrami operators on n-dimensional spheres and Euclidean spaces, respectively. In this article we consider all subgroup type coordinates corresponding to different chains of subgroups of O(n+1) and E(n), respectively. In particular, the contractions relate the graphical formalism of “trees” on spheres to the “clusters” on Euclidean spaces (introduced in this article). The contractions are considered analytically on several levels: the vector fields realizing the Lie algebras, the complete sets of commuting operators characterizing separable coordinate systems, the coordinate systems themselves and the separated eigenfunctions.
Quasilinearization method and its verification on exactly solvable models in quantum mechanics
Authors: Mandelzweig V. B.
Published: July 2002

The proof of the convergence of the quasilinearization method of Bellman and Kalaba, whose origin lies in the theory of linear programming, is extended to large and infinite domains and to singular functionals in order to enable the application of the method to physical problems. This powerful method approximates solution of nonlinear differential equations by treating the nonlinear terms as a perturbation about the linear ones, and is not based, unlike perturbation theories, on existence of some kind of small parameter. The general properties of the method, particularly its uniform and quadratic convergence, which often also is monotonic, are analyzed and verified on exactly solvable models in quantum mechanics. Namely, application of the method to scattering length calculations in the variable phase method shows that each approximation of the method sums many orders of the perturbation theory and that the method reproduces properly the singular structure of the exact solutions. The method provides final and reasonable answers for infinite values of the coupling constant and is able to handle even super singular potentials for which each term of the perturbation theory is infinite and the perturbation expansion does not exist.
Wigner–Weyl correspondence and semiclassical quantization in spherical coordinates
Authors: Poirier Bill
Published: July 2002

The Wigner–Weyl quantum-to-classical correspondence rule is nonunique with respect to coordinate choice. This ambiguity can be exploited to improve the accuracy of semiclassical approximations. For instance, the well-known Langer modification was recently derived by applying a coordinate transformation to the radial Schrödinger equation prior to using the Wigner–Weyl rule—albeit only by presuming exact quantum solutions for all nonradial degrees of freedom [J. J. Morehead, J. Math. Phys. 36, 5431 (1995)]. In this paper, the full classical Hamiltonian is derived in all degrees of freedom, using a (hyper)spherical coordinate Wigner–Weyl correspondence with a Langer-like modification of polar angles. For central force Hamiltonians, the new result is radially equivalent to that of Langer, and to the standard Cartesian form. The new correspondence is superior with respect to all angular momentum operators however, in that the resultant semiclassical eigenvalues are exact—a desirable goal, evidently achieved here for the first time.
Separation of variables for soliton equations via their binary constrained flows
Authors: Zeng Yunbo , Ma Wen-Xiu
Published: July 2002

Binary constrained flows of soliton equations admitting 2×2 Lax matrices have 2N degrees of freedom, which is twice as many degrees of freedom than in the case of monoconstrained flows. By using the normal method, their Lax matrices directly give rise to first N pairs of canonical separated variables for their separation of variables. We propose a new method to introduce the other N pairs of canonical separated variables and additional separated equations. The Jacobi inversion problems for binary constrained flows are established. Finally, the factorization of soliton equations by two commuting binary constrained flows and the separability of binary constrained flows enable us to construct the Jacobi inversion problems for some soliton hierarchies.
Kostant’s cubic Dirac operator of Lie superalgebras
Authors: Pengpan Teparksorn
Published: July 2002

We extend equal rank embedding of reductive Lie algebras to that of basic Lie superalgebras. The Kac character formulas for equal rank embedding are derived in terms of subalgebras and Kostant’s cubic Dirac operator for equal rank embedding of Lie superalgebras is constructed from both even and odd generators and their related structure constants.
Extensions of convexity models
Authors: Beltrametti E. G. , Bugajski S. , Varadarajan V. S.
Published: July 2002

The notion of convexity model is introduced to provide a general frame for statistical theories of physical interest: this frame encompasses, in particular, the classical and the quantum cases. In a convexity model the states of the physical system, and the convex structure they form, play a basic role; observables and related quantities are then naturally defined. The notion of extensions of a convexity model is studied: it appears physically relevant to cope with several needs, paradigmatically with the one of viewing the physical system as a part of a compound system. We focus attention on quantum-like extensions of both the usual classical and quantum convexity models, as well as on classical-like extensions of the quantum model. The behavior of state overlapping and state superposition under model extension is briefly examined.
Dressing symmetries of holomorphic BF theories
Authors: Ivanova T. A. , Popov A. D.
Published: July 2002

