bluuebunny/crossref_metadata_2025 huggingface dataset:
Water dimer to pentamer with an excess electron: Ab initio study
Authors: Kim Jongseob , Suh Seung Bum , Kim Kwang S.
Published: July 2002

We have studied the electronic structures, energetics, electron vertical detachment energies (VDEs), and O–H vibrational spectra of various conformers of water clusters with an excess electron [e+(H2O)n, n=2–5] or anionic water clusters [(H2O)n−] using comprehensive ab initio calculations. As noted in our preliminary work [J. Kim et al., Phys. Rev. A 59, 930 (1999)], the structure of the water dimer anion is characterized to be linear-like (slightly towards the cis conformer) but very floppy with large wide-ranging zero point vibration motion at 0 K. The lowest energy structures of the water trimer to pentamer anion are all cyclic with very small VDEs (< 0.05 eV). However, these cyclic structures which are metastable are prone to become the neutral species by releasing an excess electron because the transition barriers seem to be very small. Thus, observation of such cyclic structures would not be feasible. On the other hand, a linear water trimer structure which is 0.8 kcal/mol higher in energy than the cyclic form gives the VDE (0.14 eV) close to the experimentally observed value. A large VDE observed in the pentamer also corresponds to a slightly high energy conformer. This suggests that formation of anionic water clusters in experiments seems to be dynamically and kinetically driven.
Rotational tunneling of ammonia in (NH3)K3C60
Authors: Margadonna Serena , Prassides Kosmas , Brown Craig M. , Shimoda Hideo , Iwasa Yoshihiro , Casalta Hélène
Published: July 2002

The rotational dynamics of NH3 in the ammoniated fulleride (NH3)K3C60 are studied by the inelastic neutron scattering technique. Well-defined excitations appear in the low-energy spectra at 1.5 K as a broad band centered at ∼350 μeV with shoulders at ∼240 and 590 μeV. The temperature dependence of their intensities, energies, and widths is consistent with their assignment to rotational tunneling transitions of the NH3 molecule. The estimated barrier of the threefold hindrance potential to rotation of the H atoms about the K–N axis is ∼5.7 meV. The existence of minority hindering sites with both larger (∼8 meV) and smaller (∼2 meV) torsional barriers shows that orientational disorder effects survive in (NH3)K3C60 even at low temperatures.
Supercooling and transient phase induced nucleation in n-alkane solutions
Authors: Sirota E. B.
Published: July 2002

The supercooling exhibited by bulk solutions of the n-alkane tricosane (C23) in dodecane (C12) is measured as a function of concentration using adiabatic scanning calorimetry. For small dilutions where crystallization occurs into the rotator phase, negligible supercooling is observed. For larger dilutions where crystallization is into the herringbone crystal phase, nucleation occurs at the temperature where the rotator phase becomes stable with respect to the liquid. The supercooling in bulk n-alkane solutions is thus determined by the metastable phase diagram. This is a novel, but possibly often occurring mechanism where nucleation is induced by a transient metastable phase.
The structure and stability of Sb4H+ clusters: The importance of nonclassical structures
Authors: González Ana I. , Mó Otilia , Yáñez Manuel
Published: July 2002

The structure and relative stabilities of the different Sb4H+ clusters were investigated by means of high level ab initio calculations. For this purpose we have developed a split valence and an extended basis set for the treatment of Sb-containing compounds to be used with different effective core potentials available in the literature. The split-valence basis set reported seems to reproduce nicely the geometries and vibrational frequencies of different Sb-containing compounds, provided that electron correlation effects are included at the MP2 level. When the extended basis set is used, within the framework of the G2(ECP) theory, the atomization enthalpies of antimony derivatives are reproduced within ±3 kcal/mol. A systematic study of the Sb4H+ potential energy surface (PES) using these basis sets, showed that the global minimum is the result of the side protonation of the Sb4 tetrahedral molecule. In this species the hydrogen is covalently attached to two Sb atoms through the formation of a three-centered delocalized bonding orbital similar to the one responsible for the stability of analogous P4H+ and As4H+ side-protonated species. This “nonclassical” structure is estimated to be 26 kcal/mol more stable than the classical corner-protonated form. The stability of these “nonclassical” structures increases as one descends in the group. Concomitantly, the gas-phase basicity also increases from P4 to Sb4, the latter being about 20 kcal/mol more basic than P4 and about 14.5 kcal/mol more basic than As4. In contrast with P4 and As4, the body- centered protonated species of Sb4 is predicted to be a local minima of the PES. Similar trends have been found for BiH4+ species.
Distribution of lipids in nonlamellar phases of their mixtures
Authors: Li Xiao-jun , Schick M.
Published: July 2002

We consider a model of lipids in which a head group, characterized by its volume, is attached to two flexible tails of equal length. The phase diagram of the anhydrous lipid is obtained within self-consistent field theory, and displays, as a function of lipid architecture, a progression of phases: body-centered cubic, hexagonal, gyroid, and lamellar. We then examine mixtures of an inverted hexagonal forming lipid and a lamellar forming lipid. As the volume fractions of the two lipids vary, we find that inverted hexagonal, gyroid, or lamellar phases are formed. We demonstrate that the nonlamellar forming lipid is found preferentially at locations that are difficult for the lipid tails to reach. Variations in the volume fraction of each type of lipid tail are on the order of one to ten percent within regions dominated by the tails. We also show that the variation in volume fraction is correlated qualitatively with the variation in mean curvature of the head–tail interface.
Polymer blends near patterned surfaces
Authors: Seok Chaok , Freed Karl F. , Szleifer Igal
Published: July 2002

