bluuebunny/crossref_metadata_2025 huggingface dataset:
Combining coupled cluster and perturbation theory
Authors: Nooijen Marcel
Published: July 2002

Single reference coupled cluster (CC) singles and doubles theory is combined with low-order perturbation theory (PT) to treat ground state electron correlation. Two variants of the general scheme are discussed that differ in the type of amplitudes that are approximated perturbatively and which are treated to infinite order. The combined CC/PT methods to include ground state correlation are merged with equation-of-motion (EOM) and similarity transformed EOM methods to describe excitation spectra of the highly correlated s-tetrazine, MnO4− and Ni(CO)4 systems. It is shown that the computationally efficient CC/PT schemes can reproduce full CCSD results even if perturbation theory by itself is a very poor approximation, as is the case for many transition metal compounds. In a second test CC/PT is applied to determine ground state equilibrium molecular structures and harmonic vibrational frequencies for a set of small molecules. Using either variant of CC/PT, full CCSD geometries are easily recovered, while vibrational frequencies can be more sensitive to details of the approximation.
Constant pressure path integral molecular dynamics studies of quantum effects in the liquid state properties of n-alkanes
Authors: Balog E. , Hughes A. L. , Martyna G. J.
Published: July 2002

A computer simulation study of quantum effects in methane, butane, and octane is presented. Each molecular system is examined at three state points in the liquid region using novel extended system, multiple time step, constant pressure, path integral molecular dynamics methodology. In addition, the results of classical calculations are reported to provide a useful reference. Liquid butane is used as a test case on which to compare the predictions of two empirical force fields, CHARMM22 and AMBER95. Comparisons are made to experiment. Briefly, the models predict that quantum effects lead to an increase in molar volume of approximately 2 cm3/mole (i.e., relative to a classical calculation). However, a slight unphysical hydrogen–deuterium isotope effect is, also, observed. This may be caused by an incorrect parametrization of the anisotropy of the potential or by a reduction in the magnitude of the intermolecular induced dipole-induced dipole dispersion coefficient with increasing isotope mass that has not been parametrized in the force fields. In addition, the results show an interesting zero-point energy effect. The intramolecular regions of the radial distribution function exhibit less structure at lower temperatures than at higher temperatures. This is the inverse of the prediction of the model in the classical limit. The quantum effect occurs because the bulk density decreases faster than the intramolecular degrees of freedom lose zero-point energy as temperature increases in the highly harmonic intramolecular potential model employed in the calculations. Nonetheless, the phenomena is not likely to be an artifact and careful experiments could observe it. Finally, the efficiency of the path molecular dynamics methods employed in the studies are demonstrated on both serial and parallel computers.
Layering transition at the free surface of 12CB observed by scanning angle reflectometry
Authors: Sakamoto Naoto , Sakai Keiji , Takagi Kenshiro
Published: July 2002

The free surface of dodecylcyanobiphenyl (12CB) in its isotropic phase was observed by scanning angle reflectometry between 67.8 and 57.8 °C, the temperature slightly above the bulk phase transition temperature TIA. Reflectivities of both P- and S-polarized incident light were measured, and the magnitude of ellipticity coefficient |ρ̄| was calculated. |ρ̄| proved to have a steplike dependence on temperature. It suggests the quantized nature of layering, which has already been observed by x-ray reflectivity and ellipsometry studies. As temperature approaches TIA, two discrete transitions corresponding to the formation of a single additional layer were observed. On the other hand, refractive index of the sample liquid also measured at the above temperature range showed no such unusual temperature dependence. Thickness l of a single layer is estimated to be 3.42 nm by use of formulas based on geometrical optics together with some assumptions for the anisotropic optical properties of the molecule. Expressions for various reflectivities of light incident to the interface are briefly reviewed and comparison is made between ellipsometry and reflectometry.
The open shell single reference size-consistent self-consistent singles and doubles configuration interaction method: Application to ionization potentials
Authors: Pitarch-Ruiz J. , Sánchez-Marı́n J. , Maynau D.
Published: July 2002

