bluuebunny/crossref_metadata_2025 huggingface dataset:
Electric field impact on solvated electron reactions: Trapping of randomly walking electron
Authors: Fedorenko S. G. , Krissinel E. B. , Burshtein A. I.
Published: July 2002

The impact of an external electric field on electron seizure by neutral traps was studied within the Torrey model of a solvated electron random walk. The step length of the random motion, determined by the free diffusion of a temporarily escaped electron, increases with electric field strength, changing the reaction mechanism from a diffusional to a hopping one. The field dependence of the rate of the hopping reaction essentially differs from that obtained for diffusional trapping. Such a difference may serve for experimental discrimination between the hopping and diffusional mechanisms of this reaction.
Anisotropic diffusion of nonspherical molecules in dense liquids: A molecular dynamics simulation of isolated ellipsoids in the sea of spheres
Authors: Ravichandran S. , Bagchi B.
Published: July 2002

Detailed molecular dynamics simulations of the rotational and the translational motions of Gay–Berne ellipsoids in a sea of Lennard-Jones spheres have been carried out. It is found that while the translational motion of an ellipsoid is isotropic at low density, it becomes increasingly anisotropic with density until the ratio of the parallel to the perpendicular diffusion coefficients becomes nearly equal to the value of the aspect ratio at high density. The latter is in agreement with the prediction of Navier–Stokes hydrodynamics with slip boundary condition. The product of the translational diffusion coefficient and the rotational correlation time also attains a hydrodynamic-like density independent behavior only at high density. The reorientational correlation function becomes nonexponential at high density and low temperature where it also develops a slow decay. The perpendicular component of the velocity time correlation function exhibits a clear double minimum, only at high density, which becomes more pronounced as the aspect ratio is increased.
On the effect of Lennard-Jones parameters on the quantum mechanical and molecular mechanical coupling in a hybrid molecular dynamics simulation of liquid water
Authors: Tu Yaoquan , Laaksonen Aatto
Published: July 2002

Combined quantum mechanical/molecular mechanical (QM/MM) molecular dynamics simulations have been carried out to study liquid water. The QM forces are evaluated at the Hartree–Fock level. The QM/MM coupling potentials, constructed from the flexible TIP3P Lennard-Jones parameters, and from those modified according to the corresponding QM/MM calculations of the water dimer, are examined based on the structure of liquid water, polarization effects of the QM water molecule from the surrounding classical MM water molecules, and the interactions between the QM molecule and the MM molecules. Our simulations show that when the flexible TIP3P Lennard-Jones parameters are used, the QM/MM coupling is too strong. However, when the Lennard-Jones parameters on the QM water molecule are modified according to the corresponding QM/MM calculations of the water dimer, the coupling between the QM water molecule and MM water molecules becomes too weak. In general, our work shows that the Lennard-Jones parameters on the QM atoms have a very large effect on the combined QM/MM simulation results.
Photofragmentation studies of small selenium cluster cations Sen+ (n=3–8)
Authors: Yang Xin , Hu Yihua , Yang Shihe , Loy M. M. T.
Published: July 2002

Selenium cluster cations are produced by the combination of laser vaporization and supersonic expansion techniques. Each small cluster cation Sen+ (n=3–8) is mass selected separately and subjected to one-photon laser photodissociation processes. The parent and daughter cluster ions are detected using a reflectron time-of-flight mass spectrometer. The appearance potentials of all the observed cluster fragment ions are estimated from their yield curves as a function of the laser wavelength. The neutral dimer evaporation is found to be the lowest energy photodissociation channel. In general, the odd-numbered cluster cations have much larger dissociation thresholds than those of the even-numbered cluster cations. In addition, the dissociation thresholds of the odd-numbered cations decrease with the increasing cluster size, while those of the even-numbered clusters increase with the increasing cluster size. A sequential neutral dimer evaporation mechanism is demonstrated in the photodissociation of some cluster cations at high photon energies.
Application of time-dependent density-functional theory to the Σu−3 first excited state of H2
Authors: Cai Zheng-Li , Reimers Jeffrey R.
Published: July 2002

Recently, time-dependent density-functional (TDDFT) methods have been developed for determining the energies of molecular excited states. This, along with the somewhat similar equations-of-motion coupled-cluster (EOM-CCSD) methods, offer advantages of speed, reliability, and often accuracy over alternate complete-active-space self-consistent-field (CASSCF) based approaches, with the disadvantages associated with being essentially “single-reference” calculations. We compare results obtained using both approaches for the Σg+1 (ground) and Σu−3 (first excited) states of the simplest molecule, H2. For the excited state of this two-electron system, EOM-CCSD is equivalent to full configuration interaction, while results obtained using TDDFT are good at short bond lengths but become quite poor as the bond is stretched from its equilibrium length. The poor TDDFT result is attributed to the fact that the spin-restricted Kohn–Sham (RKS) method used to generate the ground-state density is not size consistent. We suggest that TDDFT calculations based on spin-unrestricted Kohn–Sham (UKS) calculations should provide better descriptions of molecular excited states than do current RKS-based methods, spin-contamination effects notwithstanding.
The analytic gradient for the equation-of-motion coupled-cluster energy with a reduced molecular orbital space: An application for the first excited state of formaldehyde
Authors: Baeck Kyoung K.
Published: July 2002