The complicated density profiles exhibited by compressible binary polymer blends near patterned surfaces in the one-phase region are studied employing the analytic density functional-self-consistent field theory. The density patterns are explained on the basis of the competing influences of the correlation lengths for composition and density fluctuations, the pattern spacing, and the interfacial density profiles at abrupt changes in the surface interaction. The length scale for the in-plane interfacial profiles is determined primarily by the correlation length for composition fluctuations, with the correlation length for density fluctuations exerting rather a small influence. However, the magnitude of the surface segregation depends on both correlation lengths, the pattern dimensions, and the surface–polymer potentials.
Influence of extended interactions on the surface dynamics in the catalytic CO oxidation on Pt single crystal substrate
Authors: Chávez Francisco , Vicente Luis , Perera Aurélien , Moreau Michel
Published: July 2002

The simulation of kinetic oscillations and dynamics of CO chemical fronts propagating through a Pt(100) substrate by the use of cellular automaton techniques, is reexamined with an extended interacting neighborhood model, that allows for a temperature dependence of the reaction constants. These new cellular automaton rules account for the structural phase transformations of the Pt substrate, the reaction kinetics of the adsorbed phase, and diffusion of adsorbed species. In addition it provides a richer variety of surface patterns formation. Specifically, we consider the effect of lateral interactions between adsorbed particles, this is taken into account our simulations through the definition of a site-dependent reaction constant, that is dependent of the state of the metal. This is achieved by considering an extended neighborhood of next-nearest-neighbors and beyond. For CO–CO and O–O attractive interactions, the oscillation amplitude increases as the interaction energy increases. It is shown herein that the presence of strong attractive lateral interactions in reacting adsorbate can lead to the spontaneous formation of traveling waves. The diffracting properties of the waves moving in the media with different composition (one part clean and other containing inert sites) are also investigated. It is shown that beyond a critical coverage, waves traveling from a clean part of the crystal to a partially covered surface are adsorbed by the media, destroying their coherence. Finally, it is shown that appropriate initial conditions can also lead to the formation of double stable spirals.
On the problem of rotational-state-dependent molecule–surface interaction: Relaxation, accommodation and trapping at low J
Authors: Pankov A. Yu. , Krylov S. Yu. , van Duijn E. J. , Hermans L. J. F.
Published: July 2002

In the framework of a unified kinetic theory of particle–surface interactions, dependences of the relaxation, accommodation, and trapping of molecules on their angular momentum J are discussed. One of the basic parameters of the theory, the free flight time through the interaction region, is calculated using a simple model potential for which the classical equations of motion can be integrated analytically. With increasing J, an increase in molecular relaxation and accommodation is predicted at small J, and a decrease at larger J. These results constitute a microscopically founded interpretation of recent experiments on surface light-induced drift.
Electric field effects on the helium dimer
Authors: Bruch L. W.
Published: July 2002

Three methods of perturbing the ground state of the He4 dimer by electric fields are treated: the Stark shift by large static electric fields; dissociation by a pulsed electric field; and the coupling of a plane wave to the interaction-induced quadrupole moment of the dimer. The second process, with coupling to the interaction-induced polarizability anisotropy of the dimer, appears to offer the best prospect for observable perturbation of the dimer. The estimates are based on results of ab initio calculations of properties of the He–He system.
The Hamiltonian structure of a complex version of the Burgers hierarchy
Authors: Bruschi M. , Ragnisco O.
Published: July 2002

In this paper we construct a class of integrable Hamiltonian nonlinear evolution equations generated by a purely differential recursion operator. It turns out that this hierarchy is a complex version of the Burgers hierarchy and can be linearized through a generalization of the Cole–Hopf transformation.
Expansion in condensates
Authors: Chakrabarti J. , Sajjad Zahir M.
Published: July 2002

We show that the product of local current operators in quantum chromodynamics (QCD), when expanded in terms of condensates, such as ψ̄ψ, Gaμν Gaμν, ψ̄Γ ψψ̄Γψ, fabcGaμνGbνα ×Gcαμ, etc., yields a series in Planck’s constant. This, however, provides no hint that the higher terms in such an expansion may be less significant.
Infinitesimal symmetry transformations. II. Some one-dimensional nonlinear systems
Authors: Aguirre M. , Krause J.
Published: July 2002

The converse problem of similarity analysis is discussed for the infinitesimal symmetry transformations of ordinary second-order differential equations which are nonlinear in ẋ (and may be linear or nonlinear in x). A natural classification of the problem arises, according to the highest order N of nonlinearity in ẋ. The completely general maximal Lie algebra is obtained for the case N≤3. In the case N≥4 one has, besides the system of differential equations for the infinitesimal generators, an extra set of anholonomic constraints, which operates as a symmetry-breaking mechanism producing a strong reduction in the number of surviving parameters. Miscellaneous examples are given, which illustrate some features of similarity analysis of nonlinear systems. The infinitesimal point transformation symmetries of the Van der Pol oscillator are also briefly discussed.
Representations of Kac–Moody algebras by step algebras
Authors: Mickelsson Jouko
Published: July 2002