We consider holomorphic BF theories, their solutions and symmetries. The equivalence of Čech and Dolbeault descriptions of holomorphic bundles is used to develop a method for calculating hidden (nonlocal) symmetries of holomorphic BF theories. A special cohomological symmetry group and its action on the solution space are described.
Anisotropic charged fluid spheres in D space–time dimensions
Authors: Harko T. , Mak M. K.
Published: July 2002

The equations describing the hydrostatic equilibrium (mass continuity and Tolman–Oppenheimer–Volkoff) of a static anisotropic general relativistic fluid sphere are obtained in D (D⩾4) space–time dimensions in the presence of a cosmological constant. The formalism thus developed is used to study homogeneous anisotropic constant density charged fluid spheres and homogeneous anisotropic charged spheres with a neutral isotropic core in higher dimensions. For these configurations and with a particular choice of the proper charge density a complete solution of the coupled Einstein–Maxwell equations is obtained.
Path space measure for the 3+1-dimensional Dirac equation in momentum space
Authors: Nakamura Toru
Published: July 2002

Nonstandard analysis is used to construct a measure over paths for the path integral solution to the Dirac equation in 3+1 dimension. Paths are considered in momentum space, because the Green function in the configuration space contains a derivative of δ function which keeps us from assigning a measure over paths. The solution is obtained not only as the standard part of a nonstandard path sum with respect to a nonstandard measure, but also as a standard path integral with respect to a standard measure extracted from the nonstandard one. The result is an extension of Gaveau’s work [B. Gaveau, J. Funct. Anal. 58, 310–319 (1984)].
U
q
[sl
(2|
∧
1)]
vertex operators, screen currents, and correlation functions at an arbitrary level
Authors: Zhang Yao-Zhong , Gould Mark D.
Published: July 2002

Bosonized q-vertex operators related to the four-dimensional evaluation modules of the quantum affine superalgebra Uq[sl(2|∧1)] are constructed for arbitrary level k=α, where α≠0,−1 is a complex parameter appearing in the four-dimensional evaluation representations. They are intertwiners among the level-α highest weight Fock–Wakimoto modules. Screen currents which commute with the action of Uq[sl(2|∧1)] up to total differences are presented. Integral formulas for N-point functions of type I and type II q-vertex operators are proposed.
Ill-posedness in the Einstein equations
Authors: Frittelli Simonetta , Gomez Roberto
Published: July 2002

It is shown that the formulation of the Einstein equations widely in use in numerical relativity, namely, the standard ADM form, as well as some of its variations (including the most recent conformally-decomposed version), suffers from a certain but standard type of ill-posedness. Specifically, the norm of the solution is not bounded by the norm of the initial data irrespective of the data. A long-running numerical experiment is performed as well, showing that the type of ill-posedness observed may not be serious in specific practical applications, as is known from many numerical simulations.
Structure, sound velocity, and thermal conductivity of the perovskite NdGaO3
Authors: Krivchikov A. I. , Gorodilov B. Ya. , Kolobov I. G. , Érenburg A. I. , Savitskiı̆ D. I. , Ubizskiı̆ S. B. , Syvorotka I. M. , Vasilechko L. O.
Published: July 2002

X-ray (300 K) and ultrasonic (77–270 K) studies and measurements of the thermal conductivity (30–300 K) are carried out on single-crystal samples of NdGaO3 in different crystallographic directions. The values of the lattice parameters of NdGaO3 are refined. The sound velocities in the principal crystallographic directions are measured, and the elastic constants and Debye temperature are calculated. The observed anisotropy of the thermal conductivity is described in the framework of a gaskinetic model and is linked to the anisotropy of the interaction parameters of the acoustical and optical phonons.
The hydrodynamic interaction of two slowly evaporating spheres
Authors: Oguz Hasan N. , Prosperetti Andrea , Antonelli Dario
Published: July 2002

