bluuebunny/crossref_metadata_2025 huggingface dataset:
Trapping dynamics of isobutane, n-butane, and neopentane on Pt(111): Effects of molecular weight and structure
Authors: Weaver Jason F. , Madix Robert J.
Published: July 2002

The molecular adsorption dynamics of isobutane, n-butane, and neopentane on Pt(111) was investigated using supersonic molecular beam techniques and stochastic trajectory calculations. Using the united atom approach, a single, pairwise-additive Morse Potential for methyl (methylene)–plantinum interactions quantitatively simulates the dependence of the initial trapping probability, α, on the initial translational energy, ET, and angle of incidence, θi, for each alkane. For both isobutane and n-butane, the dependence of α on ET and θi best scales with ET cos0.8θi, which is similar to that found previously for ethane and propane trapping on Pt(111). The initial trapping probability of neopentane exhibits a more pronounced dependence on θi, which scales according to ET cos1.3θi. The simulations suggest that the enhanced angular dependence of α for neopentane is related to its molecular weight. As the mass of the incident species is increased, momentum transfer to the surface becomes more efficient than the interconversion of incident parallel and normal momentum due to corrugation of the surface potential. The net effect is an increase in the trapping probability at glancing incidence compared to lighter molecules, and a resulting shift in the angular dependence of α towards normal energy scaling. The calculations also predict that collisional energy transfer to rotation is important in promoting adsorption. For each molecule, rotational excitation is determined to be the most effective energy transfer process that discriminates trapping from scattering. In addition, translational energy transfer to torsional vibration about the central C–C bond is highly efficient for n-butane, and greatly facilitates adsorption. Less excitation is predicted for C–C–C bending modes for all of these molecules.
Basis set superposition error-counterpoise corrected potential energy surfaces. Application to hydrogen peroxide⋯X (X=F−, Cl−, Br−, Li+, Na+) complexes
Authors: Daza Martha C. , Dobado J. A. , Molina José Molina , Salvador Pedro , Duran Miquel , Villaveces José Luis
Published: July 2002

Mo/ller–Plesset (MP2) and Becke-3-Lee-Yang-Parr (B3LYP) calculations have been used to compare the geometrical parameters, hydrogen-bonding properties, vibrational frequencies and relative energies for several X− and X+ hydrogen peroxide complexes. The geometries and interaction energies were corrected for the basis set superposition error (BSSE) in all the complexes (1–5), using the full counterpoise method, yielding small BSSE values for the 6-311+G(3df,2p) basis set used. The interaction energies calculated ranged from medium to strong hydrogen-bonding systems (1–3) and strong electrostatic interactions (4 and 5). The molecular interactions have been characterized using the atoms in molecules theory (AIM), and by the analysis of the vibrational frequencies. The minima on the BSSE-counterpoise corrected potential-energy surface (PES) have been determined as described by S. Simón, M. Duran, and J. J. Dannenberg, and the results were compared with the uncorrected PES.
Accurate density-functional calculation of core-electron binding energies by a total-energy difference approach
Authors: Cavigliasso Germán , Chong Delano P.
Published: July 2002

A procedure for calculating core-electron binding energies (CEBEs), based on a total-energy difference approach within Kohn–Sham density functional theory, was investigated. Ten functional combinations and several basis sets (including unscaled, scaled, and core-valence correlated functions) were studied using a database of reliable observed CEBEs. The functionals designed by Perdew and Wang (1986 exchange and 1991 correlation) were found to give the best performance with an average absolute deviation from experiment of 0.15 eV. The scaled basis sets did not perform satisfactorily, but it was found that the core-valence correlated cc-pCVTZ basis functions were an excellent alternative to the cc-pV5Z set as they provided equally accurate results and could be applied to larger molecules.
Methods for optimizing large molecules. II. Quadratic search
Authors: Farkas Ödön , Schlegel H. Bernhard
Published: July 2002

Geometry optimization has become an essential part of quantum-chemical computations, largely because of the availability of analytic first derivatives. Quasi-Newton algorithms use the gradient to update the second derivative matrix (Hessian) and frequently employ corrections to the quadratic approximation such as rational function optimization (RFO) or the trust radius model (TRM). These corrections are typically carried out via diagonalization of the Hessian, which requires O(N3) operations for N variables. Thus, they can be substantial bottlenecks in the optimization of large molecules with semiempirical, mixed quantum mechanical/molecular mechanical (QM/MM) or linearly scaling electronic structure methods. Our O(N2) approach for solving the equations for coordinate transformations in optimizations has been extended to evaluate the RFO and TRM steps efficiently in redundant internal coordinates. The regular RFO model has also been modified so that it has the correct size dependence as the molecular systems become larger. Finally, an improved Hessian update for minimizations has been constructed by combining the Broyden–Fletcher–Goldfarb–Shanno (BFGS) and (symmetric rank one) SR1 updates. Together these modifications and new methods form an optimization algorithm for large molecules that scales as O(N2) and performs similar to or better than the traditional optimization strategies used in quantum chemistry.
Free energy calculation on enzyme reactions with an efficient iterative procedure to determine minimum energy paths on a combined ab initio QM/MM potential energy surface
Authors: Zhang Yingkai , Liu Haiyan , Yang Weitao
Published: July 2002