In previous works, the size-consistent self-consistent matrix dressing method has been applied to single reference as well as to complete active space singles and doubles configuration interaction. The wave function of the dressed state was assumed to be dominated by a closed shell determinant. Here, the method has been extended to systems where the dressed state is a single-configurational doublet. The method allows for the accurate calculation of energies and wave functions of other electronic states of the same system, having or not the same symmetry, as well as in the case of closed shell systems. This statement has been thoroughly assessed by the calculation of vertical ionization energies corresponding to a few low lying states of HF+ that are compared to full CI results obtained with the cc-pVDZ basis set. The method has been applied, using larger basis sets, to the calculation of vertical ionization potentials (VIP) of HF, H2CO, N2, and NH3. The results are compared to experimental VIP values. The effects of selecting different CAS spaces and using pseudonatural adapted MO’s obtained from the CASSCF matrix densities are shown and discussed. Mean absolute error (MAE) for the calculated states is about 0.07 eV. The difficulties to improve this precision limit are shown. However, the mean signed absolute errors, that measure accuracy, can be made smaller. Small MAE can be obtained using simultaneously VTZ basis sets and intermediate levels of calculation. The possibility of this effect to be assigned to a fortuitous cancellation of errors is pointed out.
Determination of μ-v-j vector correlations in photodissociation experiments using 2+n resonance-enhanced multiphoton ionization with time-of-flight mass spectrometer detection
Authors: Pisano Patrick J. , Cline Joseph I.
Published: July 2002

A practical method is described for 2+n resonance-enhanced multiphoton-ionization probing of photofragment μ-v-j correlations arising in molecular photodissociation on a linearly polarized single-photon electric-dipole transition. The scheme uses polarized spectroscopy on the two-photon resonant transition with velocity detection by time-of-flight mass spectrometry. The technique is based on the theory of Kummel, Sitz, and Zare for polarized two-photon detection of angular momentum alignment and orientation and Dixon’s bipolar moment description of vector correlations. Optimal experimental and polarization geometries are described for selective measurement of targeted bipolar moments. The utility of the technique is demonstrated in experiments using 2+1 REMPI to probe methyl radical vector correlations in the 266 nm photodissociation of methyl iodide.
Correlation between charge-transfer complex formation and positional disorder in a binary donor–acceptor glass
Authors: Schreiber A. , Zilker S. J. , Haarer D.
Published: July 2002

We report on a novel binary glass consisting of an electron donor and an electron acceptor molecule. It contains up to 25% of charge-transfer complexes and displays excellent hole as well as electron transport properties. Charge carrier mobilities have been measured by time-of-flight for various donor–acceptor ratios and are discussed within the framework of the disorder model of Bässler and co-workers. The results demonstrate that the presence of the donor molecules has no influence on the electron transport properties. In contrast to this, the hole transport is apparently affected by dipolar interactions between donor and acceptor molecules. Surprisingly the highest nondiagonal disorder for hole transport of about Σ=5 is found in samples with similar amounts of donor and acceptor indicating that the formation of charge-transfer complexes causes additional positional disorder.
Optimal annealing schedules for two-, three-, and four-level systems using a genetic algorithm approach
Authors: White Ronald P. , Mayne Howard R.
Published: July 2002

An annealing schedule, T(t), is the temperature as function of time whose goal is to bring a system from some initial low-order state to a final high-order state. We use the probability in the lowest energy level as the order parameter, so that an ideally annealed system would have all its population in its ground-state. We consider a model system comprised of discrete energy levels separated by activation barriers. We have carried out annealing calculations on this system for a range of system parameters. In particular, we considered the schedule as a function of the energy level spacing, of the height of the activation barriers, and, in some cases, as a function of degeneracies of the levels. For a given set of physical parameters, and maximum available time, tm, we were able to obtain the optimal schedule by using a genetic algorithm (GA) approach. For the two-level system, analytic solutions are available, and were compared with the GA-optimized results. The agreement was essentially exact. We were able to identify systematic behaviors of the schedules and trends in final probabilities as a function of parameters. We have also carried out Metropolis Monte Carlo (MMC) calculations on simple potential energy functions using the optimal schedules available from the model calculations. Agreement between the model and MMC calculations was excellent.
Calculations of the dynamics of phase-locked vibrational wave packets in Na2+: Young’s double slit experiment in a molecule
Authors: Stavros V. G. , Fielding H. H.
Published: July 2002