Representations of a Kac–Moody algebra ĝ associated to a semisimple Lie algebra 𝔤, which decompose to a direct sum of finite-dimensional representations of the subalgebra 𝔤, are constructed using a step algebra method. The cases 𝔤=su(2), su(3) are considered in detail.
Application of linked Bäcklund transformations to nonlinear boundary value problems
Authors: Rogers C.
Published: July 2002

A class of nonlinear boundary value problems is reduced to linear canonical form by a combination of Bäcklund transformations.
A twistor encoding of Lienard–Wiechert fields in Minkowski space-time
Authors: Porter John R.
Published: July 2002

The twistor encoding of the anti-self-dual Lienard–Wiechert field on Minkowski space-time yields a considerably richer structure than that of the Coulomb field encoding due to the presence of a nonzero radiation field. The combination of advanced and retarded transverse fields together with the longitudinal field and the individual aspects of these fields provides this structure. Higher-order longitudinal moments can be incorporated so that general longitudinal fields can be given a twistor description.
Transforms associated to square integrable group representations. I. General results
Authors: Grossmann A. , Morlet J. , Paul T.
Published: July 2002

Let G be a locally compact group, which need not be unimodular. Let x→U(x) (x∈G) be an irreducible unitary representation of G in a Hilbert space ℋ(U). Assume that U is square integrable, i.e., that there exists in ℋ(U) at least one nonzero vector g such that ∫‖(U(x)g,g)‖2 dx<∞. We give here a reasonably self-contained analysis of the correspondence associating to every vector f∈ℋ(U) the function (U(x)g,f) on G, discussing its isometry, characterization of the range, inversion, and simplest interpolation properties. This correspondence underlies many properties of generalized coherent states.
Algebraic formulas for some nontrivial Un 6j symbols and Um
n⊃Um×Un 3j
m symbols
Authors: Haase Richard W. , Butler Philip H.
Published: July 2002

We give tables of algebraic formulas for some nontrivial 6j symbols and 3jm symbols of the unitary groups. The tables demonstrate that the building-up method can be used successfully to obtain the rank dependence of unitary group j and jm symbols. To emphasize the rank-dependent nature of this calculation, we have employed the composite Young tableaux notation (or back-to-back notation) to label the unitary group irreps. In using this notation, the transpose conjugate symmetry of the corresponding composite Young diagram leads to a new symmetry of the unitary group 6j and 3jm symbols. The transposition of the groups Um and Un gives rise to a further symmetry of the 3jm symbols of Umn⊃Um×Un.
Multiple scales analysis of a nonlinear ordinary differential equation
Authors: Gang Xu , Changqing Shu , Lei Lin
Published: July 2002

Asymptotic solutions of the nonlinear ordinary differential equation d2θ/dZ2 +a dθ/dZ +f(θ)=0 for large a are obtained by the singular perturbation method of multiple scales analysis. They are in the form of θ(Z)=A(Z/a)+B(Z/a)exp(−aZ). Initial and boundary value problems are discussed. The special case of f(θ)=γ+cos 2θ(γ<1), encountered in shearing nematic liquid crystal soliton problems and other physical systems, is solved in detail. Previously obtained analytic solutions are recovered and justified. Our results are applicable to the unsteady shearing nematic problem.
On solution spaces of massless field equations with arbitrary spin
Authors: Heidenreich W.
Published: July 2002

The solution spaces of massless field equations ⧠ Ψ=0, with Ψ being a tensor, a (multi)spinor, or a Rarita–Schwinger field, are studied. They carry indecomposable representations of the Poincaré group whose invariant subspaces are determined. There exist indefinite invariant scalar products that allow Gupta–Bleuler quantization for all spins. For particular cases like the third–rank tensor with mixed symmetry and the Rarita–Schwinger field for spin- (3)/(2), additional field equations are discussed, which project on subspaces.
The problem of ‘‘global color’’ in gauge theories
Authors: Horváthy P. A. , Rawnsley J. H.
Published: July 2002

The problem of ‘‘global color’’ (which arose recently in monopole theory) is generalized to arbitrary gauge theories: a subgroup K of the ‘‘unbroken’’ gauge group G is implementable iff the gauge bundle reduces to the centralizer of K in G. Equivalent implementations correspond to equivalent reductions. Such an action is an internal symmetry for a given configuration iff the Yang–Mills field reduces also. The case of monopoles is worked out in detail.
Birkhoff-type theorem in self-creation cosmology
Authors: Singh Tarkeshwar
Published: July 2002

It is shown that an analog of Birkhoff’s theorem of general relativity exists in a self-creation theory of gravitation, proposed by Barber, when the scalar field is independent of time.
Unbounded representations of symmetry groups in gauge quantum field theory. II. Integration
Authors: Völkel A. H.
Published: July 2002