A new practical approach to studying enzyme reactions by combining ab initio QM/MM calculations with free energy perturbation is presented. An efficient iterative optimization procedure has been developed to determine optimized structures and minimum energy paths for a system with thousands of atoms on the ab initio QM/MM potential: the small QM sub-system is optimized using a quasi-Newton minimizer in redundant internal coordinates with ab initio QM/MM calculations, while the large MM sub-system is minimized by the truncated Newton method in Cartesian coordinates with only molecular mechanical calculations. The above two optimization procedures are performed iteratively until they converge. With the determined minimum energy paths, free energy perturbation calculations are carried out to determine the change in free energy along the reaction coordinate. Critical to the success of the iterative optimization procedure and the free energy calculations is the smooth connection between the QM and MM regions provided by a recently proposed pseudobond QM/MM approach [J. Chem. Phys. 110, 46 (1999)]. The methods have been demonstrated by studying the initial proton transfer step in the reaction catalyzed by the enzyme triosephosphate isomerase (TIM).
Line tension of Langmuir monolayer phase boundaries determined with optical tweezers
Authors: Wurlitzer S. , Steffen P. , Fischer Th. M.
Published: July 2002

The line tension λ of the liquid expanded (LE)/gas (G)-phase boundary of a methyl octadecanoate Langmuir monolayer at the air/water interface is measured using fluorescence microscopy combined with optical tweezers. Silica spheres, immersed into the monolayer and manipulated by the tweezers, deform the phase boundary. After switching off the tweezers, the relaxation of the deformed region is dominated by the competition between line tension and hydrodynamic resistance while dipole–dipole forces between the molecules can be neglected. A linear relation between the deformation length and time is found, from which a line tension of λ=7.5 pN is deduced. The linearity gives an upper bound for the surface potential differences of both phases. It is shown that viscous forces from the two-dimensional LE surroundings dominate the subphase friction. The optical tweezers enable one to observe relaxations on a shorter time scale, extending the range of measurement of previous techniques toward higher line tension or lower viscosities of the monolayer and of the subphase.
Interaction of longitudinal and transverse optic modes in silica glass
Authors: Tan C. Z. , Arndt J.
Published: July 2002

The splitting between longitudinal and transverse optical modes was observed in the infrared reflection spectra of silica glasses at different incident angles. The density of states and the frequency of the longitudinal mode were found to increase with increasing incident angle. A sharp minimum in the reflectance was monitored at large incident angles. A transmission window was observed in the absorption spectra of silica glass plates. The sharp minimum in the reflectance and appearance of the transmission window are believed to be the results produced by the Doppler effect due to the interaction of longitudinal and transverse optic modes in silica glass. The phase velocity of the longitudinal mode was evaluated in terms of the relativistic Doppler shift formula.
High-pressure phases of solid nitrogen by Raman and infrared spectroscopy
Authors: Bini Roberto , Ulivi Lorenzo , Kreutz Jörg , Jodl Hans J.
Published: July 2002

Raman and infrared spectra of solid nitrogen have been collected between 25 K and room temperature up to 41 GPa. A careful analysis of the spectral band transformations occurring across the high pressure transitions among the δ, δloc, ε, and ζ phases allowed to define the phase diagram in the whole P-T region investigated. In particular, the transition between the ε and ζ phases has been observed in the range 30–230 K and the corresponding phase-boundary drawn. A significant metastability region (spanning about 10 GPa in pressure) hinders the transformation between the ε and ζ phases when pressure is varied at low temperature. Group theory arguments suggest a centrosymmetric structure for the ζ phase and the number of Raman and infrared ν1 and ν2 components can be reproduced both with cubic and tetragonal structures. An appreciable coupling among neighboring molecules is observed, at room temperature, only in the ε phase where the relative orientations of the molecules are fixed.
A resolution for the enigma of a liquid’s configurational entropy-molecular kinetics relation
Authors: Johari G. P.
Published: July 2002

The literature data on the entropy and heat capacity of 33 glass-forming liquids have been used to examine the validity of the Adam–Gibbs relation between a liquid’s configurational entropy, Sconf, and its molecular kinetics. The critical entropy, sc*, of kB ln 2 (=0.956×10−23 J molecule−1 K−1) in the equation is less than even the residual entropy per molecule in a glass at 0 K, and this creates difficulties in determining the size of the cooperatively rearranging region, z*, in the liquid. It is argued that, z*=[1−(T0/T)]−1, and the temperature-invariant energy term, Δμ, is equal to RB, which has been determined from the knowledge of the Vogel–Fulcher–Tamman parameters B and T0, with R being the gas constant, and on the basis of the argument that the preexponential term of this equation is identical to that of the Adam–Gibbs relation. As the lattice modes in a glass are lower in frequency and more anharmonic than in its crystal, its vibrational entropy, Svib, would be higher than that of the crystal phase. Therefore, Sconf of a glass (and liquid) is significantly less than the difference between the entropy of the glass (and liquid) and the entropy of its completely ordered crystal phase. Both quantities, Svib and Sconf, have been estimated without reference to the vibrational spectra. The conclusions can be tested by determining z* and Δμ from measurements of the dielectric spectra of a liquid confined to nanometer-size pores. This is elaborated by a calculation for 3-bromopentane.
Performance of CCSDT for diatomic dissociation energies
Authors: Feller David , Sordo Jose A.
Published: July 2002