The formation of specific target states in Na2+ is investigated using phase-locked femtosecond pulse sequences. The pulse sequences generate customized vibrational wave packets whose motion can be interpreted using classical physics. It is shown that, if two vibrational wave packets are initially excited at either end of the vibrational coordinate, changing the initial phase difference between them can have a profound effect on the subsequent dynamics. In particular, the choice of phase differences (2π, π, −π/2 or π/2) has a dramatic effect on the dynamics around the times of the second and fourth order partial revivals. The results are interpreted quantitatively using knowledge of the phase differences between components of fractional revivals evolving from a single wave packet. Finally, we discuss a novel detection technique for monitoring vibrational wave packet dynamics in molecular cations, which combines phase-modulated detection methods borrowed from Rydberg electron wave packet experiments and zero-kinetic energy pulsed-field ionization borrowed from high-resolution spectroscopy.
Pressure-induced volume phase transition of polyacrylamide gels in acetone–water mixtures
Authors: Kato Eiji
Published: July 2002

Equilibrium swelling curves of ionized polyacrylamide gels immersed in acetone–water mixtures were measured as a function of pressure up to pressures of 300 MPa. The gels, which shrank at atmospheric pressure, underwent an abrupt volume change (pressure-induced volume phase transition) from a shrunken state to a swollen state at the transition pressure. The transition pressure increased with an increase of acetone concentration. The pressure-induced volume phase transition can be interpreted by taking account of the free-energy change ΔV⋅P between swollen (hydrated) and shrunken (dehydrated) states. The ΔV represents the difference between the molar volume of water structured around hydrophilic groups of polyacrylamide chains and that of free water in the bulk mixtures. The estimated value of ΔV is −3.3 mL/mol, which qualitatively agrees with that obtained from the experiments of denaturation of proteins. The pressure-induced volume phase transition is generally expected in many hydrogels.
On the convergence of global thermal properties of clusters extracted from simulations
Authors: Calvo F. , Guet C.
Published: July 2002

Using standard classical molecular dynamics, we calculate the complete caloric curves of various metallic, ionic, or van der Waals clusters of different sizes. The apparent melting temperature is shown to be shifted to upper values as the simulation length τ is decreased. The shift ΔTmelt roughly scales as Nα/τβ, where N is the number of particles, α is about 0.6, and β is about 2.1.
Random walk representations for spinor and vector propagators
Authors: Jacobson Ted
Published: July 2002

A Euclid-invariant random walk representation for spin- 1/2 and vector propagators is developed in analogy to random walks with internal states.
On the zeros of the dispersion function in particle transport theory
Authors: Bowden R. L.
Published: July 2002

The zeros of the dispersion function that arise in particle transport with anisotropic scattering are studied. An algebraic test for the number of zeros is presented.
Partition functions of the quark–gluon black body and density of states
Authors: Auberson G. , Epele L. , Mahoux G. , Simão F. R. A.
Published: July 2002

The problem of the determination of the asymptotic density of states of the quark–gluon gas is reconsidered. A general method emerges, which unifies and simplifies previous derivations that can be found in the literature. It takes due account of various constraints on the configurations of the system: colorlessness, conservation of electric and baryonic charges, zero total momentum, and possibly some residual flavor symmetry. It is general enough to accommodate any constraint associated to a compact Lie group. This is shown in full detail in the case of a direct product of SU(N) groups. Explicit examples are completely worked out.
Thermodynamics and molecular freedom of dimers on plane triangular lattices
Authors: Phares Alain J. , Wunderlich Francis J.
Published: July 2002

This is an extension of three previous papers dealing with dimers on rectangular lattices (one, two, and three dimensions). The technique presented in the first paper in this series continues to be fruitful for dimers on plane triangular lattices. Entropy, isothermal compressibility, constant pressure heat capacity, and molecular freedom per dimer at close packing are obtained exactly for lattices infinite in one direction and finite in the other. Observations made in the third paper of the series concerning molecular freedom per dimer at close packing on rectangular lattices are used to extrapolate our results to infinite plane triangular lattices. At close packing, the molecular freedom per dimer on an infinite plane triangular lattice is calculated to be 2.356 527... in agreement with the value obtained by Nagle. Based on our earlier findings, the value of 2.356 527... was used to obtain the analytic fit for the thermodynamic quantities in terms of the normalized number density.
Local properties of quantum systems
Authors: Leaf Boris
Published: July 2002