Within the gauge quantum field theory of the Wightman–Gårding type, the integration of representations of Lie algebras is investigated. By means of the covariance condition (substitution rules) for the basic fields, it is shown that a form skew-symmetric representation of a Lie algebra can be integrated to a form isometric and in general unbounded representation of the universal covering group of a corresponding Lie group provided the conditions (Nelson, Sternheimer, etc.), which are well known for the case of Hilbert or Banach representations, hold. If a form isometric representation leaves the subspace from which the physical Hilbert space is obtained via factorization and completion invariant, then the same is proved to be true for its differential. Conversely, a necessary and sufficient condition is derived for the transmission of the invariance of this subspace under a form skew-symmetric representation of a Lie algebra to its integral.
On inverse scattering in an elastic medium with vertical inhomogeneities
Authors: Carrion Philip M.
Published: July 2002

This paper treats the nonlinear inverse scattering problem for an elastic horizontally stratified medium with vertical inhomogeneities. It is shown that the vector wave equation can be presented as a set of two scalar wave equations; the first scalar equation describes the propagation of normally incident compressional waves (it is assumed that we deal with compressional incident plane waves impinging on an elastic half space). Using any inverse scattering technique (based, for example, on the Gelfand–Levitan theorem) applied to this equation, the acoustic impedance can be uniquely recovered from the recorded impulse response. The second equation is valid only in the region where incident compressional waves decay exponentially (evanescent waves) and propagate with complex angles, whereas mode-converted shear waves propagate with real angles. The main contribution in this region in the high-frequency approximation comes from mode-converted shear waves. We derived a new equation which describes the propagation of mode-converted shear waves in this region. Applying any inverse scattering technique to this equation, the rigidity modulus and the density can be removed separately. Knowing the acoustic impedance, the rigidity modulus, and the density, all Lame’s parameters and the density can be recovered separately.
The symmetric group: Algebraic formulas for some S
f 6j symbols and S
f⊇S
f1×S
f2 3j
m symbols
Authors: Haase R. W. , Dirl R.
Published: July 2002

Explicit rank-dependent expressions have been obtained for some symmetric group (Sf) 6j symbols and some Sf⊇Sf1×Sf2 3jm symbols using Butler’s recursion method. A key point in deriving these results is the use of the reduced notation introduced by Murnaghan to label irreps. Various symmetries of the 6j and 3jm symbols have been imposed. These include the complex conjugation, permutation, and transpose conjugation. We incorporate a new symmetry that arises from the occurrence of the two isomorphic direct product groups Sf1×Sf2 and Sf2×Sf1 as subgroups of Sf. In relation to the tables of 6j and 3jm symbols presented, a discussion is given of the symmetric group-unitary group duality.
Spinor propagators in anti-de Sitter space-time
Authors: Janssen H. , Dullemond C.
Published: July 2002

Expressions are found for homogeneous and inhomogeneous propagators for spinor fields of arbitrary mass in anti-de Sitter space-time.
Quantum causal structures
Authors: Szabó L.
Published: July 2002

The axioms of a causal structure are reformulated. A natural generalization is suggested for the case when the subset lattice of space-time events is replaced by a lattice coming from the quantum theory.
On renormalization in nonrelativistic interaction models with infinities
Authors: Kröger Helmut , Smailagic Anais , Girard Ralph
Published: July 2002

The Green’s function of two models with nonrelativistic separable interaction giving rise to infinities in the perturbation expansion is studied. These infinities do not arise from the E+i0 limit, but come from the slow falloff behavior of the vertices, modeled after the infinities in Feynman graphs of field theory. Both models are analytically solvable. It is found that the Green’s function obtained from summing the renormalized perturbation series is identical to the direct solution of the Green’s function, which requires only an intermediate regularization. In the first model the interaction is split in a singular part giving raise to infinities and a regular part. It is shown that the Green’s function is the same as the Green’s function derived from only the regular part. This effect is similar to the effect occurring in φ4 field theory in 3+1 dimensions, where the φ4 interaction vanishes after renormalization and the S matrix is trivial. The second model is constructed such that parts of the singular interaction survive in the Green’s function.
Bundle structures in the Kerr space-time
Authors: Punsly Brian
Published: July 2002

A new extension of the Kerr space-time that was found by this author in a previous paper [J. Math. Phys. 26, 1728 (1985)] is analyzed in this article. The case of a2>m2 is of particular interest. The hypersurface at r=0 acts as if it were a ‘‘source’’ for the geometry. There exists a natural mapping of the hypersurface to a double covering of the null sphere at asymptotic infinity via the principal null congruences. After a study of the obstructions to fibering the constant time cross sections of the hypersurface at r=0, one finds that this two-surface transforms like a spinorialized version of Penrose’s null flags. This connection is made by studying the effects of Lorentz transformations at asymptotic infinity on the doubly covered null sphere. Since there exists an inequivalent bundle structure on the two-surface at r=0 that corresponds to an inequivalent spinorialized null flag, one concludes that to observers at stationary infinity the two-surface transforms as if it were a direct sum of two inequivalent Weyl spinors, a four-spinor.
Soliton transformations for axially symmetric higher-dimensional gravity. I. Generalized Neugebauer–Kramer transformations
Authors: Lee S.-C.
Published: July 2002