Calculations of 11 diatomic dissociation energies with coupled cluster theory through iterative triple excitations highlight both the strength and limitations of this method. By combining very large basis sets (through septuple zeta in some cases) and complete basis set extrapolations with corrections for core/valence correlation, scalar relativistic and atomic/molecular spin–orbit effects, it was possible to achieve excellent agreement with experiment in most cases. However, for C2 and CN the extent of the multiconfigurational nature of the molecules caused problems for the single configuration-based couple cluster methods. In the worse case, the inclusion of iterative triples resulted in a change with respect to the perturbative triples result which was of the opposite sign to the full configuration interaction change. This work emphasizes the difficulties in achieving uniform chemical accuracy even for ground state, first and second row diatomics.
Bianchi type I cosmological model with a viscous fluid
Authors: Banerjee A. , Duttachoudhury S. B. , Sanyal Abhik Kumar
Published: July 2002

Bianchi I cosmological models consisting of a fluid with both bulk and shear viscosity are studied. It is shown how the dynamical importance of the shear and the fluid density change in the course of evolution. Exact solutions with an equation of state p=ρ for a stiff fluid are also obtained in several special cases, assuming the viscosity coefficients to be the power functions of the density. The results are, in some relevant cases, compared with those of Belinskiǐ and Khalatnikov (1976) in the asymptotic limits and are seen to agree with them in that the models start with ρ=0 at the beginning and evolve with the creation of matter by the gravitational field, finally approaching the Friedmann universe.
Fermions in the space-time R×S3
Authors: Sen Diptiman
Published: July 2002

Quantum field theories on the surface of a four-dimensional sphere are considered. The Hamiltonian is rotation invariant and its eigenvalues are discrete. Scalar, vector, and spinorial functions on S3 are discussed. The most general Lagrangians for Dirac, Weyl, and Majorana fermions are derived. They are different from the ones in existing literature. The wave functions and propagator are obtained and formulas for matrix elements involving spinors are presented. The discrete symmetries—parity, charge conjugation, and time reversal—are described. The Lagrangian in R×S3 transforms in a nontrivial way under these. Finally, the fermionic Lagrangian is rederived using the tetrad formalism, and conformal transformations are discussed. This leads to a generalization of the formalism to a time-dependent radius of curvature. As a particular case, a new Lagrangian for de Sitter space is obtained, which, however, is not invariant under the full de Sitter group.
Canonical transformations and exact invariants for dissipative systems
Authors: Pedrosa I. A.
Published: July 2002

A simple treatment to the problem of finding exact invariants and related auxiliary equations for time-dependent oscillators with friction is presented. The treatment is based on the use of a time-dependent canonical transformation and an auxiliary transformation.
A search for bilinear equations passing Hirota’s three-soliton condition. IV. Complex bilinear equations
Authors: Hietarinta Jarmo
Published: July 2002

In this paper the results of a search for complex bilinear equations with two-soliton solutions are presented. The following basic types are discussed: (a) the nonlinear Schrödinger equation B(Dx, ...)G⋅F=0, A(Dx,Dt) F⋅F=GG*, and (b) the Benjamin–Ono equation P(Dx, ...)F⋅F*=0. It is found that the existence of two-soliton solutions is not automatic, but introduces conditions that are like the usual three- and four-soliton conditions. The search was limited by the degree of A=2, and by degree of P≤4. The main results are the following: (1) (iaD3x+DxDt +iDy+b)G⋅F=0, D2xF⋅F=GG*; (2) (D2x+aD2y +iDt+b)G⋅F =0, DxDy F⋅F=GG*; (3) (iaD3x+D2x +iDt)F⋅F*=0; and (4) (DxDt+i(aDx +bDt))F⋅F*=0.
On redshift and parallaxes in general relativistic kinematical world models
Authors: Perlick V.
Published: July 2002

A Lorentzian space-time (M,g), along with an observer field (=timelike vector field) V, are considered. Several theorems are presented that are concerned with the redshift and parallaxes in such a model. Here the term ‘‘parallaxes’’ stands for the relative motion of two observers at the celestial sphere of a third observer. As an important mathematical tool, the index form along a lightlike geodesic is used.
Automorphisms and general charge conjugations
Authors: Cieciura Grzegorz , Szczyrba Igor
Published: July 2002

It is shown how outer automorphisms of a semisimple Lie algebra and automorphisms of the corresponding root system describe conjugations of general charges. New results about representations of semidirect products of non-Abelian Lie groups and about projective representations of finite groups are derived.
Accuracy-weighted variational principle for degenerate continuum states
Authors: Danos Michael
Published: July 2002

A variational principle for continuum states is given that permits numerical solution by the Ritz method. It allows one to maximize the accuracy of the solution in preselected regions of space, and also allows the selection of that solution from the perhaps infinitely degenerate solution set that is needed in the particular application.
Effective actions with vector-axial-vector couplings on Riemann–Cartan manifolds
Authors: Cognola Guido , Giacconi Paola , Soldati Roberto
Published: July 2002

