bluuebunny/crossref_metadata_2025 huggingface dataset:
Quantum dynamics of the O(3P)+CH4→OH+CH3 reaction: An application of the rotating bond umbrella model and spectral transform subspace iteration
Authors: Yu Hua-Gen , Nyman Gunnar
Published: July 2002

We have applied the rotating bond umbrella (RBU) model to perform time-independent quantum scattering calculations of the O(3P)+CH4→OH+CH3 reaction based on a realistic analytic potential energy surface. The calculations are carried out in hypercylindrical coordinates with a log-derivative method incorporating a guided spectral transform (GST) subspace iteration technique. A single sector hyperspherical projection method is used for applying the boundary conditions. The results show that ground-state CH4 gives CH3 that is rotationally cold. For CH4 initially vibrationally excited in the C–H stretch or the H–CH3 bending mode, a bimodal CH3 rotational distribution has been observed. The product OH is a little vibrationally excited, while the umbrella mode of CH3 is moderately excited. Vibrational excitation enhances the reactivity substantially. The calculated rate constants are in good agreement with experimental measurements.
Mapping of simulated localized fluctuations onto a macrosystem: Direct counting in the macrosystem to confirm statistical mechanical theory
Authors: Bowles Richard K.
Published: July 2002

It has been shown that an appropriate model dependent volume scale is required to map the number of clusters observed in a simulation cell onto the macrovolume. Statistical mechanical theory shows that for overlapping clusters in an ideal gas the volume scale should be kT/(P+Pn). The same volume scale has been predicted for nonoverlapping clusters, but is restricted to only very rare clusters. An alternative theory suggests that the volume scale should be the volume of the cell v̂. In this work we count, by computer simulation, the number of overlapping and nonoverlapping clusters in the macrovolume of a one-dimensional ideal gas. The results confirm that the first volume scale is indeed correct suggesting that its underlying statistical theory should be valid for other models. For nonoverlapping clusters that are not rare the alternative volume scale is a good approximation, however, estimates show that for very rare clusters, such as those used in nucleation, the two volume scales for nonoverlapping clusters differ by up to two orders of magnitude.
Calculation of helical twisting power for liquid crystal chiral dopants
Authors: Cook Melanie J. , Wilson Mark R.
Published: July 2002

The helical twisting power βM determines the pitch of the chiral nematic phase produced when a nematic liquid crystal is doped with a low concentration of chiral solute molecules. Molecules with large βM values have potential applications in electro-optic displays and in optical data storage. This paper describes a new simulation technique which allows the prediction of both the sign and magnitude of βM. The method employs Monte Carlo simulations of a fully atomistic model of a chiral dopant in the presence of a twisted nematic solvent composed of Gay–Berne particles. Calculations are presented for five different chiral dopants, with results that are in good agreement with existing experimental data.
Electric fields in ice and near water clusters
Authors: Batista Enrique R. , Xantheas Sotiris S. , Jónsson Hannes
Published: July 2002

We have studied the electric field near water clusters and in ice Ih using first principles calculations. We employed Mo/ller–Plesset perturbation theory (MP2) for the calculations of the clusters up to and including the hexamer, and density functional theory (DFT) with a gradient dependent functional [Perdew–Wang (PW91)] for ice Ih as well as the clusters. The electric field obtained from the first principles calculations was used to test the predictions of an induction model based on single center multipole moments and polarizabilities of an isolated water molecule. We found that the fields obtained from the induction model agree well with the first principles results when the multipole expansion is carried out up to and including the hexadecapole moment, and when polarizable dipole and quadrupole moments are included. This implies that accurate empirical water interaction potential functions transferable to various environments such as water clusters and ice surfaces could be based on a single center multipole expansion carried out up to the hexadecapole. Since point charges are not included, the computationally intensive Ewald summations can be avoided. Molecular multipole moments were also extracted from the first principles charge density using zero flux dividing surfaces as proposed by Bader. Although the values of the various molecular multipoles obtained with this method are quite different from the ones resulting from the induction model, the rate of convergence of the electric field is, nevertheless, quite similar.
Modeling ionic mobilities by scattering on electronic density isosurfaces: Application to silicon cluster anions
Authors: Shvartsburg Alexandre A. , Liu Bei , Jarrold Martin F. , Ho Kai-Ming
Published: July 2002

We have developed a new formalism to evaluate the gas-phase mobility of an ion based on elastic scattering on an electronic density isosurface (SEDI). In this method, the ion is represented by a surface of arbitrary shape defined as a set of points in space where the total electron density assumes a certain value. This value is the only adjustable parameter in the model. Conceptually, this treatment emulates the interaction between a drifting ion and the buffer gas atoms closer than the previously described methods, the exact hard spheres scattering (EHSS) model and trajectory calculations, where the scattering occurs in potentials centered on the nuclei. We have employed EHSS, trajectory calculations, and SEDI to compute the room temperature mobilities for low-energy isomers of Sin (n⩽20) cations and anions optimized by density functional theory (DFT) in the local density approximation and generalized gradient approximation. The results produced by SEDI are in excellent agreement with the measurements for both charge states, while other methods can fit the mobilities for cations only. Using SEDI, we have confirmed the structural differences between Sin+ and Sin− predicted by DFT calculations, including the major rearrangements for n=9, 15, 16, and 18. We have also assigned the multiple isomers observed in recent high-resolution mobility measurements for Sin+ with n=17–19, some of them to near-spherical cage-like geometries.
Roto-translational diffusion of biaxial probes in uniaxial liquid crystal phases
Authors: Brognara Andrea , Pasini Paolo , Zannoni Claudio
Published: July 2002