The Stokes flow induced by the slow evaporation or condensation of two spheres is studied. The phase-change velocity is prescribed and uniform over the surfaces of the spheres. Exact expressions are obtained for the streamfunction and the drag forces. Simpler expressions applicable to a variety of limit cases (distant spheres, a source and a sphere, and a sphere and a plane) are presented. When only one sphere is evaporating, depending on the distance from the other sphere, the flow may exhibit a variety of interesting behaviors such as smooth-boundary separation, closed recirculating eddies, and infinite open eddies.
Viscous flow down a slope in the vicinity of a contact line
Authors: Goodwin Ralph , Homsy G. M.
Published: July 2002

The two-dimensional base state that ultimately exhibits a contact-line-related instability is investigated by a combination of analysis and numerical solution. Globally, these flows may be characterized as having a down-slope length scale that is much greater than the length scale normal to the slope. This allows a solution by matched expansions, where the outer solution is governed by simple kinematics and describable by lubrication theory. In order to complete the solution, the flow in an inner region near the contact line must be determined. It is shown that it is not possible to model the flow in the inner region using the lubrication approximations while also requiring both that (1) the free surface meets the plane at the contact line and (2) the rate of change of the curvature of the free surface be bounded at the contact line. However, the full two-dimensional Stokes equations allow the inner solution to be determined. A boundary integral technique is used to obtain numerical solutions to the problem in which a contact angle boundary condition is imposed. Solutions are reported for a wide range of the three relevant parameters: the capillary number, the contact angle, and the inclination angle. The computations reveal that the free surface develops a hump near the contact line as a result of a stress field that results from kinematic considerations. A scaling analysis of the numerical results verifies that, except possibly at very small contact angles, the lubrication approximations are inappropriate near the contact line.
Viscoelastic Poiseuille flow through a curved channel: A new elastic instability
Authors: Joo Yong Lak , Shaqfeh Eric S. G.
Published: July 2002

The linear stability of the inertialess, pressure-driven Poiseuille flow of an Oldroyd-B fluid through a slightly curved channel is considered. The flow is shown to be unstable in certain flow parameter regimes. The critical conditions and the structure of the vortex flow at the onset of instability are presented. These results reveal that there is a purely elastic, instability in the flow, and the instability is a stationary mode in contrast to the elastic, oscillatory instability that occurs in Taylor-Couette flow [see Larson, Shaqfeh, and Muller, J. Fluid Mech. 218, 573 (1990)]. In addition, the mechanism of the instability is investigated through an examination of the disturbande-energy equation.
Magnetic island formation in three-dimensional plasma equilibria
Authors: Hegna Chris C. , Bhattacharjee A.
Published: July 2002

The formation of magnetic islands as a result of plasma pressure in three-dimensional equilibria is investigated by a boundary-layer analysis. Away from a rational surface (‘‘exterior region’’), the plasma current is calculated exactly from the equilibrium equations. The singularity in the current thus calculated is resolved by analysis of the equilibrium equations in the vicinity of the rational surface (‘‘inner region’’). The Δ′ parameter of tearing mode theory is used to match the inner and outer regions. The island width is found to depend on the resistive interchange criterion, as seen in the work of Glasser, Greene, and Johnson [Phys. Fluids 18, 875 (1975)]. Estimates of island sizes for different stellarator experiments are given.
Support of the model for ‘‘Vertical displacement episodes’’ from numerical simulation of episodes observed in the DIII-D tokamak
Authors: Jensen Torkil H. , Skinner David G.
Published: July 2002

The plasma of a tokamak with a vertically elongated cross section is normally kept in its central position by the action of a feedback system that controls currents in external coils. If this control becomes unsuccessful, a vertical displacement episode develops. During such an episode, the vacuum vessel may be subject to large vertical forces. Since these forces are large enough to impact the design of future devices, there is a need to understand them. In this paper a comparison is described between data from such vertical displacement episodes observed in the DIII-D tokamak [Bull. Am. Phys. Soc. 31, 1533 (1986)] to those from a numerical simulation code designed to realize a previously suggested conceptual model for the plasma physics part of a displacement episode. The comparison suggests validity of the model and that the code provides a realization of the model. Other code runs suggest that before reasonable predictions can be made on vertical forces in future devices, specific scenarios for the time development of the currents of external coils during an episode are needed.
Fluctuations and low-frequency stability
Authors: Litwin C.
Published: July 2002