The general forms of quantum effective actions in the presence of vector and axial-vector gauge potentials on Riemann–Cartan manifolds with torsion are discussed. The relations between different forms of anomalies are elucidated.
Quasiprobability distributions for open quantum systems within the Lindblad theory
Authors: Isar Aurelian , Scheid Werner , Sandulescu Aurel
Published: July 2002

The Lindblad master equation for the damped quantum harmonic oscillator is transformed into Fokker–Planck equations for quasiprobability distributions. A comparative study is made for the Glauber P representation, the antinormal-ordering Q representation and the Wigner W representation. It will be proven that the variances for the damped harmonic oscillator found with these representations are the same. By solving the Fokker–Planck equations in the steady state, it will be shown that the quasiprobability distributions are two-dimensional Gaussians with widths determined by the diffusion coefficients.
Partial *-algebras and Volterra convolution of distribution kernels
Authors: Epifanio Giuseppina , Trapani Camillo
Published: July 2002

The set of distribution kernels is considered as a partial *-algebra when the multiplication of two kernels is defined as their Volterra convolution. The partial *-algebra of distribution kernels corresponding to a certain partial *-algebra of closable operators in L2(Ω) is studied.
The Gel’fand–Tsetlin representations of the unitary Cayley–Klein algebras
Authors: Gromov N. A.
Published: July 2002

The explicit expressions of the operators of the irreducible representations of the unitary Cayley–Klein algebras un(j) are obtained from the well-known Gel’fand–Tsetlin representations of un . The contractions of the representations of u2(j1) and u3(j1,j2) are regarded as examples. This approach gives the representations of the contracted algebras in different bases, for example, in discrete and continuous ones. Possible contractions of the irreducible representations are discussed.
On the structure and properties of the singularity manifold equations of the KP hierarchy
Authors: Konopelchenko Boris , Strampp Walter
Published: July 2002

This paper is concerned with the Painlevé expansion and the singularity manifold (SM) equation of the Kadomtsev–Petviashvili (KP) equation. Several aspects of the interrelation between the SM equation and the KP auxiliary linear system are studied. It is shown that the simultaneous Painlevé expansion for the KP potential u and the KP eigenfunction ψ can be treated as a Bäcklund-gauge transformation. Two methods for the derivation of the SM equation based on this treatment are proposed and their equivalence is proved. The interrelation between the SM equation and the vertical hierarchy of the KP eigenfunction equations is discussed. The explanation of the coincidence of the KP eigenfunction equation of the second level and the KP SM equation is given. Compact forms of the hierarchy of SM equations of the KP hierarchy are presented. The connection between the KP singularity manifold function φ and the KP eigenfunctions ψ and the adjoint KP eigenfunctions ψ* is derived. The bilinear-bilocal description of the hierarchy the KP SM equations is given within the framework of Sato’s τ-function theory.
Collineations of Godel-type space-times
Authors: Melfo A. , Nún̄ez L. , Percoco U. , Villalba V. M.
Published: July 2002

Ricci collineations for Gödel-type space-times are studied. The members of this family of metrics admitting these symmetries are identified. It is shown that these space-times do not admit Homothetic vector fields. Also, the unique Affine Collineation, associated to Gödel-type space-times, is exhibited.
Characterizations of cyclic *-representations with equal weak and strong commutants
Authors: Stochel Jan , Todorov Todor. S.
Published: July 2002

A purely algebraic normality property for states on abstract *-algebras is singled out and used to characterize Abelian unbounded Gelfand–Naimark–Segal (GNS) representations with a coincident weak and strong commutant and to give equivalent conditions of this coincidence. Various properties of standard GNS representations generated by measure-defined states are examined. Normality of bounded states is discussed and connections to MASA are given.
New metrics for spinning spheroids in general relativity
Authors: Halilsoy Mustafa
Published: July 2002

The quaternionic version of the Ernst formalism is used to propose an alternative generalization of the Zipoy–Voorhees metric that represents spinning spheroids. Rotating discs and their superposition that generalize the static Curzon solution arises as a particular member of the class. Some features are different from the well-known Kerr and Tomimatsu–Sato solutions.
Conformal symmetry inheritance with cosmological constant
Authors: Tariq N. , Tupper B. O. J.
Published: July 2002

A study is made of space-times satisfying the Einstein field equations with a nonzero cosmological constant and admitting a conformal Killing vector (CKV), ξa, which is such that the Lie derivative of the energy-momentum tensor in the direction of ξa is zero. This condition is necessary, but not sufficient, to ensure that the physical quantities associated with the energy-momentum tensor inherit the CKV symmetry. It is shown that this condition leads to two classes of space-times, each of which may be regarded as generalizations of the de Sitter space-times. The possible physical interpretations of these models are discussed.
Generalization of Jacobi’s decomposition theorem to the rotation and translation of a solid in a fluid
Authors: Chiang R. C. , Shieh S. Y.
Published: July 2002

Jacobi found that the rotation of a symmetrical heavy top about a fixed point can be decomposed into a product of the torque-free rotations of two triaxial bodies about their centers of mass. This theorem is generalized to the Kirchhoff’s case of the rotation and translation of a symmetrical solid in a fluid.
The propagator in the radial gauge
Authors: Modanese Giovanni
Published: July 2002