Local properties of a quantum system are defined as the expectation values of its observables in a microstate of some complete set of commuting observables. An equation for the time evolution of local properties is obtained for any system whose statistical operator (density matrix) evolves by unitary transformation in accordance with the von Neumann equation. The formalism is applied to the example of a system of one particle. In this case the local properties are fields, the time-evolution equation is an equation of continuity with source terms. For constants of motion the source terms vanish, giving equations of continuity for the fields. For each scalar field a flux vector for its transport current is defined. For momentum, a stress tensor is obtained. The effects on local properties of realization of a latent ensemble of the statistical operator (an entropy-increasing mechanism recently proposed to explain approach to equilibrium) are also considered; a non-negative local entropy production is identified, as well as a discontinuous redistribution of local properties among microstates.
Relaxation of the Dicke maser model
Authors: Goderis D. , Verbeure A. , Vets P.
Published: July 2002

For the Dicke maser model the approach to equilibrium for a quantum version of a detailed balance evolution is studied rigorously. The exponential decay with a relaxation time of the order ‖T−Tc‖−1 for T≤Tc is proved. A complete spectral resolution of the evolution is obtained.
Solitary wave solutions of a system of coupled nonlinear equations
Authors: Guha-Roy C.
Published: July 2002

A class of coupled nonlinear wave equations is presented. It is shown that the coupled equation possesses solitary wave solutions. Some comments are made on the previously obtained solutions of a similar class of equations.
Perturbative results from the 1/N expansion for screened Coulomb potentials
Authors: Lai C. H.
Published: July 2002

The energy eigenvalues for the Hulthén, Yukawa, and exponential-cosine screened Coulomb potentials are calculated in the 1/N expansion. States with up to three nodes in the wave functions are considered. We obtain the perturbative results up to the order of λ8, where λ is the screening parameter.
Relativistic Coulomb Sturmian matrix elements and the Coulomb Green’s function of the second-order Dirac equation
Authors: Hostler Levere
Published: July 2002

Matrix elements with respect to a discrete ‘‘Sturmian’’ basis set of the operator r1/2gr1/2, where g is the Coulomb Green’s function of the ‘‘second-order’’ Dirac equation, are investigated. Closed expressions, involving Gaussian hypergeometric functions, can be obtained for the matrix elements. This calculation illustrates contour integration techniques capable of yielding closed expressions for a number of overlap integrals associated with the relativistic Kepler problem.
Gauge group cohomology in the monopole sector of Yang–Mills theories
Authors: Bakas I. , McMullan D.
Published: July 2002

The theory of Chern–Simons secondary characteristic classes is used to study the gauge group cohomology associated with Yang–Mills theories in sectors with persistent boundary effects. A generalized ‘‘descent’’ tower of globally defined cocycles (for manifolds with boundaries) is adopted and its relevance to monopole physics is investigated by means of the Christ–Jackiw interpretation for Yang–Mills dyons. In particular, it is found that three-cocycles can arise in the monopole sector of gauge theories and explicit formulas are derived for their description.
On the monotonic dependence of atomic excitation energies on the nuclear charge parameter Z
Authors: Hogreve H.
Published: July 2002

The dependence of atomic excitation energies, i.e., differences of two energy levels, on the nuclear charge parameter Z is examined. For various transitions of heliumlike atoms the associated excitation energies are shown to be monotonic functions of Z. These results and physical arguments suggest the conjecture that such a monotony is a general fact in the nonrelativistic Schrödinger theory of atoms. The proofs given here use upper and lower energy bounds that for two-electron systems are available as explicit expressions in closed form.
Geometrical classification scheme for weights of Lie algebras
Authors: Capps Richard H.
Published: July 2002