The field equations for axially symmetric gravitational fields in 4+K dimensions with K-dimensional toroidal compatification can be reduced to those of a generalized nonlinear sigma model. The dual symmetry of this model is considered first. Then the soliton transformations for these equations are derived using the method of Belinskii and Zakharov consequently generalizing their results to the higher-dimensional case. From the result of one-soliton transformation, a series of discrete symmetries generalizing the Neugebauer–Kramer transformation in the four-dimensional case are obtained. The basic properties of these new transformations are studied.
The asymptotic calculation of Wiener integrals occurring in quantum and statistical physics: A divergency problem
Authors: Moretti Paolo
Published: July 2002

The asymptotic expression of a Wiener functional integral using the eigenvalues of the associated Sturm–Liouville equation is obtained, correcting previous formulas giving a divergent result.
Geometrostatis and the current algebra of nonlinear sigma models on supergroup manifolds
Authors: Kobayashi K.
Published: July 2002

The radiative correction of nonlinear sigma models on supermanifolds that have invertible metrics is investigated. It will be shown that the equation of motion for Riemannian supergravity (nonstandard supergravity) is derived from a consistency condition. This condition can be satisfied in the case of supergroup manifolds. We shall explicitly construct the model following the methods of Braaten, Curtright, and Zachos [E. Braaten, T. L. Curtright, and C. K. Zachos, Nucl. Phys. B 260, 630 (1985)] and of Witten [E. Witten, Commun. Math. Phys. 92, 455 (1984)]. Finally, super-Kac–Moody algebras of these models are derived.
On the inverse problem and prolongation structure for the modified anisotropic Heisenberg spin chain
Authors: De Archan K. , Roy Chowdhury A.
Published: July 2002

A modified form of the anisotropic Heisenberg spin chain has been considered. By use of the prolongation structure technique of Wahlquist and Estabrook, the elliptic Lax pair associated with this equation has been deduced. A variant of the Reimann–Hilbert problem on the torus is used to indicate the way to the solution of the inverse problem.
Explicit description of ansatz E
n for the Ernst equation in general relativity
Authors: Nagatomo Kiyokazu
Published: July 2002

For the Ernst equation, a hierachy of ansatz that generates determinantal solutions of the Ernst equation is proposed. The ansatz is described explicitly in the inverse scattering formalism and it is shown that the corresponding exact solutions are determinantal solutions that have been constructed by Kyriakopoulos [Phys. Rev. D 30, 1158 (1984)] and Vein [Class. Quantum Gravit. 2, 899 (1985)].
The case against intermediate statistics
Authors: Lavenda B. H. , Dunning-Davies J.
Published: July 2002

It is shown that intermediate statistics do not correspond to any physical process. The stationary probability distributions of intermediate statistics are not compatible with any mechanism which allows a variation between Fermi–Dirac and Bose–Einstein statistics. The binomial and negative binomial distributions, characterizing Fermi–Dirac and Bose–Einstein statistics, respectively, transform into the Poisson distribution, descriptive of classical statistics, as the number of energy cells increases without limit. These distributions are shown to be the laws of error leading to the average value as the most probable value.
On theories of gravitation with nonsymmetric connection
Authors: Jakubiec Andrzej , Kijowski Jerzy
Published: July 2002

For a large class of theories of gravitation with nonsymmetric connection, based on general nonlinear Lagrangians, it is proved that the theory is equivalent to the standard Einstein theory of gravitation interacting with additional matter fields.
Symmetries of the self-dual Einstein equations. I. The infinite-dimensional symmetry group and its low-dimensional subgroups
Authors: Boyer C. P. , Winternitz P.
Published: July 2002

This is the first of two papers in which the authors give a complete classification of symmetry reduced solutions of Plebanski’s potential equation for self-dual Einstein spaces. In this first part the infinite pseudogroup of symmetries of Plebanski’s equation is described, and the conjugacy classes of all local subgroups of dimensions one, two, and three over both the real and complex numbers are classified. Then in the second paper, this classification is used to obtain all symmetry-reduced solutions.
Note on asymptotic series expansions for the derivative of the Hurwitz zeta function and related functions
Authors: Rudaz S.
Published: July 2002

Asymptotic series for the Hurwitz zeta function, its derivative, and related functions (including the Riemann zeta function of odd integer argument) are derived as an illustration of a simple, direct method of broad applicability, inspired by the calculus of finite differences.
Accuracy of eigenvalues: A comparison of two methods
Authors: Goyal I. C. , Gallawa R. L. , Ghatak A. K.
Published: July 2002

The problem of estimating the eigenvalues λ of the equation d2ψ/dx2+λf(x)ψ(x)=0, where f(x) is smooth and positive in the interval [0,l] and the imposed boundary conditions are ψ(0)=ψ(l)=0 is revisited. Two methods, the Wentzel–Kramers–Brillouin (WKB) method and Langer’s method, which until very recently has been virtually ignored, are compared. The variational principle further improves the accuracy of the eigenvalues. The results obtained when the WKB and Langer’s results are used as trial functions with the variational principle are also compared. Results are given in tabular form. The comparison shows that the Langer solution is the better of the two when the turning point [zero of f(x)] is close to the region of interest. If, however, the turning point is far from the region of interest, the two methods yield similar results. The reason for this is discussed.
Estimations for negative spectral bands of three-dimensional periodical Schrödinger operator
Authors: Galloonov G. V. , Oleinik V. L. , Pavlov B. S.
Published: July 2002