The analytic gradient method for the equation-of-motion coupled-cluster (EOM-CC) energy has been extended to employ a reduced molecular orbital (MO) space. The geometrical and the vibrational properties of the first excited singlet state of formaldehyde have been studied by using several different sizes of dropped MO space. It is shown that reliable results can be produced with high efficiency by employing the EOM-CC with a reduced MO space, which provides a new hierarchy in the study of photochemical processes in molecules.
Quantum Monte Carlo investigation of small He4 clusters with a He3 impurity
Authors: Bressanini Dario , Zavaglia Matteo , Mella Massimo , Morosi Gabriele
Published: July 2002

Small helium (4He) clusters containing the lighter isotope He3 are studied by means of quantum Monte Carlo methods. Accurate ground state energies and structural properties are obtained using accurate trial wave functions and the Tang–Tonnies–Yiu (TTY) helium–helium pair potential. The dimer He4–3He is not bound; as well as the trimer He4He23. The smallest cluster containing He3 is He24He3 with a nonrigid structure having a marked linear contribution. Interestingly, this weakly bound system, with an energy one order of magnitude less than the He34 trimer, is able to bind another He3 atom, forming the tetramer He24He23, which shows the odd feature of having five out of six unbound pairs. In general, the substitution of a single He4 atom in a pure cluster with a He3 atom leads to an energetic destabilization, as the pair He4–3He is not bound. The isotopic impurity is found to perturb only weakly the distributions of the remaining He4 atoms, which retain the high floppiness already found in the pure clusters. As the number of atoms increases the isotopic impurity has the marked tendency to stay on the surface of the cluster. This behavior is consistent with the formation of the so-called “Andreev states” of a single He3 in liquid He4 helium and droplets, where the impurity tends to form single-particle states on the surface of the pure He4.
Relations among the modern theories of diffusion-influenced reactions. II. Reduced distribution function theory versus modified integral encounter theory
Authors: Sung Jaeyoung , Lee Sangyoub
Published: July 2002

It is shown that exactly the same results of the modified integral encounter theory (MET) of diffusion-influenced reactions can be derived from the nonequilibrium reduced distribution function (RDF) theory. The method of solution of the RDF theory is much simpler than that of the MET, and shows clearly that the sophisticated approximation scheme employed in the latter is effectively equivalent to a simple truncation approximation adopted in the former. We evaluate the relative accuracy of the various theories by comparing the theoretical results with the results of an accurate Brownian dynamics simulation and the exact theory that are available for simple reaction models.
Lattice density functional theory predictions of order–disorder phase transitions
Authors: Aranovich G. L. , Donohue M. D.
Published: July 2002

Calculations of lattice density-functional theory (DFT) are performed for systems that have both attractive and repulsive forces. Order–disorder phase transitions are observed.
Direct calculation of anharmonic vibrational states of polyatomic molecules using potential energy surfaces calculated from density functional theory
Authors: Wright Nicholas J. , Gerber R. Benny
Published: July 2002

Potential energy surface points computed from variants of density functional theory (DFT) are used to calculate directly the anharmonic vibrational frequencies of H2O, Cl−H2O, and (H2O)2. The method is an adaptation to DFT of a recent algorithm for direct calculations of anharmonic vibrational frequencies using ab initio electronic structure codes. The DFT calculations are performed using the BLYP and the B3LYP functionals and the results are compared with experiment, and also with those calculated directly from a potential energy surface obtained using ab initio Möller-Plesset second–order perturbation theory (MP2). The direct calculation of the vibrational states from the potential energy points is performed using the correlation-corrected vibrational self-consistent field (CC-VSCF) method. This method includes anharmonicity and correlations between different vibrational modes. The accuracy of this method is examined and it is shown that for the experimentally measured transitions the errors in the CC-VSCF calculations are much less than the errors due to the potential energy surface. By comparison with the experimentally measured frequencies the CC-VSCF method thus provides a test for the quality of the potential energy surfaces. The results obtained with the B3LYP functional, in contrast to those of the BLYP functional, are of comparable quality to those obtained with MP2. The B3LYP anharmonic frequencies are in good agreement with experiment, showing this DFT method describes well the anharmonic part of the potential energy surface. The BLYP results systematically underestimate both the harmonic and anharmonic frequencies and indicate that using this functional for the description of hydrogen-bonded systems may cause significant errors.
Dephasing of an anharmonic vibration in solution
Authors: Williams Ryan B. , Loring Roger F.
Published: July 2002

An approximate analytical solution of the generalized Langevin equation for a cubic oscillator [J. Chem. Phys. 110, 10899 (1999)] is applied to the vibrational dephasing of a diatomic molecule with cubic anharmonicity in a Lennard-Jones solvent. This method presents an improvement over conventional perturbative approaches.
Isomer structures and vibrational assignment of the methyl-p-aminobenzoate(H2O)1 complex
Authors: Longarte A. , Fernández J. A. , Unamuno I. , Castaño F.
Published: July 2002