Every weight of a Lie algebra belongs to one particular Weyl orbit. The depth within an orbit has been defined as the minimum number of Weyl reflections associated with simple roots that are necessary to transform the weight into the dominant weight of the orbit. A simple set of classification parameters that measures the depth and distinguishes between different weights of the same depth is introduced. The parameters are geometrical in that they are related directly to the orientation of the weight vector. They correspond to a particular member of the Weyl group that transforms the weight into the dominant weight. A simple rule is given for listing all the weights of an orbit in terms of the parameters.
Solutions of the wave equations with boundary conditions on the hyperplane z−c
t=0
Authors: Hillion P.
Published: July 2002

The boundary value problem for the wave equation is discussed with data φ(r) on the hyperplane z−ct=0. We give the general form of the solution when φ(r) is an entire function of r2 of order 1 and type 0<τ<∞. As a particular case the focus wave mode solutions of the wave equation are obtained.
The derivation of the regularized chiral Jacobian using the zeta function method
Authors: Wang Rong-tai
Published: July 2002

Using the zeta function method, a general formula for the regularized chiral Jacobian to theories including non-Hermitian Dirac operators 𝒟 defined in arbitrary even-dimensional Euclidean space is derived. The agreement of this formula with the results obtained in the differential geometric approach is also clarified.
World sheet diffeomorphisms and the canonical string
Authors: Kuchař K. V. , Torre C. G.
Published: July 2002

The degree to which the phase space of a closed bosonic string carries a representation of the two-dimensional diffeomorphism group Diff(M) is investigated. In particular, homomorphic mappings from the associated Lie algebra diff(M) into the Poisson algebra of functions on three natural phase spaces associated with the string are constructed. Two of these spaces are extended phase spaces based on the conformal and harmonic gauges, respectively. The third space is essentially the original phase space; the homomorphism in this case relies on the validity of the light-cone gauge. Homomorphisms from diff(M) into the extended phase spaces of the Batalin–Fradkin–Vilkovisky formalism are also constructed. While the methods used to represent diff(M) cannot be extended to represent all of Diff(M), the phase spaces do carry a representation of the subgroup of conformal isometries. It is argued that this subgroup is sufficiently large to serve as the dynamical group for the string. The implications of this work for a true Dirac quantization of the string via operator representations of diff(M) are discussed.
Singularly perturbed Chern–Simons theory
Authors: Nash Charles
Published: July 2002

The Chern–Simons theory of an SU(2) gauge theory in three dimensions is looked at from a perturbative point of view. The pure Chern–Simons action is generalized by adding a conventional Yang–Mills action term. This acts as a singular perturbation. The resulting theory has a moduli space containing that of the pure Chern–Simons version; for certain discrete values of the perturbation parameter lying in the spectrum of an appropriate elliptic operator the enlargement of the moduli space can be made explicit. The extrema can be classified by a Hessian with a finite index and nullity without recourse to spectral flow. Corrections to the resultant quantum theory are also calculated. Also, the quantum theory of the present model should be better behaved than in the unperturbed case.
The Fock representation of osp(∞‖∞) and the orthogonal symplectic super KP hierarchy
Authors: Ikeda Kaoru
Published: July 2002

The Fock representation of the Lie superalgebra osp(∞‖∞), from which is derived the super boson–fermion correspondence of osp(∞‖∞) is discussed. Solutions of the OSp–SKP hierarchy in terms of the neutral super free fermions are constructed.
A new approach to global stability analysis of one-dimensional continuous dissipative systems
Authors: Santamato E. , Abbate G. , Maddalena P.
Published: July 2002

It is proved by a direct construction that symmetry-breaking instabilities in one-dimensional dissipative continuous systems can be studied in terms of a suitable function G whose minima correspond to stable steady states of the system, while other extremal points correspond to unstable states. The existence of such a function is proved for a large class of continuous dissipative physicochemical systems in one spatial dimension. The function G is exact, in the sense that it is obtained by taking into account all nonlinear terms in the evolution equations of the system. Since in some respect this function has properties similar to the Ginzburg–Landau function widely used in second-order phase transitions, it is called the nonlinear Ginzburg–Landau function (NLGLF) of the system. The NLGLF may be useful for studying the global stability under symmetry-breaking conditions as well as the character (first and second order) of the transitions between different steady states. The construction of the NLGLF usually requires simple numerical or analytical calculations. A specific example, taken from the physics of liquid crystals, has been worked out analytically in the present paper.
Stability analysis of the Yagle–Levy multidimensional inverse scattering algorithm
Authors: Cheney Margaret
Published: July 2002