We discuss the problem of roto-translational diffusion of a rigid biaxial molecule dissolved in a uniaxial smectic liquid crystal phase. We examine distorted rod and disklike molecules and show how biaxiality and roto-translational coupling can produce significant effects on some of the correlation functions and spectral densities most useful in analyzing experimental observables.
A simple model for product rovibrational distributions in elementary chemical reactions
Authors: Truhins Kaspars , Marsh Richard , McCaffery Anthony J. , Whiteley Thomas W. J.
Published: July 2002

We explore the application of a simple model of collisional processes, developed initially for inelastic collisions, to the analysis of product rovibrational states in elementary chemical reactions. The model depicts collisional transfer as a process of momentum exchange (predominantly linear-to-angular momentum) and is modified to take account of change in center-of-mass and enthalpy change that accompany reaction. The kinematics of center-of-mass shift derived by Elsum and Gordon [J. Chem. Phys. 76, 3009 (1982)] lead to two limiting cases based on the parameter β. The kinematic extremes alternatively may be specified in terms of the molecular torque arm about which interconversion of linear and angular momentum is effected. This torque arm length approximates to the product bond length when β≃0 and the reactant bond length when β≃90°. Our approach shares elements in common with the classical kinematic model of Elsum and Gordon but is somewhat simpler and more transparent. The method is shown to give accurate peak values of v, j states of the products of a wide range of elementary reactions for which experimental data is available. Monte Carlo trajectory calculations based on the physical principles described here give excellent fits to experimental v, j distributions in F+I2→IF+I, H+D2→HD+D, and Cl+H2→HCl+H using input data consisting of atomic radii, atomic masses, velocities, and reaction enthalpies.
On the equivalence of continuum and lattice models for fluids
Authors: Panagiotopoulos Athanassios Z.
Published: July 2002

It was demonstrated that finely discretized lattice models for fluids with particles interacting via Lennard-Jones or exponential-6 potentials have essentially identical thermodynamic and structural properties to their continuum counterparts. Grand canonical histogram reweighting Monte Carlo calculations were performed for systems with repulsion exponents between 11 and 22. Critical parameters were determined from mixed-field finite-size scaling methods. Numerical equivalence of lattice and continuous space models, within simulation uncertainties, was observed for lattices with ratio of particle diameter σ to grid spacing of 10. The lattice model calculations were more efficient computationally by factors between 10 and 20. It was also shown that Lennard-Jones and exponential-6 based models with identical critical properties can be constructed by appropriate choice of the repulsion exponent.
Effects of density on the local dynamics and conformational statistics of polyethylene: A molecular dynamics study
Authors: Karatasos K. , Adolf D. B. , Hotston S.
Published: July 2002

Molecular dynamics simulations of united atom (UA) linear polyethylene were performed as a function of density, for systems of two well-separated chain lengths (N=20, N=100). The role of the exact shape of the torsional angle potential is investigated by invoking two commonly cited alkane torsional potentials [Ryckaert–Bellemans (R&B), Steele]. The increase in second-neighbor torsional angle coupling with increasing density and decreasing conformational transition rates is presented quantitatively for the first time. The simulated local orientational dynamics were also studied by means of geometric autocorrelation functions (ACFs). These ACFs were analyzed by a method that emphasizes the distribution of relaxational processes, thereby providing specific information on the relevant spectral characteristics of each process. For all densities and chain lengths studied, two peaks are observed that are well separated in time. Only for the longer chains at the highest density studied does a third intermediate peak develop. Further insight into density-induced changes to the local dynamics is obtained through the distribution of angular jumps which give rise to decay of the geometric ACFs.
Electrostatic specificity in molecular ligand design
Authors: Kangas Erik , Tidor Bruce
Published: July 2002

Designing ligand molecules that bind with high affinity and specificity to a target molecule (or a family of related targets) is a fundamental goal of molecular biophysical research. While it is generally recognized that electrostatic interactions can contribute to binding specificity, it is unclear whether the inclusion of interactions that result in tight binding also necessarily leads to highly specific binding. Here we make use of recently developed charge-optimization techniques to explore the affinity–specificity relation in the context of electrostatic interactions. Using model problems we find that affinity-optimized electrostatic interactions do not necessarily create specificity. Furthermore, we develop several rigorous methods that indicate how best to perturb affinity-optimized ligand-charge distributions to increase specificity with minimal sacrifice in affinity for the target or target set. We provide a theoretical framework for improving specificity against any number of known receptors and/or binding modes as well as against uncharacterized receptors.
Forced Rayleigh scattering studies of mixtures of amplitude and phase gratings in methyl yellow/alcohol solutions
Authors: Park Ha Seon , Chang Taihyun , Spiegel Daniel R.
Published: July 2002