Electromagnetic fluctuations can cause a modification of time-averaged plasma dynamics. Their presence manifests itself through ponderomotive and magnetization forces. For incompressible transverse plasma motions, the ponderomotive force is mainly responsible for an alteration of the momentum balance while the magnetization causes primarily a modification of Ohm’s law. These modifications can substantially affect the low-frequency stability. Specifically, it can be shown that the ponderomotive force of fluctuations driven by velocity-space instabilities can stabilize the ideal internal kink mode in a tokamak and the flute mode in a tandem mirror reactor. Magnetization force of fluctuations can also affect the resistive modes. For the resistive internal kink, thought to be responsible for sawtooth oscillations, this effect can be stabilizing.
Theory of the tokamak beta limit and implications for second stability
Authors: Ramos J. J.
Published: July 2002

A comprehensive picture of the tokamak stability limits against ideal magnetohydrodynamic (MHD) pressure-gradient-driven modes is put forward. The approach is based on scaling arguments for large q, and affords a first principle understanding of the Troyon limit once the normalized ratio βaB/I is modified by an extra q0 factor. The effects related to a possible access to the second stability region are clarified.
Force-free magnetic field in the axisymmetric torus of arbitrary aspect ratio
Authors: Tsuji Yasumasa
Published: July 2002

The equation ∇×B=αB is solved analytically in a toroidal coordinates system for the axisymmetric torus of arbitrary aspect ratio without the approximation of large aspect ratios.The solution is derived from the Helmholtz equation and is expressed in the series that contains the associated Legendre functions. A set of fundamental solutions is presented, each of which approaches asymptotically the solution for cylindrical geometry, whose azimuthal dependence is cos lψ, in the limit of large aspect ratios. The force-free magnetic field is given in the form of the infinite series of these solutions. By using the set of fundamental solutions, the contour of the magnetic surface, eigenvalues, and F-Θ curves of the circular cross section are calculated.
The structure of magnetic fluctuations in tokamaks: Observations in the TEXT tokamak
Authors: Kim Y. J. , Gentle K. W. , Ritz Ch. P. , Rhodes T. L. , Bengtson R. D.
Published: July 2002

The structure of the magnetic fluctuations in a tokamak has been determined from extensive measurements using a variety of probes outside the limiter in TEXT [Plasma Phys. Controlled Nucl. Fusion 27, 1335 (1985)]. The spectrum has been measured to 500 kHz, but little energy is present above 150 kHz. The spectrum ranges from low-frequency, low-m-number modes with high coherence to higher m values at higher frequencies, which have limited poloidal and temporal coherence but are specifically correlated with electrostatic fluctuations in the edge. Although these magnetic fluctuations are not directly significant for transport, they are a useful indication of edge turbulence. They are associated with turbulence only inside the limiter. The correlation length along field lines is long, and the phase variation of the correlated components suggests k∥/k⊥ ≂ 0.005. These magnetic signals are consistent with a modest modulation of the plasma resistivity in the edge as in resistivity-gradient-driven modes, but the magnetic fluctuation signal is not proportional to the applied E∥. Their response to many other perturbations is reported.
Suprathermal and relativistic electrons produced in laser–plasma interaction at 0.26, 0.53, and 1.05 μm laser wavelength
Authors: Rousseaux C. , Amiranoff F. , Labaune C. , Matthieussent G.
Published: July 2002

Very energetic electrons produced in laser–plasma interactions at 0.26, 0.53, and 1.05 μm laser wavelength have been measured. The targets were 1.5 μm plastic foils and the laser intensity was around 1015 W/cm2. Detailed measurements of the electron distribution performed at a 0.26 μm laser wavelength exhibit an angular distribution strongly peaked along the laser axis at the highest energies (above 200 keV). Electrons up to 1.3 MeV have been observed in the 1.05 μm experiments. The hot temperatures inferred from the measured energy distributions are of the order of 100 keV in the 1.05 μm experiments, and 50 keV in the 0.53 μm/0.26 μm experiments. The experimental electron emission features are discussed with a special focus on the relation between the linear as well as the nonlinear electron plasma wave generation mechanisms and the maximum energy reached by an electron trapped in this wave.
Thomson scattering in pair plasmas
Authors: Sincell Mark W. , Krolik Julian H.
Published: July 2002

The photon–electron scattering cross section is calculated for a plasma composed of electrons and a positively charged particle of arbitrary mass. When me=m+ (i.e., for a pair plasma), all effects due to collective processes in the plasma exactly cancel.