Methyl-p-aminobenzoate(H2O)1 complex, henceforth MAB(H2O)1, prepared by pulsed supersonic expansion, has been examined by a broad range of laser based spectroscopic, mass and isomer selective techniques and density functional theory (DFT) calculations, in order to identify its isomer structures, ionization energies, and vibrational frequencies. The experimental techniques used include laser induced fluorescence (LIF), mass resolved excitation spectroscopy (MRES) either with one (REMPI) or two laser colors (R2PI), laser excited dispersed emission (DE), high resolution MRES, pressure controlled R2PI, hole burning (HB) spectroscopy, and photoion fragmentation threshold (PIFT). Experimental results have been interpreted, rationalized and extended with density functional theory (DFT) computations at the B3LYP/6-31G and B3LYP/6-31+G* levels. Although bare MAB molecule have four possible solvation sites, prone to yielding hydrogen bonds with the water molecule, LIF, R2PI, and HB spectroscopy of MAB(H2O)1 only pick out the presence of three blue shifted isomers, each accompanied by a number of vibrational features extending to ≈500 cm−1. The high intensity bands have been demonstrated to originate in three isomers and their ionization energies, dispersed emission, vibrational spectra, and photoion fragmentation threshold have been measured and characterized. Isomer shifts and structures are discussed in the light of experimental and theoretical results.
Multiscale filter diagonalization method for spectral analysis of noisy data with nonlocalized features
Authors: Chen Jianhan , Mandelshtam Vladimir A.
Published: July 2002

Stability and performance of the filter diagonalization method (FDM) for harmonic inversion [i.e., fitting a time signal by C(t)=∑k dke−itωk] of noisy data are examined. Although FDM is capable to extract accurately the parameters of narrow spectral peaks, in the presence of broad peaks (or strong background spectrum) and noise, the FDM ersatz spectrum, i.e., I(ω)=∑kdk/(ωk−ω), maybe distorted in some regions and be sensitive to the FDM parameters, such as window size, window position, etc. Some simple hybrid methods, that can correct the ersatz spectrum, are discussed. However, a more consistent approach, the multiscale FDM, is introduced to solve the instability problem, in which some coarse basis vectors describing (in low resolution) the global behavior of the spectrum are added to the narrow band Fourier basis. The multiscale FDM is both stable and accurate, even when the total size of the basis (i.e., the number of coarse plus narrow band basis vectors) used is much smaller than what would previously be considered as necessary for FDM. This, in turn, significantly reduces the computation cost. Extension of the 1D multiscale FDM to a multidimensional case is also presented.
The rolling transition of a Gaussian chain end-grafted at a penetrable surface
Authors: Skvortsov A. M. , Klushin L. I. , van Male J. , Leermakers F. A. M.
Published: July 2002

A Gaussian chain at a liquid–liquid interface is considered. The solvents are represented by an external potential field u that has a constant value in one half-space and is zero elsewhere. One end of the chain is fixed at the boundary where the external potential field changes its value. For this model the exact partition function is available. The system features a first-order phase transition for which the external potential is the control parameter; the chain rolls from one half-space to the other upon changing the sign of the external potential. The chain distributes its N segments over both regions when the external potential difference between the two regions |u|≪1/N, otherwise the chain puts virtually all its segments in the region with the lowest potential. The relation between the problem of a Gaussian chain at a solid/liquid boundary and that of a chain at a liquid/liquid interface, is illustrated. Applications of the model are discussed.
Phase behavior of a hard sphere interaction site model of benzene
Authors: Schroer J. W. , Monson P. A.
Published: July 2002

We present a study of the phase diagram for a hard sphere interaction site model of benzene using Monte Carlo computer simulation. The investigation considered the fluid phase and three types of solid phases. Two of these are similar to experimentally determined structures of benzene and the third is a structure which allows the system to reach a high packing density at high pressure through a columnar-like arrangement of the molecules. Extensive calculations of the solid and fluid thermodynamic properties were made. The results show that, for the solid phase, the structure which enables the closest packing of molecules is the most stable one. The solid structures similar to those of benzene, while apparently mechanically stable, were found to be thermodynamically metastable for this purely hard core system. The simulation results have been used to test the accuracy of the cell theory for the solid phase and an equation of state for the fluid phase due to Boublik, as well as phase diagram predictions obtained by using these approximations in combination.
Forces between like-charged walls in electrolyte solution: Molecular solvent effects at the McMillan–Mayer level
Authors: Otto Frank , Patey G. N.
Published: July 2002

The force between two like-charged walls immersed in electrolyte solution is obtained for models that include solvent effects at the McMillan–Mayer (MM) level. In these models the solvent is not represented by discrete particles but exerts its influence through solvent-averaged ion–ion potentials of mean force which serve as effective potentials. This simplification allows the numerical solution of accurate anisotropic integral equation theories, and the anisotropic hypernetted-chain (AHNC) approximation is used in the present calculations. It is shown that the MM results may differ significantly from those of the primitive model (PM) which treats the solvent as a dielectric continuum. Most interestingly, we find that at the MM level the force between like-charged walls at small separations and with realistic surface charges can be attractive for monovalent counterions. This attraction is due to solvent effects on the effective counterion–counterion interaction and not to the correlated charge fluctuations that give rise to the attractions found for divalent counterions in the PM case. The possible relevance of our observations in the interpretation of experimental force measurements is briefly discussed.
Small angle neutron scattering study on the salt-induced phase separation of 1-propanol aqueous solution
Authors: Yoshida K. , Misawa M. , Maruyama K. , Imai M. , Furusaka M.
Published: July 2002