Forced Rayleigh scattering (FRS) studies have been carried out on methyl yellow/alcohol solutions at two different probe wavelengths (633 and 543 nm). The signal shapes observed at the two wavelengths are quite different: using ethanol and 2-propanol as solvents, we observe at 633 nm a decay–grow–decay (DGD) shape similar to profiles frequently reported in the literature, while at 543 nm we observe a DGD shape in which the signal at the local minimum does not reach the baseline. In principle, the nonzero minimum can be accounted for by a difference (due to amplitude/phase-grating mixtures) in the phase shifts of light scattered from the photoproduct and ground-state molecules. To test this hypothesis, we first show in a straightforward manner that the signal can be approximated as the product of a polynomial and an exponential decay, which allows for data reduction of profiles with zero or nonzero phase-shift differences. Using this approach, the diffusion coefficients measured using the two probe wavelengths are found to be the same to within an uncertainty of 2%–3%. The results provide strong evidence that the difference in signal shapes is caused by amplitude/phase-grating mixtures within the methyl yellow/alcohol system, and imply that diffusion coefficients can be measured without difficulty for other FRS systems characterized by such mixtures.
Molecular beam study of the Π6X 6Δ electronic transition in FeCl
Authors: Lei Jie , Dagdigian Paul J.
Published: July 2002

The Π6–X 6Δ band system of Fe35Cl near 357 nm has been recorded at 0.3 and 0.08 cm−1 resolution by laser fluorescence excitation in a free-jet supersonic expansion of photolyzed Fe(CO)5 diluted in seed gases containing CCl4. The ΠΩ′6=Ω″−1–X 6ΔΩ″ subbands for Ω′=7/2, 5/2, and 3/2 and v′⩽4 of the Δv=1, 0, −1, and −2 sequences were assigned, and excitation energies and rotational constants were derived for the relevant upper and lower vibronic levels. With the exception of the (0,0) band, for which one subband could be rotationally analyzed, it was not possible to assign any of the subbands with Ω′=1/2, −1/2, or −3/2; these fine-structure components are expected to be strongly affected by homogeneous spin–orbit interactions with nearby sextet electronic states, leading to large Λ doubling in the Ω′=1/2 and −1/2 components. A subband with a large upper-state Λ doubling was rotationally analyzed and assigned as the Π1/26–X 6Δ3/2 (0,0) subband. The effect of the off-diagonal spin–orbit interactions is discussed in light of the present results and previous theoretical work.
Mass spectra of metal-doped carbon and fullerene clusters
Authors: Klingeler R. , Bechthold P. S. , Neeb M. , Eberhardt W.
Published: July 2002

We present a systematic study of the abundancies of metal-doped cluster cations MxCn+ (M=Ca,Sc, Y, La, Ce, Gd; x=1,2) produced in a laser vaporization source. The mass spectra of MCn+ and M2Cn+ reveal the onset of endohedrally doped fullerenes from which the smallest possible cage sizes can be deduced. Y2Cn and La2Cn show a distinct transition from alternation odd–even to even–odd at n=69 and n=71, respectively, which can be explained by a substantial change in the doped fullerene structure, i.e., from networked to bi-endohedral systems. A metal induced cluster formation pathway is briefly discussed.
Hamiltonian picture of the free electron laser and unitary symmetries
Authors: Dattoli G. , Mignani R.
Published: July 2002

It is shown that—in analogy to what has been recently suggested for a quantum n-level system—in a multimode analysis of the free electron laser (FEL) Hamiltonian picture, one can use the (n2−1)-dimensional vector F↘ of SU(n) to describe the main FEL dynamics. The FEL coherence properties are discussed by this group-theoretical approach, and a critical analysis of related Casimir invariants and conservation laws is given.
Three remarks on Powers’ theorem about irreducible fields fulfilling CAR
Authors: Baumann Klaus
Published: July 2002

First it is shown that within a relativistic Fermi field theory, a bound ∥Ψk( f,t)∥ ≤C∥ f ∥2 already implies canonical anticommutation relations (CAR). Then under Powers’ assumptions a linear, first-order differential equation for the fields ψk(x,t) is derived. This shows that in the set of generalized free fields fulfilling CAR only the free fields are irreducible at time zero. Finally Fermi fields in two space-time dimensions are considered. It is shown that only four-fermion interaction might be compatible with CAR and a bound on the coupling strength is derived.
Formal power series solutions of supersymmetric (N=3) Yang–Mills equations
Authors: Harnad J. , Jacques M.
Published: July 2002

Formal power series solutions of the linear system with one spectral parameter associated to the constraint equations for Yang–Mills superconnections on N-extended super-Minkowski space are considered. For N=3 the integrability equations reduce to the supersymmetric field equations. The method of approach is identical to that used by Takasaki for the self-dual equations, based upon formal power series in a spectral parameter and in spatial variables. The problem is reduced to a linear system of equations for a superfield with values in an ∞-dimensional Grassmann manifold. The formal solution is expressed in terms of data on a (3‖2N)-dimensional superhypersurface. However, a difficulty arises with respect to the Cauchy problem, which becomes formally solvable only for an extended system, breaking the relativistic invariance through introduction of additional superfields.
Transition probability spaces
Authors: Pulmannová Sylvia
Published: July 2002

Hilbert-space representations of transition probability spaces are studied. The notions of superposition and the superposition principle are introduced. It is shown that, provided the superposition principle and the postulate of minimal superposition are satisfied, transition probability space can be represented by a generalized Hilbert space.
Realization of Poincaré group induced by a second-order ordinary differential system. Noninteraction theorem
Authors: Jaen X. , Llosa J. , Marqués F. , Montoto A.
Published: July 2002