The solutions of the equation for the propagator in the radial gauge xμ Aμ(x) = 0 are studied. After finding a particular solution Γμρ(x,y), the most general solution G0μρ(x,y) of the homogeneous equation is written. It is shown that Γρμ(y,x) is not a solution; moreover, it is impossible to symmetrize Γμρ(x,y) by addition of a homogeneous solution. A ‘‘symmetrized’’ generalization of the equation for the propagator is thus proposed. The photon propagator can also be calculated in this gauge using the field strength Fμρ(x), but it turns out to exist only in (4−ε) dimensions.
Rigidity of c1-self-dual connections on quaternionic Kähler manifolds
Authors: Nagatomo Yasuyuki
Published: July 2002

In Galicki and Poon [J. Math. Phys. 32, 1263 (1991)], certain self-dual connections are defined on quaternionic Kähler manifolds. In this paper, it is proved that there is essentially only one c1-self-dual connection over any simply connected quaternionic Kähler manifold with nonzero scalar curvature.
Analytical evaluation of a class of phase-modulated lattice sums
Authors: Allen Scott , Pathria R. K.
Published: July 2002

Making use of the Poisson summation formula in m dimensions, a class of phase-modulated lattice sums is evaluated analytically. The resulting formulas provide a broad generalization of the results reported previously and are of considerable use in the analysis of finite-size effects in systems undergoing phase transitions, especially when the boundary conditions imposed are other than periodic.
Bound states for square well potentials extending to infinity in D≥2
Authors: Rupertsberger H.
Published: July 2002

It is well known that quantum mechanics allows the penetration into classically forbidden regions (tunneling). Less well known seems to be the fact that in some sense the converse is true also. Potentials with classically allowed regions where a particle can move freely to infinity can nevertheless lead to bound states in quantum mechanics due to the stringent requirements of the boundary conditions, thus forbidding an escape to infinity. This effect is demonstrated by using an obvious generalization of the well-known one-dimensional (D=1) square well potential to arbitrary space dimensions.
Group analysis and linearization procedure for a nonautonomous model describing rate-type materials
Authors: Manganaro N. , Valenti G.
Published: July 2002

A nonhomogeneous and nonautonomous 2×2 quasilinear system of first order describing rate-type materials is considered within the framework of similarity reduction procedures. Classes of exact similarity solutions to the governing model as well as functional forms for the material response function involved have been determined. Reductions to linear form have been carried out for different forms of constitutive laws. The present approach can be used for solving initial or boundary value problems.
About the Luttinger modela)
Authors: Verbeure A. , Zagrebnov V. A.
Published: July 2002

The Luttinger model is revised with the emphasis on its infinite-volume formulation. The study poses the ground state problem for the model and shows the solvability of its associated collective excitations (zero-sound) equation.
The critical surface for the tridimensional massless Gaussian fixed point: An unstable manifold with two relevant directions
Authors: Pereira Emmanuel A.
Published: July 2002

The domain of attraction is determined in a small neigborhood of the tridimensional massless Gaussian fixed point, obtaining a critical surface in a manifold with one marginal and two relevant directions (besides the marginal direction due to the field strengh renormalization). The results are proven within the context of a hierarchical approximation.
Robustness in quantum measurements
Authors: Breuer Thomas , Amann Anton , Landsman Nicolaas P.
Published: July 2002

Conditions are formulated under which a representation of an intrinsic C*- algebra of (often quasilocal) observables of an infinite system is appropriate to describe measurement-type processes: such a representation should allow for the description of robust experiments, it should be separable, and the pointer observable should be in its weak closure. If the pointer values are discrete the existence of such a measurement representation can be proven. If the pointer can take continuously many values, then the existence can only be proven under the additional assumptions of having an asymptotically Abelian system or dealing with type I representations. In the constructed measurement representations the pointer observable turns out to be classical. The structure of the representation suggests that spontaneous symmetry breaking might be a physical explanation of the emergence of the classical pointer.
On symmetries, conservation laws, and variational problems for partial differential equations
Authors: Rosenhaus V. , Katzin Gerald H.
Published: July 2002

The problem of the correspondence between symmetries and conservation laws for partial differential equations is considered. For Lagrangian systems the set of Noether (variational) symmetries can be shown to lead to the set of all local conservation laws. For partial differential equations without well-defined Lagrangian functions there is no universal correspondence between symmetries and conservation laws. In this article it is shown that for a large class of differential equations there is a natural way to associate conservation laws with symmetries. The class consists of many interesting equations, e.g., Korteweg–de Vries equation, Kadomtsev–Petviashvili equation, Boussinesq equation, nonlinear diffusion equation, Monge–Ampère equation, regularized long-wave equation, and Navier–Stokes equations. Characteristics of the corresponding conservation laws are calculated and examples are given. For Lagrangian systems the consistency of the approach with the standard Noether results is discussed.
Finite-dimensional irreducible representations of reflection algebra for su(1,1)q vertex model: Classification, boson–fermion realizations, and Yang–Baxterization
Authors: Fu Hong-Chen , Li Xiang-Sheng
Published: July 2002