Small angle neutron scattering (SANS) measurements have been carried out over a wide range of Q from 0.003 to 7 Å−1 on the 1-propanol-water solution with KCl and that without KCl in relation to the salt-induced reentrant phase-separation phenomena. The Q dependence of the SANS intensity for both solutions is characterized by the same fractal structure with the fractal dimension df of 1.9. The only difference between the two solutions is the value of correlation length ξ. In the solution without KCl the value of ξ is rather small, ranging from 7.4 to 6.2 Å depending on temperature, while in the solution with KCl it becomes very large, from 48 to 355 Å or more depending on temperature, and diverges toward the phase-separation temperatures in a similar way for both the upper and lower one-phase regions. No significant differences have been found on the growing structure of fluctuation in the upper and lower one-phase regions.
Superfield actions for N=2 degenerate central charges
Authors: Hassoun J. , Restuccia A. , Taylor J. G.
Published: July 2002

We construct the superfield actions for degenerate (spin-reducing) multiplets of N=2 extended supersymmetry as integrals over all superspace. This requires the integration over the two available central charges as well. We evaluate the detailed component contributions to these actions and show they are total derivatives with respect to central charge dimensions. The resulting spectrum of the theories are analyzed in four dimensions in terms of various boundary conditions in the higher dimensions and the nature of the integration domain.
An approximate solution of the monomer–dimer problem on a square lattice. II
Authors: Phares Alain J. , Shaw Donald E. , Wunderlich Francis J.
Published: July 2002

The mathematical method developed in paper I is applied to obtain the partition function and thermodynamical properties of the monomer–dimer problem for a square lattice in terms of the absolute activity x. We also obtain by extrapolation an approximate expression of the partition function which is accurate to better than 0.1% in the range 0≤x≤10. The expectation of the statistics 〈θ(x)〉 is calculated in two different ways and numerical results agree to better than 3%, thus showing the consistency of the underlying mathematical method. Consistent with earlier studies, there is no phase transition. Approximation methods used in earlier work are also found to be in good agreement with our analytic study.
Supertwistor realization of SU(2,2/1)
Authors: Luehr C. P. , Rosenbaum M.
Published: July 2002

A space of supertwistors is introduced as a graded vector space by starting with ordinary twistor space multiplied with even Grassmann coefficients and combining it by an othogonal direct sum with a one-dimensional space multiplied with odd Grassmann coefficients. A treatment of the algebraic properties of supertwistor space and of Grassmann-linear transformations on this space lead to a systematic procedure for deriving the structure equations for the graded Lie algebra su (2,2/1).
Multiplicity-free Wigner coefficients for semisimple Lie groups. I. The U(n) pattern calculus
Authors: Gould M. D.
Published: July 2002

This is the first paper in a series of two dedicated to a new algebraic determination of the multiplicity-free reduced Wigner coefficients for the Lie groups U(n) and O(n). The approach employed enables a direct (nonrecursive) derivation of reduced Wigner coefficients. The absolute value squared of the reduced Wigner coefficients is expressed as a rational polynomial function (numerator polynomial divided by denominator polynomial) whose Weyl group symmetries are seen to fall out naturally in our approach from the transformation properties of polynomial functions determined by Casimir invariants. A unified treatment of the composition laws of reduced Wigner coefficients and the evaluation of their associated denominator polynomials is presented, which applies to both U(n) and O(n). An explicit formula for the numerator polynomials of U(n) is also derived. The numerator polynomials for the orthogonal groups will be given in the second paper of the series.
Recurrence relations for two-center harmonic oscillator integrals
Authors: Morales J. , Sandoval L. , Palma A.
Published: July 2002

General recurrence relations for the calculation of two-center harmonic oscillator (HO) integrals are obtained by means of a hypervirial-like-theorem commutator algebra procedure, combined with a second quantization formalism. The method is based on a linear transformation between the creation and annihilation operators of two displaced HO with different frequencies. Ansbacher’s recurrence relations for the calculation of Franck–Condon factors are obtained straightforwardly from the proposed general recurrence relations. The application to polynomial, exponential, and Gaussian operator integrals is shown and new recurrence relations are given. In all cases, the proposed recurrence relations reduce, as particular cases, to the corresponding formulas for the calculation of one-center integrals.
Nonlinear representations of Poincaré group in three dimensions
Authors: Bertrand J. , Rideau G.
Published: July 2002

The method of formal series is applied to the construction of nonlinear representations of Poincaré’s group in three dimensions. The first term of the series must be a linear massless representation. In the special case of discrete helicities, the cocycles of extension of these representations by their tensor product with a nonzero quadratic term are determined. It turns out that a nonlinear representation must have a helicity zero representation as leading term. It is proved by induction how to avoid the successive obstructions to the computation of each term in the series.
Variational principle and conservation laws for nonbarotropic flows
Authors: Mathew George , Vedan M. J.
Published: July 2002