A generalization of the predictive relativistic mechanics is studied where the initial conditions are taken on a general hypersurface of M4. The induced realizations of the Poincaré group are obtained. The same procedure is used for the Galileo group. Noninteraction theorems are derived for both groups.
Summation-free expression for some special Clebsch–Gordan coefficients
Authors: Rashid M. A.
Published: July 2002

The known general formula for the Clebsch–Gordan coefficients of the three-dimensional rotation group involves one summation that results in explicit summation-free expressions for the coefficients where either one of the angular momenta is the sum of the other two or the magnetic quantum number corresponding to one of the angular momenta takes its maximum value in magnitude. By using very different techniques, explicit expressions for the coefficients 〈 j1, 0;  j2, 0‖ j, 0〉, 〈 j1, (1)/(2) ; j2, − (1)/(2) ‖ j, 0〉 are also obtained where the integral or half-integral nature of the  j’s is indicated by the magnetic quantum number involved. Here the expressions depend upon whether  j1+ j2+ j is an even or an odd integer. For these coefficients, the magnetic quantum numbers involved take their minimum value in magnitude. By using the recursion relation for the coefficients of the form 〈 j1, m,  j2, −m, ‖ j, 0〉, these coefficients can be calculated in terms of the above known ones provided the explicit value of the coefficient 〈 j1, 1;  j2, −1‖ j, 0〉 is known, where  j1+ j2+ j is an odd integer. (The recursion relation for these coefficients in terms of 〈 j1, 0;  j2, −1‖ j, 0〉 becomes a triviality since 〈 j1, 0;  j2, 0‖ j, 0〉 vanishes when  j1+ j2+ j is an odd integer.)

The main purpose of this paper is to give an explicit expression for the coefficients 〈 j1, 1;  j2, −1‖ j, 0〉, where  j1+ j2+ j is an odd integer. This expression is obtained by using a complicated transformation between hypergeometric functions, which seems to have been neglected so far. For the coefficients where the magnetic quantum numbers have their minimum value in magnitude, this transformed expression becomes summation-free and the explicit values of the three already known coefficients and the fourth so far unknown are obtained. Further study of this transformation may be useful on its own because it provides a link between very different types of expressions. For completeness, explicit expressions for the coefficient 〈 j1, 1;  j2, −1‖ j, 0〉, where  j1+ j2+ j is an even integer, and of 〈 j1, 1;  j2, 1‖ j, 2〉 and 〈 j1, (1)/(2) ;  j2, − (1)/(2) ‖ j, 0〉, where  j1+ j2+ j is an even or an odd integer, are given.
Symmetry groups of state vectors in canonical quantum gravity
Authors: Witt Donald M.
Published: July 2002

In canonical quantum gravity, the diffeomorphisms of an asymptotically flat hypersurface S, not connected to the identity, but trivial at infinity, can act nontrivially on the quantum state space. Because state vectors are invariant under diffeomorphisms that are connected to the identity, the group of inequivalent diffeomorphisms is a symmetry group of states associated with S. This group is the zeroth homotopy group of the group of diffeomorphisms fixing a frame of infinity on S. It is calculated for all hypersurfaces of the form S=S3/G-point, where the removed point is thought of as infinity on S and the symmetry group S is the zeroth homotopy group of the group of diffeomorphisms of S3/G fixing a point and frame, denoted π0 DiffF(S3/G). Before calculating π0 DiffF (S3/G), it is necessary to find π0 of the group of diffeomorphisms. Once π0 Diff(S3/G) is known, π0 Diffx0(S3/G) is calculated using a fiber bundle involving Diff(S3/G), Diffx0(S3/G), and S3/G. Finally, a fiber bundle involving DiffF(S3/G), Diff(S3/G), and the bundle of frames over S3/G is used along with π0 Diffx0(S3/G) to calculate π0 DiffF(S3/G). The groups π0 DiffF(S3/G) are comprised of SU(2) coverings of SO(3) crystallographic groups, the product of these with a cyclic group, cyclic groups, and the product of two cyclic groups.
Fermion excitations of the nonlinear Schrödinger field in the attractive case
Authors: Garbaczewski Piotr
Published: July 2002

The recent inverse scattering method analysis by L. Martínez Alonso [J. Math. Phys. 25, 1935 (1984)] is extended to demonstrate that the Bose quantized (attractive) nonlinear Schrödinger field in 1+1 dimensions, admits fermion excitations in its (quantum soliton) spectrum.
Another identity among squares of eigenfunctions
Authors: Sachs R. L.
Published: July 2002

A variant of an identity of H. P. McKean and E. Trubowitz [Commun. Pure Appl. Math. 29, 143 (1976)] for Hill’s equation is derived via contour integration. The identity is 1=∑∞j=0(−1) j‖y2(1, λij) ‖ ⋅  f2j(x).
On the classical limit of phase-space formulation of quantum mechanics: Entropy
Authors: Wang Lipo
Published: July 2002

The classical limits of phase-space formulation of quantum mechanics are studied. As a special example, some properties of both quantum mechanical and classical entropies are discussed in detail.
Numerical integration in many dimensions. III
Authors: Schwartz Charles
Published: July 2002