Finite-dimensional irreducible representations of a reflection algebra related to the reflection equation for the su(1,1)q model are classified. It is proven that this algebra has two inequivalent one-dimensional and one two-dimensional irreducible representations. Some indecomposable representations are also constructed and the (q-boson–)fermion realizations are explicitly presented. Finally, the Yang–Baxterization of this algebra and its constant solutions (the one-dimensional representations) is investigated.
Long-range scattering for three-body Stark Hamiltonians
Authors: Adachi Tadayoshi
Published: July 2002

The existence and the asymptotic completeness of the Graf-type modified wave operators for three-body Stark Hamiltonians with long-range potentials are proven under the condition that the electric field is sufficiently strong and the particles are accelerated with different acceleration.
Four-dimensional quantum affine algebras and space–time q-symmetries
Authors: Ballesteros A. , Herranz F. J. , del Olmo M. A. , Santander M.
Published: July 2002

A global model of the q deformation for the quasiorthogonal Lie algebras generating the groups of motions of the four-dimensional affine Cayley–Klein (CK) geometries is obtained starting from the three-dimensional deformations. It is shown how the main algebraic classical properties of the CK systems can be implemented in the quantum case. Quantum deformed versions either of the space–time or space symmetry algebras [Poincaré (3+1), Galilei (3+1), 4-D Euclidean as well as others] appear in this context as particular cases. For some of these classical algebras several q deformations are directly obtained.
Analytical solutions of spherically symmetric collapse of an anisotropic fluid body into a black hole
Authors: Das A. , Tariq N. , Biech T.
Published: July 2002

Einstein’s field equations in a spherically symmetric case are investigated for an anisotropic fluid body. An equation of state T44=−k2T11 is imposed. On the boundary of the star, the junction conditions [Tab]nb=0 of Synge are required to be satisfied. In the interior of the fluid body the three strong energy inequalities of Hawking are required to hold. A class of analytical solutions, involving three parameters, are found which satisfy all the equations and the inequalities prior to the collapse of the boundary inside the event horizon. However, inside the black hole, the fluid undergoes a metamorphosis. It still remains an anisotropic fluid with positive energy density and ‘‘radial’’ pressure, but the fluid motion is superluminous or tachyonic.
Asymptotic properties of large random matrices with independent entries
Authors: Khorunzhy Alexei M. , Khoruzhenko Boris A. , Pastur Leonid A.
Published: July 2002

We study the normalized trace gn(z)=n−1 tr(H−zI)−1 of the resolvent of n×n real symmetric matrices H=[(1+δjk)Wjk√n]j,k=1n assuming that their entries are independent but not necessarily identically distributed random variables. We develop a rigorous method of asymptotic analysis of moments of gn(z) for | Iz|≥η0 where η0 is determined by the second moment of Wjk. By using this method we find the asymptotic form of the expectation E{gn(z)} and of the connected correlator E{gn(z1)gn(z2)}−E{gn(z1)}E{gn (z2)}. We also prove that the centralized trace ngn(z)−E{ngn(z)} has the Gaussian distribution in the limit n=∞. Based on these results we present heuristic arguments supporting the universality property of the local eigenvalue statistics for this class of random matrix ensembles.
Ribbon tableaux, Hall–Littlewood functions, quantum affine algebras, and unipotent varieties
Authors: Lascoux Alain , Leclerc Bernard , Thibon Jean-Yves
Published: July 2002

We introduce a new family of symmetric functions, which are q analogs of products of Schur functions, defined in terms of ribbon tableaux. These functions can be interpreted in terms of the Fock space representation ℱq of Uq(s𝔩n), and are related to Hall–Littlewood functions via the geometry of flag varieties. We present a series of conjectures, and prove them in special cases. The essential step in proving that these functions are actually symmetric consists in the calculation of a basis of highest weight vectors of ℱq using ribbon tableaux.
Fermion determinants and effective actions
Authors: Mukku C.
Published: July 2002

Configuration space heat-kernel methods are used to evaluate the determinant and hence the effective action for a SU(2) doublet of fermions in interaction with a covariantly constant SU(2) background field. Exact results are exhibited that are applicable to any Abelian background on which the only restriction is that (B2−E2) and E⋅B are constant. Such fields include the uniform field and the plane wave field. The fermion propagator is also given in terms of gauge covariant objects. An extension to include finite temperature effects is given and the probability for creation of fermions from the vacuum at finite temperature in the presence of an electric field is discussed.
Operator ordering index method for multiple commutators and Suzuki’s quantum analysis
Authors: Abe Mitsuo , Ikeda Noriaki , Nakanishi Noboru
Published: July 2002

General formulas are presented for the multiple commutator involving a function of an operator A in terms of (multiple) commutators involving A by using “operator ordering indices.” It is pointed out that this analysis essentially reproduces the quantum analysis, proposed by Suzuki very recently, in a more transparent way. Extension to the case of several operators is also made in an elegant form.
Bound states in Galilean-invariant quantum field theory
Authors: Corley S. R. , Greenberg O. W.
Published: July 2002

We consider the nonrelativistic quantum mechanics of a model of two spinless fermions interacting via a two-body potential. We introduce quantum fields associated with the two particles as well as the expansion of these fields in asymptotic “in” and “out” fields, including such fields for bound states, in principle. We limit our explicit discussion to a two-body bound state. In this context we discuss the implications of the Galilean invariance of the model and, in particular, show how to include bound states in a strictly Galilean-invariant quantum field theory.
Noninvertible N=1 superanalog of complex structure
Authors: Duplij Steven
Published: July 2002