The asymptotic estimations, as period tends to infinity, for negative spectral bands of three-dimensional periodical Schrödinger operator who’s potential was generated by shifting along the cubic lattice of a negative function with compact support are described herein. The problem is of primary importance for solid state physics.
All space–times admitting strongly synchronizable reference frames are static
Authors: Kuang Zhiquan , Liang Canbin
Published: July 2002

The clock synchronization procedure associated with the usual definition of a locally synchronizable reference frame is inevitably approximate in nature. A new definition of local synchronizability, referred to as ‘‘strong synchronizability,’’ is suggested in this article. Roughly, a reference frame is called strongly synchronizable if, locally, all observers in it have common simultaneity surfaces. It will be proved that the sufficient and necessary condition imposed on a space–time for admitting a strongly synchronizable reference frame is that it be static.
On the supersymplectic homogeneous superspace underlying the OSp(1/2) coherent states
Authors: El Gradechi Amine M.
Published: July 2002

In this work Onofri and Perelomov’s coherent states methods are extended to the recently introduced OSp(1/2) coherent states. These latter are shown to be parametrized by points of a supersymplectic supermanifold, namely, the OSp(1/2)/U(1) homogeneous superspace, which is clearly identified with a supercoadjoint orbit of OSp(1/2) by exhibiting the corresponding equivariant supermoment map. Moreover, this supermanifold is shown to be a nontrivial example of Rothstein’s supersymplectic supermanifolds. More precisely, it is shown that its supersymplectic structure is completely determined in terms of SU(1,1)-invariant (but unrelated) Kähler 2-form and Kähler metric on the unit disc. This result leads to the definition of the notions of a super-Kähler supermanifold and a super-Kähler superpotential, the geometric structure of the former being encoded into the latter.
Motion of particles in five-dimensional Kaluza–Klein space–time
Authors: Banerjee A. , Sil A. , Chatterjee S.
Published: July 2002

Study of radial and circular geodesics including those of tachyons in two spherically symmetric vacuum five-dimensional space–time is done. One of them is of Schwarzschild type and the other the so-called soliton solution. We obtain results which are different from the usual analogous four-dimensional (4D) ones. It is found that all the circular geodesics irrespective of whether they are timelike, null, or spacelike will be stable in the region r≳6M. It has also been shown that in a homogeneous cosmological model where the isotropic 3 space expands but the extra space contracts with time, the existence of tachyon is possible. This is in contradiction to the analogous 4D result obtained previously.
Reducible Boson fermion realizations for osp(1‖2) and osp(3‖2) superalgebras
Authors: Daumens Michel
Published: July 2002

The osp(1‖2) algebra is first realized through one boson and two fermion pairs of creation annihilation operators and then both osp(1‖2) and osp(3‖2) are realized in terms of three boson and two fermion pairs. All these realizations are reducible, and the reduced states are labeled by the total occupation number.
De Rham complexes of q-analog of general linear group GLq(N)
Authors: Sun Xiaodong , Wang Shikun
Published: July 2002

In this paper, a set of De Rham complexes of quantum group GLq(N) determined by one parameter r is given, and it is proven that the differential calculi on the quantum group GLq(N) given in this paper are bicovariant. The noncommutative differential calculi on the quantum groups SLq(N) and SUq(N) are also discussed.
On the possibility of localized wave propagation using a classical two-fluid model of superconductors
Authors: Overfelt P. L.
Published: July 2002

In this paper, the classical two-fluid model for superconductors is used to determine the time-dependent partial differential equations (PDEs) which govern wave propagation in superconducting media. These equations are then solved exactly in both two and three dimensions using localized wave solutions rather than the traditional eigenfunction solutions. We have applied these localized wave solutions to the problem of a symmetric superconducting slab, neglecting the normally conducting current density, and found that the resultant focus wave mode magnetic field solution expels flux from the interior of the slab and can regain its initial amplitude as it travels along the surface of the slab. A comparison of the transverse part of the localized wave solution with the transverse part of the more usual plane wave solution shows remarkable agreement.
Dirac equation and Clifford algebra
Authors: Vrbik Jan
Published: July 2002

The Dirac equation is rewritten in the framework of a Clifford algebra, revealing some new features, of which the most interesting is the U(1)×SU(2) symmetry of the corresponding Lagrangian.
Exchange relations and correlation functions for a quantum particle on the SU2 group manifold
Authors: Furlan Paolo , Stanev Yassen S. , Todorov Ivan T.
Published: July 2002

The SO4 invariant quantum dynamics of a point particle moving on the 3 sphere (or equivalently, of the relative motion of the spherical top) is considered. Quantum exchange relations for different times are derived with an ‘‘R matrix’’ depending on the time difference and on the conserved angular momentum. Their implications for correlation functions are spelled out. The chiral exchange relations of Alekseev and Faddeev [Commun. Math. Phys. 141, 413–422 (1991)] are also extended to different times.
S-matrix, resonances, and wave functions for transport through billiards with leads
Authors: Albeverio S. , Haake F. , Kurasov P. , Kuś M. , Šeba P.
Published: July 2002