Extending a previous line of work, a powerful computational method is found for numerical integration in many dimensions of functions of the form F( f1(x1 ,x2)+f2(x2 ,x3)+ f3(x3 ,x4) +⋅⋅⋅+fd(xd,x1)).
Necessary versus sufficient conditions for exact solubility of statistical models on lattices
Authors: Lochak P. , Maillard J. M.
Published: July 2002

It is shown that under rather mild conditions the triangle relation represents a necessary condition for the existence of commuting transfer matrices of arbitrary size. The cases of spin models and vertex models are treated separately.
Infinite-dimensional symmetry algebras and an infinite number of conserved quantities of the (2+1)-dimensional Davey–Stewartson equation
Authors: Omote Minoru
Published: July 2002

An infinite-dimensional symmetry algebra of the Davey–Stewartson equation is explicitly presented. It is shown that this algebra is a gauge generalization of the symmetry transformation for the Schrödinger equation, and that the Virasoro algebra appears as the subalgebra. An infinite number of conserved quantities associated with the transformations are also obtained.
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g of a Dirac particle in two-dimensional space-time
Authors: Ichinose Takashi , Tamura Hiroshi
Published: July 2002

The path space measures that have been constructed in the present authors’ previous papers to give path integral formulas in quantum mechanics for a Dirac particle in two-dimensional space-time are shown to be concentrated on those paths that have differential coefficients equal to plus or minus the light velocity in every finite time interval except at finitely many instants of time.
Long-time behavior of two-point functions of a quantum harmonic oscillator interacting with bosons
Authors: Arai Asao
Published: July 2002

A class of exactly soluble models of a one-dimensional quantum harmonic oscillator interacting with bosons moving in the d-dimensional space Rd is considered and the long-time behavior of the two-point function of the oscillator at zero temperature and at finite temperatures is analyzed. It is shown that the two-point functions decay with a power-law respectively as the time tends to infinity and that, in the case where the boson is massless, the two-point function at zero temperature decays faster than those at finite temperatures, while, in the case where the boson is massive, they decay with the same order. Further, the dependence of the decay order on d as well as on the infrared behavior of the one-boson energy and the momentum cutoff function in the interaction Hamiltonian is clarified in each case.
Zeeman’s lemma on Robertson–Walker space-times
Authors: Lester J. A.
Published: July 2002

Zeeman’s lemma states that transformations of Minkowski space-time that preserve timelike causality also preserve lightlike causality. The significance of this lemma is that it makes possible an explicit determination of the ‘‘causal automorphisms’’ of Minkowski space-time without recourse to regularity assumptions: they must be orthochronous Lorentz transformations. Here Zeeman’s lemma for Robertson–Walker space-times is proved, a result again tantamount to obtaining the causal automorphisms of these space-times explicitly.
Comment on ‘‘A metric space construction for the boundary of space-time’’ by D. A. Meyer [J. Math. Phys. 2
7, 124 (1986)]
Authors: Kriele Marcus
Published: July 2002

For his metric space construction Meyer incorrectly derived several results. Meyer’s proofs are corrected or disproved by counterexamples. The physical relevance of his construction is further examined.
Free Green’s function in a harmonic oscillator basis
Authors: Silvestre-Brac B. , Gignoux C. , Ayant Y.
Published: July 2002

A closed and analytical formula is given for the free Green’s function in a harmonic oscillator basis. It is very useful for solving the Lippman–Schwinger equation for the scattering of two clusters within the resonating group method formula.
Path integration over the n-dimensional Euclidean group
Authors: Böhm M. , Junker G.
Published: July 2002

The path integral for the n-dimensional free particle is considered. According to the underlying symmetry, the short time propagator is expanded in zonal spherical functions of the Euclidean group G=T n ■ SO(n) with respect to the subgroup H=SO(n). The group theoretical approach to path integration, including the radial part, is explicitly demonstrated.
Integrability condition and finite-periodic Toda lattice
Authors: Okubo Susumu
Published: July 2002

A further generalization to construct integrable dynamical systems with hierarchy has been developed, based upon a generalization of the zero Nijenhuis tensor condition in a symplectic manifold with double symplectic structures. As an example, the periodic Toda lattice Hamiltonian has been shown to satisfy these conditions. The case of the three-dimensional Coulomb potential problem has also been analyzed in a similar fashion.
An extensions theory setting for scattering by breathing bag
Authors: Kuperin Yu. A. , Makarov K. A. , Pavlov B. S.
Published: July 2002

A model of the scattering of a structureless pointlike particle on a spherical bag with an internal structure, imitating ‘‘quark’’ degrees of freedom, is considered. It is assumed that the bag is a dynamical object and its radius plays the role of additional dynamical variable. The energy of the collision is distributed among the quark excitations and the vibration degrees of freedom of the bag surface. In the frame of the theory of extensions the Hamiltonian of the coupled bag-quark system interacting with the pointlike particle is constructed. The formal multichannel S matrix of the problem is obtained.
A turbulence model with stochastic soliton motion
Authors: Qian S. , Chen H. H. , Lee Y. C.
Published: July 2002