We consider an alternative tangent space reduction in N=1 superspace, which leads to some odd N=1 superanalog of complex structure (the even one is widely used in two-dimensional superconformal theories and in the fermionic string theory calculations via super Riemann surfaces). New N=1 superconformal-like transformations are similar to the antiholomorphic ones of the complex function theory. They are dual to the ordinary superconformal transformations subject to the Berezinian addition formula presented, noninvertible, highly degenerated and twist parity of the tangent space in the standard basis, and they also lead to some “mixed cocycle condition.” A new parametrization for the superconformal group is presented which allows us to extend it to a semigroup and to unify the description of old and new transformations.
The interacting-free quantum stochastic limit of quantum field theory
Authors: Gough John
Published: July 2002

The Quantum Stochastic Limit of a quantum mechanical particle coupled to a quantum field without the neglect of the response details of the interaction (i.e., not making the dipole approximation) is made following the scheme of Accardi and Lu and the corresponding Quantum Stochastic Structure is derived. The stochastic sector for the noise is constructed and is shown to be of a qualitatively new type. We also include a physical discussion on the limit noise which obeys Interacting-Free statistics and include a new shorter proof of the noise convergence and also a new construction of Interacting-Free Fock Space.
Fock representations of exchange algebras with involution
Authors: Liguori A. , Mintchev M. , Rossi M.
Published: July 2002

An associative algebra AR with exchange properties generalizing the canonical (anti)commutation relations is considered. We introduce a family of involutions in AR and construct the relative Fock representations, examining the positivity of the metric. As an application of the general results, we rigorously prove unitarity of the scattering operator of integrable models in 1+1 space-time dimensions. In this context the possibility of adopting various involutions in the Zamolodchikov–Faddeev algebra is also explored.
Conditions for the existence of higher symmetries of evolutionary equations on the lattice
Authors: Levi D. , Yamilov R.
Published: July 2002

In this paper we construct a set of five conditions necessary for the existence of generalized symmetries for a class of differential-difference equations depending only on nearest neighboring interaction. These conditions are applied to prove the existence of new integrable equations belonging to this class.
Random cascades on wavelet dyadic trees
Authors: Arneodo A. , Bacry E. , Muzy J. F.
Published: July 2002

We introduce a new class of random fractal functions using the orthogonal wavelet transform. These functions are built recursively in the space-scale half-plane of the orthogonal wavelet transform, “cascading” from an arbitrary given large scale towards small scales. To each random fractal function corresponds a random cascading process (referred to as a W-cascade) on the dyadic tree of its orthogonal wavelet coefficients. We discuss the convergence of these cascades and the regularity of the so-obtained random functions by studying the support of their singularity spectra. Then, we show that very different statistical quantities such as correlation functions on the wavelet coefficients or the wavelet-based multifractal formalism partition functions can be used to characterize very precisely the underlying cascading process. We illustrate all our results on various numerical examples.
Exact spectral values for discrete quantum pendulum-integrals
Authors: Kellendonk Johannes
Published: July 2002

For specific choice of parameters the spectrum of the discrete quantum pendulum-integral contains the eigenvalues of a finite matrix which depends analytically on the flux. Under natural continuity assumptions these eigenvalues include the spectral values which may be obtained by the algebraic Bethe ansatz.
Hydrodynamic behavior of Brownian particles in a position-dependent constant force field
Authors: Barbachoux C. , Debbasch F. , Rivet J. P.
Published: July 2002

The diffusion equation in physical space–time for a Brownian particle driven by an external force field has been derived by Smoluchowski in the two particular cases where the external field is uniform or varies linearly with position (elastic force). In more general cases, correction terms must be added to the Smoluchowski equation. We show here how to use a multi-scale Chapman–Enskog expansion to obtain, in the hydrodynamic limit, the first corrective terms to the Smoluchowski equation, without any restriction on the friction coefficient, and for any sufficiently small position-dependent constant force field. We also compare our approach with the works of Wilemski, Titulaer, and van Kampen.
Hamiltonian structures of generalized Manin–Radul super-KdV and constrained super KP hierarchies
Authors: Tu Ming-Hsien , Shaw Jiin-Chang
Published: July 2002

A study of Hamiltonian structures associated with supersymmetric Lax operators is presented. Following a constructive approach, the Hamiltonian structures of Inami–Kanno super-KdV hierarchy and constrained modified super-KP hierarchy are investigated from the reduced supersymmetric Gelfand–Dickey brackets. By applying a gauge transformation on the Hamiltonian structures associated with these two nonstandard super-Lax hierarchies, we obtain the Hamiltonian structures of generalized Manin–Radul super-KdV and constrained super-KP hierarchies. We also work out a few examples and compare them with the known results.
On an application of Crum–Krein transform to expansions in products of solutions of two Sturm–Liouville equations
Authors: Khristov E. Kh.
Published: July 2002

By using the Crum–Krein transform we construct explicit formulas allowing us to reduce the problem of expansions in products of solutions for two Sturm–Liouville problems on the semiaxis with general boundary conditions to the same problem for two Sturm–Liouville problems with zero boundary conditions. We also obtain the transformation formulas for the corresponding Λ operators.
On the signature of certain intersection forms
Authors: Xu Feng
Published: July 2002