For a simple model describing the S-matrices of open resonators the statistical properties of the resonances are investigated, as well as the wave functions inside the resonator.
Infinite degeneracy for a Landau Hamiltonian with Poisson impurities
Authors: Pulé J. V. , Scrowston M.
Published: July 2002

We consider a single-band approximation to the random Schrödinger operator in an external magnetic field. The random potential consists of delta functions of random strengths whose positions have a Poisson distribution. We prove that if the magnetic field is sufficiently high compared to the density of scatterers, then with probability one there exists an infinitely degenerate eigenenergy coinciding with the first Landau level in the absence of a random potential.
Geodesics and geodesic deviation for impulsive gravitational waves
Authors: Steinbauer R.
Published: July 2002

The geometry of impulsive pp-waves is explored via the analysis of the geodesic and geodesic deviation equation using the distributional form of the metric. The geodesic equation involves formally ill-defined products of distributions due to the nonlinearity of the equations and the presence of the Dirac δ-distribution in the space–time metric. Thus, strictly speaking, it cannot be treated within Schwartz’s linear theory of distributions. To cope with this difficulty we proceed by first regularizing the δ-singularity, then solving the regularized equation within classical smooth functions and, finally, obtaining a distributional limit as solution to the original problem. Furthermore, it is shown that this limit is independent of the regularization without requiring any additional condition, thereby confirming earlier results in a mathematically rigorous fashion. We also treat the Jacobi equation which, despite being linear in the deviation vector field, involves even more delicate singular expressions, like the “square” of the Dirac δ-distribution. Again the same regularization procedure provides us with a perfectly well behaved smooth regularization and a regularization-independent distributional limit. Hence it is concluded that the geometry of impulsive pp-waves can be described consistently using distributions as long as careful regularization procedures are used to handle the ill-defined products.
Abelian Chern–Simons theory. I. A topological quantum field theory
Authors: Manoliu Mihaela
Published: July 2002

We give a construction of the Abelian Chern–Simons gauge theory from the point of view of a 2+1-dimensional topological quantum field theory. The definition of the quantum theory relies on geometric quantization ideas that have been previously explored in connection to the non-Abelian Chern–Simons theory [J. Diff. Geom. 33, 787–902 (1991); Topology 32, 509–529 (1993)]. We formulate the topological quantum field theory in terms of the category of extended 2- and 3-manifolds introduced in a preprint by Walker in 1991 and prove that it satisfies the axioms of unitary topological quantum field theories formulated by Atiyah [Publ. Math. Inst. Hautes Etudes Sci. Pans 68, 175–186 (1989)].
Solitary excitations of a two-dimensional electron gas
Authors: Nerses A. , Kunhardt E. E.
Published: July 2002

The nonlinear collective excitations of a two-dimensional electron gas (2DEG) formed at the interface of a heterostructure are presented. A matrix formulation of the coupled particle dynamics–electromagnetic field equations permits the extraction of the equation of evolution for these excitations. The stationary solutions of the equation are presented. A new class of solitary excitations is shown to form part of the nonlinear mode spectrum of excitations of the 2DEG in the low wave-vector plasmon–polariton regime.
Transition probabilities between quasifree states
Authors: Scutaru H.
Published: July 2002

We obtain a general formula for the transition probabilities between any state of the C* algebra of the canonical commutation relations (CCR-algebra) and a squeezed quasifree state (Theorem III.1). Applications of this formula are made for the case of multimode thermal squeezed states of quantum optics using a general canonical decomposition of the correlation matrix valid for any quasifree state. In the particular case of a one-mode CCR-algebra we show that the transition probability between two quasifree squeezed states is a decreasing function of the geodesic distance between the points of the upper half-plane representing these states. In the special case of the purification map it is shown that the transition probability between the state of the enlarged system and the product state of real and fictitious subsystems can be a measure for the entanglement.
Is there a stable hydrogen atom in higher dimensions?
Authors: Burgbacher Frank , Lämmerzahl Claus , Macias Alfredo
Published: July 2002

The Schrödinger equation in higher dimensions is considered. It consists of the kinetic energy part given by the corresponding Laplace operator, and a term describing the interaction with the electrostatic field of a point charge. From Rutherford-type scattering experiments one can conclude that the potential of a point charge is ∼1/r irrespective of the dimension of the space where the experiment is carried through. Also the structure of the kinetic energy is unchanged in higher dimensions so that one is lead to the result that there exist stable atoms in higher spatial dimensions d⩾4. The solutions and energy eigenvalues to this Schrödinger equation in higher dimensions are presented. As a consequence, the dimensionality of space can be read off from the spectral scheme of atoms: The three-dimensionality of space is a consequence of the existence of the Lyman series. Another consequence is that the Maxwell equations in higher dimensions must be modified in order to have the 1/r-potential as solution for a point charge.
A second-order solution for the solitary wave in a rotational flow
Authors: Chow Kwok W.
Published: July 2002