A dissipative Benjamin–Ono equation is used to study fluid and plasma turbulence. The system is studied by an exact nonlinear mode truncation method in which a finite number of poles are used to present the solution. The justification of the pole expansion approach is discussed with the proof of a completeness theorem. The stability and spectrum analysis show that asymptotic behavior of the system is completely represented by a finite number of nonlinear modes. The behavior of those nonlinear modes resembles solitons, and exhibits a wide range of bifurcation phenomena and routes to turbulence.
The group theoretical analysis of gravitational instanton equations
Authors: Przanowski M.
Published: July 2002

Group theoretical properties of certain nonlinear partial differential equations playing a distinguished role in the gravitational instanton theory and in complex relativity are studied. It is demonstrated that, in general, the groups of contact transformations admitted by these equations appear to be the first prolongations of appropriate point transformation groups. An exceptional case leading to the Gibbons–Hawking metric is examined in detail.
On the Legendre transformation for a class of nonregular higher-order Lagrangian field theories
Authors: Magnano Guido , Ferraris Marco , Francaviglia Mauro
Published: July 2002

In the framework of higher-order calculus of variations, the generalized Legendre transformation for a wide class of Lagrangians is considered, which depend in a nonregular way on the derivatives of maximal order. A rigorous theory is discussed for Lagrangians depending on a constant rank set of affine combinations of these derivatives. This allows the reduction of the Poincaré–Cartan formalism and the Hamiltonian formalism to the appropriate constraint in the appropriate phase space of the problem. The case considered here covers many important physical examples, such as the Yang–Mills theories (at order one) and relativistic metric theories of gravitation (at order two).
On the nth-order structure of solitonic wormholes
Authors: Degen F.
Published: July 2002

The structure of the equations describing a solitonic wormhole in the Einstein–Yang–Mills–Higgs system for an arbitrary compact and connected gauge group 𝒢 and representation of an arbitrary Higgs field Q is studied. The general structure of these equations and its use in deriving the first-order equations, which result by applying the operator ON=limN→0 ∂/∂N to the original equations, where N is the lapse function, is discussed. It is also possible to write down the nth-order equations, which are obtained by applying n times the operator ON, for a certain class of solutions. These nth-order equations are then specialized to the model with 𝒢=SU(2) and Q in the adjoint representation. These nth-order equations on the background of a non-Abelian zero-order solution, which can be gauge transformed to satisfy the ’t Hooft ansatz at the internal infinity of the hole, are solved. The technique used to solve the system is that of harmonic expansion, yielding an algebraic system of equations which can be interpreted as an eigenvalue problem. The eigenvalues are functions of the parameters of the model and zero-order quantities. Thus, depending on the values of these parameters, nontrivial nth-order solutions may exist or not. Those cases in which there exist nontrivial solutions are stated. Only for those cases can it be expected that global non-Abelian solitonic wormholes are found.
The noisy shift map
Authors: Carlson Lee , Schieve W. C.
Published: July 2002

Starting from the topological conjugacy of a chaotic discrete map with the shift map on symbol space, ideas from the Baxter eight-vertex model and a stochastic difference equation due to Falk are used to define a notion of a noisy shift map on symbol space. Its long-time behavior is determined, along with a discussion of the ramifications of this result on the effects of noise on chaotic discrete dynamical systems.
Hyperinflation in the Ising model on quasiperiodic chains
Authors: Odagaki T.
Published: July 2002

Using a hyperinflation rule, the free energy of the two component Ising system on a chain with an arbitrary quasiperiodic order is shown to be given by an average of the free energy of each component, in agreement with the result obtained by the transfer matrix formalism.
Effective interactions involving massive and massless particles of spin 1/2, 1, 3/2, and 2
Authors: Spehler D.
Published: July 2002

The Bargman–Wigner theory is used in order to quantize and build interactions ‘‘à la Fermi’’between massive or massless particles with spin 1/2 , 1, (3)/(2) , and 2.
Gauge transformations in Dirac theory of constrained systems
Authors: Galvão Carlos A. P. , Boechat João Batista T.
Published: July 2002

According to Dirac’s prescription the generator of gauge transformations for a constrained system endowed with primary and secondary first class constraints is constructed as a linear combination of all these (first class) constraints. Using the total Hamiltonian to generate the dynamics of the system it is shown that the time evolution of the coefficients of the secondary constraints in the generator of gauge transformations is not independent but is determined by the coefficients of the primary constraints. This result is applied to some physically interesting systems.
Novel correspondence of the fixed-seniority and the fixed-isospin averages in their reduction formulas
Authors: Nomura Masao
Published: July 2002

It is shown that known reduction formulas for partial averages of two different kinds, the fixed-seniority and the fixed-isospin averages, are transcribed into each other by replacement of arguments. The average here is that of a general k-body operator in a finite space of fermions (bosons). Description of the formulas in a common form in terms of eigenvalues of Casimir operators is also exploited.
On supersymmetric harmonic oscillators and the Green–Cusson Ansätze
Authors: Beckers J. , Debergh N.
Published: July 2002

New properties on parabosonic and parafermionic Cusson’s realizations of the Green’s Anzätze are first obtained. Then paraproperties are shown to have a specific interest for our real world, where bosons and fermions have to be superposed if Nature is supersymmetric, these results being obtained on supersymmetric harmonic oscillators. In particular, from the Green–Cusson Ansätze, we construct a class of supersymmetric Hamiltonians that are more general than the ones issued from standard or spin–orbit coupling considerations. We explicitly consider the simplest (previously unknown) super-Hamiltonian constructed from paraproperties in quantum mechanics and establish its invariance Lie superalgebra.
Bäcklund transforms of chiral fields
Authors: Kramer D. , Neugebauer G. , Matos T.
Published: July 2002