We prove a conjecture of Zuber on the signature of intersection forms associated with affine algebras of type A, which is based on connections between N=2 integrable models in two dimensions and certain class of graphs.
Elementary Toda orbits and integrable lattices
Authors: Faybusovich Leonid , Gekhtman Michael
Published: July 2002

We show that key features of several important integrable lattices appear naturally in a framework of the full Toda flows. Using special symplectic leaves for these flows, we construct a family of bi-Hamiltonian integrable lattices that interpolates between the nonrelativistic and relativistic Toda lattices.
Classification of three-dimensional Lie bialgebras
Authors: Gomez Xavier
Published: July 2002

The paper contains a classification of the three-dimensional real and complex Lie bialgebras, with a description of the corresponding Drinfel’d doubles.
Acoustic emission accompanying the superconducting transition in HTS ceramics TlBaCuO
Authors: Ostrovskii I. V. , Salivonov I. N.
Published: July 2002

A peak of acoustic emission (AE) is observed experimentally at the superconducting transition temperature in samples of the superconducting ceramics Tl2Ba2CuO6+x. AE signals have been recorded by a piezoelectric transducer with the resonant frequency 1 MHz in the temperature range 80–300 K. Relaxation anomalies are attributed to a change in the charge state of linear defects and variations of the parameters of the cuprate layer in the samples.
A simple derivation of the time-dependent convective-diffusion equation for surfactant transport along a deforming interface
Authors: Stone H. A.
Published: July 2002

A derivation of the convective-diffusion equation for transport of a scalar quantity, e.g., surfactant, along a deforming interface is outlined. The direct contribution of interface deformation, giving rise to concentration variations as a result of local changes in interfacial area, is shown explicitly in a simple manner.
The motion of an inviscid drop in a bounded rotating fluid
Authors: Bush J. W. M. , Stone H. A. , Bloxham J.
Published: July 2002

The motion of a buoyant inviscid drop rising vertically along the rotation axis of a rapidly rotating low viscosity fluid bounded above and below by rigid horizontal boundaries is considered in the case that the drop is circumscribed by a Taylor column that spans the entire fluid depth. Both the shape and steady rise speed of the drop are deduced as a function of the interfacial tension. The analysis demonstrates that the drop assumes the form of the prolate ellipsoidal figure of revolution which would arise in the absence of any relative motion in the surrounding fluid. The hydrodynamic drag on the drop follows simply from the analysis of Moore and Saffman [J. Fluid Mech. 31, 635 (1968)], who considered the equivalent motion of a rigid particle. The rise speed of a deformed inviscid drop is approximately one-half that of an identically shaped rigid particle; in particular, the rise speed of a spherical inviscid drop is 0.41 that of a rigid sphere.
A note on Bragg scattering of surface waves by sinusoidal bars
Authors: Kirby James T.
Published: July 2002

The reflection of linear surface waves by sinusoidal bottom undulations is considered in the case where the incident wave is not necessarily close to the resonant frequency. For finite detuning away from the resonant frequency, two previous solutions are shown to give results which are inconsistent with direct numerical solutions, especially when the results are extended to oblique incidence. The correction to the methods is given, and various consequences of the new results are examined.
Resistive tearing instability with equilibrium shear flow
Authors: Chen X. L. , Morrison P. J.
Published: July 2002

The effect of equilibrium velocity shear on the resistive tearing instability has been systematically studied, using the boundary layer approach. Both the ‘‘constant-ψ’’ tearing mode, which has a growth rate that scales as S−3/5, and the ‘‘nonconstant-ψ’’ tearing mode [Δ′(αS)−1/3≫1], which has a growth rate that scales as S−1/3, are analyzed in the presence of flow. Here S is the usual ratio of the resistive diffusion and Alfvén times. It is found that the shear flow has a significant influence on both the external ideal region and the internal resistive region. In the external ideal region, the shear flow can dramatically change the value of the matching quantity Δ′. In the internal resistive region, the tearing mode is sensitive to the flow shear at the magnetic null plane: G′(0). When G′(0) is comparable to the magnetic field shear, F′(0), the scalings of the constant-ψ tearing mode are changed and the Δ′>0 instability criterion is removed, provided G′(0)G″(0)−F′(0)F″(0)≠0. The scalings of the nonconstant-ψ tearing mode remain unchanged. When the flow shear is larger than the magnetic field shear at the magnetic null plane, both tearing modes are stabilized. Finally, the transition to ideal instability is discussed.
Multiframe interferometric study of a laser irradiated plasma in the presence of the two plasmon decay instability
Authors: Meyer J. , Houtman H.
Published: July 2002

The temporal development of the electron density distribution in a CO2-laser produced plasma is studied interferometrically at 10.5 GHz framing rates with 50 psec resolution. The plasma is produced in a helium gas jet target and has a maximum density of 5×1018 cm−3. Thomson scattering of probe ruby laser radiation in a second experiment shows that the two plasmon decay instability is excited in this plasma and appears in multiple bursts. Excellent correlation between the temporal variations of the density scale length just below quarter critical density and that of the two plasmon decay wave intensity demonstrates the instability quenching property of ponderomotive profile steepening.