A variational formulation for nonbarotropic perfect fluid flow is presented. By introducing suitable field variables, Euler’s equations of motion from the variational principles are obtained. The conservation laws of energy, impulse, and angular momenta follow from application of Noether’s theorem.
Lyapunov exponents as a measure of the size of chaotic regions
Authors: Cleary Paul W.
Published: July 2002

Chaotic orbits in conservative dynamical systems are partitioned into a number of distinct regions by sets of cantori. This causes long time scale oscillations in the corresponding Lyapunov spectrums. A direct correlation between the magnitude of the maximal Lyapunov exponent and the size of the corresponding chaotic region in the surface of section appears to exist for the two-dimensional conservative systems examined.
Space-time geometry of relativistic particles in four-dimensional phase space
Authors: Kim Chang-Ho , Kim Y. S.
Published: July 2002

The Wigner phase-space picture of Dirac’s two-oscillator representation of O(3,2) is given. This constitutes a real representation of Sp(4) which allows us to study the symmetry of the O(3,2) de Sitter group using canonical transformations in four-dimensional phase space. It is also possible to study subgroups of O(3,1) in this phase space. The phase-space picture is given for the two-oscillator model of van Dam, Ng, and Biedenharn [Phys. Lett. B 158, 227 (1985)] for the little groups for massive and massless particles. In this formalism, Lorentz transformations can be described in terms of canonical transformations in phase space. It is particularly convenient for studying infinite-momentum/zero-mass limit of the O(3)-like little group for a massive particle. It is shown that the trivial representation of the E(2)-like little group for a massless particle emerges from this limiting process. The origin of gauge degree of freedom is discussed.
Natural bundles. I. A minimal resolution of superspace
Authors: Swift S. Timothy
Published: July 2002

In this, the first of a sequence of papers applying infinite dimensional natural bundle techniques to problems in general relativity and other field theories, we construct a minimal resolution of the singularities in the space of geometries or superspace of a closed manifold M. The basic properties of two natural bundles associated with M are also discussed. Subsequent articles will develop the theory in the context of spin and the diffeomorphism group, the Yang–Mills moduli space, and nonlinear sigma models.
Quasiperiodic systems without Cantor-set-like energy bands
Authors: Iguchi Kazumoto
Published: July 2002

A class of quasiperiodic systems is proposed that does not show the Cantor-set-like energy bands. The general aspects of such systems are investigated.
C-Integrable nonlinear partial differential equations in N+1 dimensions
Authors: Calogero F.
Published: July 2002

Two techniques are introduced, which are suitable to manufacture C-integrable nonlinear PDEs (i.e., nonlinear PDEs solvable by an appropriate Change of variables) in N+1 dimensions. Several examples are exhibited.
Focused waves and the scalar wave equation
Authors: Palmer Matthew R. , Donnelly Rod
Published: July 2002

New solutions of the free space wave equation are studied and particular forms of these new solutions lead naturally to the localized wave solutions that have recently been reported in the literature. Localized waves exhibit a high degree of spatial and temporal localization. Choosing the characteristic variables, (z−ct, z+ct), the Green’s function is constructed for the scalar wave equation. With this form for the Green’s function, it is shown how a relatively simple line source of infinite extent, aligned with the propagation axis, gives rise to a propagated field which exhibits a degree of transverse focusing.
Canonical and differential realizations of OSP(3‖2) superalgebra
Authors: Daumens M.
Published: July 2002

The osp(3‖2) superalgebra is realized, first by means of two supervectorial operators canonically conjugated, and then by differential operators acting on functions defined on E(3‖2). As for the vectorial representation of osp(1‖2) the eigenvalue problem yields to the superspherical harmonics.
Isospectral flow in loop algebras and quasiperiodic solutions of the sine-Gordon equation
Authors: Harnad J. , Wisse M.-A.
Published: July 2002

The sine-Gordon equation is considered in the Hamiltonian framework provided by the Adler–Kostant–Symes theorem. The phase space, a finite dimensional coadjoint orbit in the dual space 𝔤* of a loop algebra 𝔤 , is parameterized by a finite dimensional symplectic vector space W embedded into 𝔤* by a moment map. Real quasiperiodic solutions are computed in terms of theta functions using a Liouville generating function which generates a canonical transformation to linear coordinates on the Jacobi variety of a suitable hyperelliptic curve.
SU(∞) (super)gauge theories and self-dual (super)gravity
Authors: Castro Carlos
Published: July 2002

It is shown that SU(∞) self-dual Yang–Mills equations on a four-dimensional flat Euclidean background are equivalent to Plebanski’s second heavenly equation for the self-dual gravitational background, which is associated with the cotangent space of a suitable Riemann surface. The Riemann surface in question is nothing but the internal two-dimensional surface required in the formulation of SU(∞) self-dual Yang–Mills theories. Such equivalence only occurs when a dimensional reduction has taken place. After a discussion of Euclidean supersymmetries the results are generalized to self-dual super-Yang–Mills theories and self-dual supergravity.
The Hurwitz transformation and generalized Cayley–Klein parameterization
Authors: Davtyan Levon S.
Published: July 2002