The action of the Bäcklund transformations on the axisymmetric chiral fields is investigated. In particular, it is calculated how the superpotential Γ associated with any chiral field is affected by the Bäcklund transformations.
Even sectors of Lie superalgebras as locally convex Lie algebras
Authors: Pestov Vladimir
Published: July 2002

Let g be a finite-dimensional Lie superalgebra over a graded-commutative local augmented Arens–Michael ground algebra Λ. A Lie group is associated with a number of pleasant properties to the even sector 𝔤0 viewed as an ordinary complete locally convex Lie algebra (which is in general infinite dimensional).
The weak coupling limit for Fermions
Authors: Accardi L. , Frigerio A. , Lu Y. G.
Published: July 2002

It will be shown that, in the weak coupling limit, the matrix elements in the collective number vectors of the evolution in the interacting picture of a quantum system coupled to a quasifree Fermion bath with a laser type interaction, converge to the matrix elements in some number vectors, of a unitary quantum stochastic process satisfying a quantum stochastic differential equation driven by a Fermion Brownian motion with covariance uniquely determined by the initial Fermion bath.
Extended tangent bundle formalism for time-dependent Lagrangian systems
Authors: Rañada Manuel F.
Published: July 2002

The Lagrangian formalism for time-dependent systems is developed using vector fields defined in the extended tangent bundle T(Q×R). The definition of the time-independent extended Lagrangian function L associated to a time-dependent Lagrangian L is given and then the techniques of symplectic mechanics are used to prove some properties of the equations determining the Euler–Lagrange vector field. The relations between the time-independent and the time-dependent Helmholtz conditions are analyzed from a geometric perspective and, finally, the Noether theorem for the extended Lagrangian L is considered.
The anomalous Ward identities in gauge and gravitational theories
Authors: Jiang Wenxin
Published: July 2002

In this paper a simple derivation of the anomalous Ward identity in the Aa0=0 gauge of Yang–Mills theory is presented. The same method is also applied to the gravitational case and the anomalous Ward identities in both the quasiconformal gauge and the spatial gauge are obtained. The relation between the Schwinger terms and the consistent anomalies is discussed as an application of these Ward identities.
Generalized graphs and unitary irrational central charge in the superconformal master equation
Authors: Halpern M. B. , Obers N. A.
Published: July 2002

For each magic basis of Lie g, it is known that the Virasoro master equation on affine g contains a generalized graph theory of conformal level-families. In this paper, it is found that the superconformal master equation on affine g×SO(dim g) similarly contains a generalized graph theory of superconformal level-families for each magic basis of g. The superconformal level-families satisfy linear equations on the generalized graphs, and the first exact unitary irrational solutions of the superconformal master equation are obtained on the sine-area graphs of g=SU(n), including the simplest unitary irrational central charges c=6nx/(nx+8 sin2(rsπ/n)) yet observed in the program.
Quadrics on real Riemannian spaces of constant curvature: Separation of variables and connection with Gaudin magnet
Authors: Kuznetsov Vadim B.
Published: July 2002

The integrable systems are considered which are connected with separation of variables in real Riemannian spaces of constant curvature. An isomorphism is given for these systems with hyperbolic Gaudin magnet. Using this isomorphism, the complete classification of separable coordinate systems is provided by means of the corresponding L-operators for the Gaudin magnet.
Existence of gauge field in any partially integrable systems
Authors: Okubo Susumu
Published: July 2002

For any integrable and, more generally, any partially integrable model, the existence is shown of a Yang–Mills gauge field with zero curvature, whose gauge group consists of all general coordinate transformations. It has been suggested that this fact may have some connection with existence of an affine connection in the space with zero Riemann curvature tensor. A BRST-like quadratically nilpotent operator is also constructed for any theory with Poisson bracket structure whenever such a connection with zero Riemann curvature exists.
On the composition factors of Kac modules for the Lie superalgebras sl(m/n)
Authors: Hughes J. W. B. , King R. C. , Van der Jeugt J.
Published: July 2002

In the classification of finite-dimensional modules of Lie superalgebras, Kac distinguished between typical and atypical modules. Kac introduced an induced module, the so-called Kac module V̄(Λ) with highest weight Λ, which was shown to be simple if Λ is a typical highest weight. If Λ is an atypical highest weight, the Kac module is indecomposable and the simple module V(Λ) can be identified with a quotient module of V̄(Λ). In the present paper the problem of determining the composition factors of the Kac modules for the Lie superalgebra sl(m/n) is considered. An algorithm is given to determine all these composition factors, and conversely, an algorithm is given to determine all the Kac modules containing a given simple module as a composition factor. The two algorithms are presented in the form of conjectures, and illustrated by means of detailed examples. Strong evidence in support of the conjectures is provided. The combinatorial way in which the two algorithms are intertwined is both surprising and interesting, and is a convincing argument in favor of the solution to the composition factor problem presented here.
Quantum particle in a box with moving walls
Authors: Dodonov V. V. , Klimov A. B. , Nikonov D. E.
Published: July 2002