A second-order solution for the solitary wave in a rotational flow is derived. This would serve as the leading-order correction to the Korteweg–de Vries (KdV) soliton. Coefficients for the higher-order KdV equation are found from a sequence of boundary value problems. Their explicit numerical values are given for the simple example of a linear shear.
On the shape and dynamics of wall structures in turbulent channel flow
Authors: Guezennec Yann G. , Piomelli Ugo , Kim John
Published: July 2002

Turbulence-producing events in turbulent channel flow were found to be predominantly associated with asymmetric vortical structures rather than pairs of counter-rotating structures. An asymmetry-preserving averaging scheme was devised, allowing a picture of the ‘‘average’’ structure that more closely resembles the instantaneous one to be obtained. In addition, these structures were found to persist for long distances with little change while convecting downstream.
Sensitivity to initial conditions in the merging of two-layer baroclinic vortices
Authors: Verron J. , Hopfinger E. J. , McWilliams J. C.
Published: July 2002

Merging of geostrophic vortices in a two-layer stratified fluid is studied by means of direct numerical simulations. It is shown that the influence of density stratification on merging depends strongly on the initial shape of the vortices. When potential vortices are initially confined to the upper layer, with zero potential vorticity in the lower layer, the strength of the stratification is found to have no effect on merging. On the contrary, when the vortices initially have all their relative vorticity in the upper layer, with the lower layer at rest, the merging conditions are radically different. In the latter case, the most striking phenomenon is the pronounced scale selectivity that stratification has on merging. This behavior is provisionally interpreted as a consequence of the different far-field flow patterns for the different vortex profiles.
Topology and transport properties of large-scale organized motion in a slightly heated rough wall boundary layer
Authors: Bisset D. K. , Antonia R. A. , Raupach M. R.
Published: July 2002

Large-scale temperature discontinuities are detected in a high Reynolds number boundary layer over a slightly heated rough wall. In the streamwise and normal plane of the measurements, the discontinuities form (as for smooth wall boundary layers) the boundaries between successive spanwise vortexlike structures, flattened against the wall. The regions immediately downstream from the discontinuities are particularly important for the transport of heated, low-momentum fluid away from the wall. The proportions contributed by the detected organized motion to the velocity and temperature variances are similar to those in smooth wall boundary layers. The proportions contributed to mean products, especially to the Reynolds shear stress, are significantly higher than over smooth walls at similar Reynolds numbers. The detected organized motion in the rough wall boundary layer resembles that in a smooth wall boundary layer of similar skin friction coefficient (and hence much lower Reynolds number).
Monte Carlo implementation of a single-scalar mapping closure for diffusion in the presence of chemical reaction
Authors: Valiño Luis , Gao Feng
Published: July 2002

It is shown how to implement, via a Monte Carlo method, a single-scalar mapping closure for diffusion when chemical reactions or other processes are present. The mixing term in the one-point probability density function (pdf) equation of the scalar is closed via a mapping. The chemical term, closed in the pdf formulation, is treated exactly. To isolate each process, a fractional step technique is used. The methodology is the same if more processes are present. As an example, the pdf equation of one scalar reacting with itself in a statistically homogeneous forced turbulent flow is solved. Comparisons with computed direct numerical simulation data are excellent.
On the relation of near-wall streamwise vortices to wall skin friction in turbulent boundary layers
Authors: Kravchenko Arthur G. , Choi Haecheon , Moin Parviz
Published: July 2002

Databases from direct numerical simulations of fully developed turbulent channel flow were used to examine the relation between skin-friction on the wall and streamwise vortices observed near the wall. It is shown that the wall shear rate correlates with streamwise vortices near the wall and that the maximum correlation occurs downstream and with lateral displacement from the location of skin-friction measurement. Conditionally-averaged statistics taken near high skin-friction regions indicate that the higher skin-friction values are associated with streamwise vortices located closer to the wall. Visual studies of the time evolution of near-wall streamwise vortices and skin-friction on the wall also indicate that the high skin-friction footprints on the wall can be attributed to streamwise vortices.
Numerical simulation and physical analysis of high Reynolds number recirculating flows behind sudden expansions
Authors: Gagnon Yves , Giovannini André , Hébrard Patrick
Published: July 2002

This work presents the results of numerical simulations of unsteady recirculating flows at high Reynolds number. The two geometries investigated are a two-dimensional channel that incorporates a sudden expansion in the form of a single backward-facing step and a two-dimensional channel that incorporates a sudden expansion in the form of a double symmetrical backward-facing step. The random vortex method (RVM) is used in this study. This grid-free Lagrangian method solves the unsteady, incompressible Navier–Stokes equations and the continuity equation, with the appropriate physical boundary conditions, using a formulation in vorticity variables. In order to show the ability of the RVM an extensive set of numerical results is presented and compared with experimental results from the literature. In particular, the dissymmetrical behavior of the flow in the double expansion channel, as observed experimentally, is simulated accurately. Frequency analyses and autocorrelation analyses show that the flows are characterized by dominant frequencies and turbulent length scales that are function of the position inside the channels. Those frequencies and turbulent length scales are related to the dynamics of the flow fields.