The fiber bundles and global rotations arising in the Kustaanheimo–Stiefel and Hurwitz transformations are studied. Generalized Cayley–Klein parameterization is introduced in a functional form and is used for the analysis of fibration in Hurwitz transformations. Essential differences in fibration structure between these transformations similar in Cartesian description are established in the angular map.
The relation between the Berry and the Anandan–Aharonov connections for U(𝒩) bundles
Authors: Bohm A. , Mostafazadeh A.
Published: July 2002

The geometric phase has been defined as the holonomy of two bundles with different base spaces and different connections. In this article we establish the relation between the Berry–Simon and the Anandan–Aharonov definitions for a large class of cyclic Hamiltonians (with 𝒩-fold degeneracy) using the classifying theorem for principal fiber bundles.
Lax–Phillips theory for scattering by thin elastic bodies
Authors: Pokrovski A. A. , Badanin A. V.
Published: July 2002

The scheme of construction of linear self-adjoint operators for acoustic systems with an interaction of sound and vibration is proposed. Kinetic energy of a system induces the basic Hilbert space L2(Ω), where Ω denotes the domain filled with fluid. Potential energy of the system induces the quadratic form on this Hilbert space and, consequently, the positive operator that governs the evolution. Unlike earlier theories, our operators are perturbations of the Laplace operator in L2 spaces. The operators may also be obtained as extensions of symmetric operator (−Δ) defined on C∞0(Ω) into a wider Hilbert space. Functions from their domains have an additional smoothness of their derivatives on the boundary; the smoothness follows from the elasticity of the boundary. The scheme allows one to describe inhomogeneities of vibrating objects concentrated at a point or on a line (such as cracks and stiffeners). It is demonstrated that Lax–Phillips scattering theory may be generalized for scattering by thin elastic objects. The necessary condition for the existence of the incoming and the outgoing subspaces is derived in terms of spectral properties of the operator of the isolated elastic object.
Hodograph equations in relativistic gas dynamics admitting an infinite number of symmetries
Authors: Carbonaro P. , Giambò S.
Published: July 2002

A straightforward application of the Lie-group theory to the linear equation, which describes the relativistic one-dimensional flow in the hodograph plane, is carried out. It is shown that, for particular equations of state, one has an infinite number of symmetries. In this case, transformations can be found that reduce the hodograph equation to a form directly integrable. The remarkable aspect of the analysis is that one of these equations of state is identified as that characterizing a one-dimensional fully degenerate Fermi gas. Astrophysicists might find this result useful in practical applications.
Reality of complex affine Toda solitons
Authors: Zhu Z. , Caldi D. G.
Published: July 2002

There are infinitely many topological solitons in any given complex affine Toda field theory and most of them have complex-energy density. When we require the energy density of the solitons to be real, we find that the reality condition is related to a simple ‘‘pairing condition.’’ Unfortunately, rather few soliton solutions in these theories survive the reality constraint, especially if one also demands positivity. The resulting implications for the physical applicability of these theories are briefly discussed.
Superposition of a static perfect fluid and a radial electric field
Authors: Cataldo Mauricio , Salgado Patricio
Published: July 2002

We obtain a two-parameter set of solutions, which represents a spherically symmetric space–time with a superposition of a neutral fluid and an electric field. The electromagnetic four-potential of this Einstein–Maxwell space–time is taken in the form A=(q/n)rn dt, when n ≠ 0 and A=q ln r dt, when n=0 (where q and n are arbitrary constants). Some particular solutions obtainable from the general solution are presented.
Infinite dimensional Morse theory and Fermat’s principle in general relativity. I
Authors: Perlick Volker
Published: July 2002

The following theorem may be viewed as the general relativistic version of Fermat’s principle. Among all lightlike curves connecting a given point p to a given timelike curve γ in a Lorentzian manifold, the geodesics are characterized by stationary arrival time. Here ‘‘arrival time’’ refers to a smooth parametrization of γ. In this article the first steps are taken to make infinite dimensional Morse theory applicable to this variational problem. The space of trial curves is made into a Hilbert manifold by imposing an H2 Sobolev condition and Fermat’s principle is reformulated in this infinite dimensional setting. Moreover, a Morse index theorem is presented. The mathematical formalism developed here aims at applications to the gravitational lens effect.
Killing spinors and separability of Rarita–Schwinger’s equation in type {2,2} backgrounds
Authors: Silva-Ortigoza G.
Published: July 2002

It is shown that in a type {2,2} solution of the Einstein vacuum field equations, which admits a two-index Killing spinor, a differential operator can be constructed that maps a solution of the Rarita–Schwinger equation into a solution of its complex conjugate. Furthermore, by considering the Plebański–Demiański metric, which contains all the vacuum type {2,2} metrics, it is shown that the separable solutions of the Rarita–Schwinger equation are eigenfunctions of a certain differential operator with the Starobinsky constant as the eigenvalue.
A new form of Einstein’s equations
Authors: Wallner R. P.
Published: July 2002