The analytical expressions for the energy gain and transition probabilities between energy levels of a nonrelativistic quantum particle confined in a box with uniformly moving walls, including the cases of adiabatic motion and a sudden change of the size of the box was obtained.
Phase-integral approach to quantum-mechanical tunneling
Authors: Dalarsson Nils
Published: July 2002

The phase-integral method is applied to the problem of quantum-mechanical tunneling in one-dimensional double-well potentials. Thus the results for the energy splitting of the nth level Δn up to the seventh-order of phase-integral approximation in the closed form in terms of the complete elliptic integrals are obtained. Furthermore the asymptotic approximations of the complete elliptic integrals to the first-order phase-integral result are used to calculate the quantity W(0) which appears in the expression for Δn obtained applying the LSZ procedure to the instanton-dominated Green function with 2n legs. Thus it is confirmed that the instanton calculus gives a correct value for the energy splitting of the nth level.
Circular-sector quantum-billiard and allied configurations
Authors: Liboff Richard L.
Published: July 2002

The circular-sector quantum-billiard problem is studied. Numerical evaluation of the zeros of first-order Bessel functions finds that there is an abrupt change in the nodal-line structure of the first excited state of the system (equivalently, second eigenstate of the Laplacian) at the critical sector-angle θc=0.354π. For sector-angle θ0, in the domain 0<θ0<θc, the nodal curve of the first excited state is a circular-arc segment. For θc<θ0≤π, the nodal curve of the first excited state is the bisector of the sector. Otherwise nondegenerate first excited states become twofold degenerate at the critical-angle θc. The ground- and first-excited-state energies (EG,E1) increase monotonically as θ0 decreases from its maximum value, π. A graph of E1 vs θ0 reveals an inflection point at θ0=θc, which is attributed to the change in Bessel-function contribution to the development of E1. A proof is given for the existence of a common zero for two Bessel functions whose respective orders differ by a noninteger. Application of these results is made to a number of closely allied quantum-billiard configurations.
On the commutator of two 2-forms in Minkowski space–time
Authors: Coll Bartolomé , San José Martínez Fernando
Published: July 2002

In the space–time of general relativity, 2-forms play several important roles. But their commutators are generally seen as elements related to their algebraic aspects, rather than to their geometric ones. Here a clear geometric meaning of the commutator of two 2-forms is given. To obtain it, some simple notions on the Minkowski tangent space are needed. The characteristic tetrad and the characteristic planes of two generic planes are introduced. For nongeneric planes (those that cut each other or coincide), the matrix of their intersections and of the intersections of their orthogonals is considered, and some of its properties analyzed. The orthogonal cut of a plane is defined and the planes that orthogonally cut two given planes are studied. These results allow one to relate very easily the invariant planes of the commutator of two 2-forms to the invariant planes of the 2-forms: the first ones are the single orthogonal cut of the last ones. Some applications are indicated.
Mixed states with positive Wigner functions
Authors: Bröcker T. , Werner R. F.
Published: July 2002

The Wigner distribution function of a pure quantum state is everywhere positive if and only if the state is coherent, according to a result of Hudson. The characterization of mixed states with a positive Wigner function is a special case of the problem of determining functions satisfying a twisted positive definiteness condition for a prescribed set of twisting parameters (i.e., functions with given ‘‘Wigner spectrum’’ in the sense of Narcowich). If a state is a convex combination of coherent states, it has the property that the Wigner spectrum contains the unit interval, which in turn implies that the Wigner function is positive. It is shown by explicit examples that the converses of both implications are false. The examples are taken from a low-dimensional section of the state space, in which all Wigner spectra can be computed. In this set counterexamples to a conjecture by Narcowich concerning the Wigner spectrum of products are also found, as well as a state whose Wigner spectrum is a convergent sequence of discrete points.
Boson–fermion model with two-body interactions: Exact results
Authors: Wang Y. , Pu Fu-Cho
Published: July 2002

A one-dimensional boson–fermion model with two-body interactions between the two types of chiral fermions is considered. It is shown that the model is exactly soluble and the general Bethe eigenstates are constructed. On the basis of the Bethe ansatz equations, the ground state, the low lying elementary excitations, and the thermodynamics are also given in some closed integral equations.
Isomorphisms between the Batalin–Vilkovisky antibracket and the Poisson bracket
Authors: Barnich Glenn , Henneaux Marc
Published: July 2002

One may introduce at least three different Lie algebras in any Lagrangian field theory: (i) the Lie algebra of local BRST cohomology classes equipped with the odd Batalin–Vilkovisky antibracket, which has attracted considerable interest recently; (ii) the Lie algebra of local conserved currents equipped with the Dickey bracket; and (iii) the Lie algebra of conserved, integrated charges equipped with the Poisson bracket. We show in this paper that the subalgebra of (i) in ghost number −1 and the other two algebras are isomorphic for a field theory without gauge invariance. We also prove that, in the presence of a gauge freedom, (ii) is still isomorphic to the subalgebra of (i) in ghost number −1, while (iii) is isomorphic to the quotient of (ii) by the ideal of currents without charge. In ghost number different from −1, a more detailed analysis of the local BRST cohomology classes in the Hamiltonian formalism allows one to prove an isomorphism theorem between the antibracket and the extended Poisson bracket of Batalin, Fradkin, and Vilkovisky.