We derive the field equations of general relativity from a complex Lagrangian of particular simplicity. In this way we exhibit that Einstein’s vacuum equations are equivalent to the existence of certain covariantly constant vector- and bivector-valued two-forms. We discuss the implications this brings along for the exploration of new (hidden) symmetries as well as for the construction of new solutions. We even engage the equations’ simplicity for the construction of the most general (local) solution of the vacuum equations of general relativity and show that formally the general solution can be expressed in terms of Weyl’s conformal tensor and several arbitrary forms acting as ‘‘constants of integration.’’ In a 3+1 decomposition we demonstrate how the simple structure of the Lagrangian equations continues for the Hamilton equations, and compare the result with Ashtekar’s approach.
Quantum chaos in the group-theoretical picture
Authors: Kon’kov L. E. , Prants S. V.
Published: July 2002

The dynamical-group approach is developed and applied to investigate the problems of controllability and quantum chaos in two fundamental models of the matter–radiation interaction. It provides a new insight into the dynamics of nonstationary quantum process of the interaction between two-level atoms and a single-mode radiation field without and with the feedback. A sequence of transitions from the quasiperiodicity to chaos has been numerically observed for two-level atoms interacting with a self-consistently generated radiation field. The unitary irreducible representations of the SU(2) group of dynamical symmetry in a noncanonical parametrization is constructed, allowing one to use the results for describing the time evolution of any driven quantum system with the underlying SU(2) symmetry.
Conformal gauge theory of (2+1)-dimensional gravity
Authors: Stedile E. , Duarte R.
Published: July 2002

A conformal gauge theory of (2+1)-dimensional gravity is developed within a fiber-bundle structure. Here gravitational field variables are triads and Lorentz gauge potentials, both introduced under a nonlinear realization, which leads to a spontaneous break of symmetry. The most general gravitational Lagrangian density is given in a quadratic form of the conformal invariant gauge fields. We also obtain the Poincaré gauge theory in vacuum. In a weak-field limit the gravitational field equations for a static and spinless point-like source, are naturally reduced to the Newtonian case.
Superposition formulas for pseudounitary matrix Riccati equations
Authors: Lafortune Stéphane , Winternitz Pavel
Published: July 2002

The purpose of this article is to derive a superposition formula for the pseudounitary matrix Riccati equation of dimension N≥2. The superposition formula will be written in closed form in terms of five particular solutions satisfying certain well-specified conditions defining a fundamental set. Examples will be studied in order to show how the superposition formula works and how it can be used in numerical calculations.
An elegant solution of the n-body Toda problem
Authors: Anderson Arlen
Published: July 2002

The solution of the classical open-chain n-body Toda problem is derived from an ansatz and is found to have a highly symmetric form. The proof requires an unusual identity involving Vandermonde determinants. The explicit transformation to action-angle variables is exhibited.
Soliton solutions and gauge equivalence for the problem of Zakharov–Shabat and its generalizations
Authors: Vaklev Y.
Published: July 2002

In a paper by Takhtadjan and Faddeev [Hamiltonian approach to the soliton theory (in Russian) (Nauka, Moskov, 1986)] the N-soliton solutions, related to the nonlinear Schrödinger equation (NSE), are given. A generalization of this approach allows us to apply it not only to the NSE, but to the whole hierarchy of the Zakharov–Shabat problem, to the quadratic bundle problem, and to the ones gauge equivalent to them [where one can find, for example, the Heisenberg ferromagnet equation, the relativistic Mikhailov model (which, in appropriate reduction, is equivalent to the massive Thirring model), the derivative nonlinear Schrödinger equation (which is equivalent to the derivative Landau–Lifshitz equation), etc.]. We have used an appropriate reduction, giving us interesting, from a physical point of view, results. Thus we manage to obtain the soliton solutions for the whole hierarchy of the quadratic bundle problem (free and under reduction) and for the ones gauge equivalent to it. This result was first announced in previous articles by Vaklev, but here we manage to solve the determinants given there and to present the searched result as simple fractions of products of numerical differences.
The Casimir energy of the twisted string loop: Uniform and two segment loops
Authors: Bayin Selçuk Ş. , Krisch J. P. , Özcan Mustafa
Published: July 2002

We calculate the Casimir energy of a two segment loop of string with one normal boundary point and one twisted boundary point. The energy is renormalized relative to the twisted uniform loop. The use of the twisted loop in simplifying untwisted loop calculations is discussed.
Symmetry and history quantum theory: An analog of Wigner’s theorem
Authors: Schreckenberg S.
Published: July 2002

The basic ingredients of the ‘‘consistent histories’’ approach to quantum theory are a space 𝒰𝒫 of ‘‘history propositions’’ and a space 𝒟 of ‘‘decoherence functionals.’’ In this article we consider such history quantum theories in the case where 𝒰𝒫 is given by the set of projectors 𝒫(𝒱) on some Hilbert space 𝒱. We define the notion of a ‘‘physical symmetry of a history quantum theory’’ (PSHQT) and specify such objects exhaustively with the aid of an analog of Wigner’s theorem. In order to prove this theorem we investigate the structure of 𝒟, define the notion of an ‘‘elementary decoherence functional,’’ and show that each decoherence functional can be expanded as a certain combination of these functionals. We call two history quantum theories that are related by a PSHQT ‘‘physically equivalent’’ and show explicitly, in the case of history quantum mechanics, how this notion is compatible with one that has appeared previously.
Frames: A maximum entropy statistical estimate of the inverse problem
Authors: Rebollo-Neira L. , Fernandez-Rubio J. , Plastino A.
Published: July 2002

A maximum entropy statistical treatment of an inverse problem concerning frame theory is presented. The problem arises from the fact that a frame is an overcomplete set of vectors that defines a mapping with no unique inverse. Although any vector in the concomitant space can be expressed as a linear combination of frame elements, the coefficients of the expansion are not unique. Frame theory guarantees the existence of a set of coefficients which is “optimal” in a minimum norm sense. We show here that these coefficients are also “optimal” from a maximum entropy viewpoint.
Quantum space–time and classical gravity
Authors: Madore J. , Mourad J.
Published: July 2002

A method has been recently proposed for defining an arbitrary number of differential calculi over a given noncommutative associative algebra. As an example a version of quantized space–time is considered here. It is found that there is a natural differential calculus over this version of quantized space–time using which the only possible torsion-free, metric-compatible, linear connection has zero curvature. It is then the noncummutative version of Minkowski space–time. Perturbations of this calculus are shown to give rise to nontrivial gravitational fields.
Elbow scattering and inverse scattering applications to LKdV and KdV
Authors: Sabatier Pierre C.
Published: July 2002

It is well known that many integrable partial differential equations are consistency conditions of a “Lax pair” of linear differential equations whose variables x,t can be considered as coordinates in a plane. The standard inverse scattering method, and the standard direct linearization methods, are related to the scattering problem defined on the x-axis. In a previous paper, the scattering problem defined on the t-axis was considered. Here, the scattering on an unbounded line of the plane, an “elbow,” is defined and it is shown how it can yield new reconstruction methods for the solutions of the consistency condition. The results are neither as complete or as much interesting as the standard IST, but their derivation shows that defining the “wanted” class of solutions is crucial, and it helps understanding why the standard IST is so “simple.”
Ionization of a model atom by perturbations of the potential
Authors: Rokhlenko Alexander , Lebowitz Joel L.
Published: July 2002

We study the time evolution of the wave function of a particle bound by an attractive δ-function potential when it is subjected to time-dependent variations of the binding strength (parametric excitation). The simplicity of this model permits certain nonperturbative calculations to be carried out analytically both in one and three dimensions. Thus the survival probability of bound state |θ(t)|2, following a pulse of strength r and duration t, behaves as |θ(t)|2−|θ(∞)|2∼t−α, with both θ(∞) and α depending on r. On the other hand, a sequence of short pulses produces an exponential decay over an intermediate time scale.
Exact evolution operator on noncompact group manifolds
Authors: Krausz Nurit , Marinov M. S.
Published: July 2002

Free quantum motion on group manifolds is considered. The Hamiltonian is given by the Laplace–Beltrami operator on the group manifold, and the purpose is to get the (Feynman’s) evolution kernel Kt. The spectral expansion, which produced a series of the representation characters for Kt in the compact case, does not exist for noncompact group, where the spectrum is not bounded. In this work real analytical groups are investigated, some of which are of interest for physics. An integral representation for Kt is obtained in terms of the Green’s function, i.e., the solution to the Helmholz equation on the group manifold. The alternative series expressions for the evolution operator are reconstructed from the same integral representation, the spectral expansion (when exists) and the sum over classical paths. For noncompact groups, the latter can be interpreted as the (exact) semiclassical approximation, like in the compact case. The explicit form of Kt is obtained for a number of noncompact groups.
On the Miura Map between the dispersionless KP and dispersionless modified KP hierarchies
Authors: Chang Jen-Hsu , Tu Ming-Hsien
Published: July 2002

The Miura map between the dispersionless KP and dispersionless modified KP hierarchies is investigated. It is shown that the Miura map is canonical with respect to their bi-Hamiltonian structures. Moreover, inspired by the works of Takasaki and Takebe, the twistor construction of solution structure for the dispersionless modified KP hierarchy is given.
Nonlinear Hodge maps
Authors: Otway Thomas H.
Published: July 2002

We consider maps between Riemannian manifolds in which the map is a stationary point of the nonlinear Hodge energy. The variational equations of this functional form a quasilinear, nondiagonal, nonuniformly elliptic system which models certain kinds of compressible flow. Conditions are found under which singular sets of prescribed dimension cannot occur. Various degrees of smoothness are proven for the sonic limit, high-dimensional flow, and flow having nonzero vorticity. The gradient flow of solutions is estimated. Implications for other quasilinear field theories are suggested.
Constrained three- and four-vortex problems
Authors: Rott Nicholas
Published: July 2002

Vortex dynamics in plane ideal flow is strongly simplified for systems with vanishing total circulation. The additional constraint of vanishing total flow impulse leads to further simplifications. For three and four vortices, the cases are discussed where orbit shapes in properly moving configuration planes are given in closed (implicit) form. Then the remaining problems are reduced to quadratures.