A layer-stripping algorithm suggested by Yagle and Levy for solving a multidimensional inverse scattering problem is analyzed. It is shown that the unfiltered version of the algorithm is unstable; for the filtered version, it is proven that the reconstruction depends continuously on the data.
Nonspurious harmonic oscillator states in single particle coordinates
Authors: Novoselsky Akiva , Katriel Jacob
Published: July 2002

A procedure for the construction of nonspurious harmonic oscillator wave functions with arbitrary permutational symmetry has recently been proposed. The resulting wave functions are expressed in terms of normalized Jacobi coordinates, and involve a new type of harmonic oscillator coefficients of fractional parentage. A simple algorithm to transform these states from the Jacobi coordinates to the single particle coordinates is presented. This is a generalization to an arbitrary number of particles of the harmonic oscillator transformation from center-of-mass and relative coordinates to single particle coordinates.
Future null infinity of Robertson–Walker space-times
Authors: Moreschi Osvaldo M.
Published: July 2002

The future null infinity for all noncontracting Robertson–Walker space-times is studied systematically. A theorem is proved that establishes the expected relation between the nature of ℐ+ and the appearance or absence of cosmic event horizons.
Lagrange multipliers and Gauss–Bonnet-type invariants in Riemann–Cartan space
Authors: de Azeredo Campos R.
Published: July 2002

A Lagrange multiplier approach is applied to Gauss–Bonnet-type invariants in Riemann–Cartan geometry. Lanczos-type identities are then derived. The use of the variational procedure in the context of gravitational theories with a Gauss–Bonnet invariant limit is discussed.
Deformations of complex structures and conformal field theories on Riemann surfaces
Authors: Guadagnini E. , Martellini M. , Mintchev M.
Published: July 2002

The role of complex structure deformations in representing the Virasoro algebra associated to any conformal field theory on a genus p≥1 compact Riemann surface is investigated.
Lorentz action on the space of relative velocities and relativity on a three-manifold
Authors: Sen D. K.
Published: July 2002

The space of relative velocities in special relativity has a three-dimensional hyperbolic structure. This provides not only a geometric interpretation of the Einstein velocity addition law, but also a purely three-dimensional reformulation of both special and general relativity on a three-manifold whose tangent bundle is endowed with a hyperbolic distance function on each fiber. Here the basic concepts are that of local physical observers and local time in terms of nonsingular vector fields and their local flows. The hyperbolic structure on the tangent space enables one to define a relative velocity function between two physical observers, as well as space and time measurements and inertial physical observers. It is possible to rederive Lorentz time dilation and gravitational and cosmological redshifts and reformulate Maxwell (or Yang–Mills) equations in a purely three-dimensional framework instead of the traditional four-dimensional space-time approach.
State function and spectral properties of a two-component interacting Fermi gas
Authors: McGuire J. B.
Published: July 2002

Rules are derived for the computation of the spectrum and state function of a system of N fermions in one dimension interacting with a delta function potential. The system is composed of fermions of two types of internal symmetry. The rules are valid for an arbitrary number of either symmetry type and any value of the delta function interaction strength. The state functions satisfy periodic boundary conditions, and therefore describe the interacting system at nonzero density.
New class of nonlinear realizations of extended graded anti-de-Sitter supersymmetry OSP (N,4), N≥2
Authors: Mozrzymas M.
Published: July 2002

The nonlinear realizations of N-extended graded anti-de-Sitter supersymmetry with three different ways of splitting into linearly and nonlinearly realized sectors of OSP (N,4) superalgebra are considered. Nonlinear transformation laws are derived for Goldstone fermions and Goldstone scalars that describe a spontaneously broken sector in extended anti-de-Sitter supersymmetry. Cartan forms on the supercosets are derived and corresponding nonlinear Lagrangians for Goldstone fermions and scalars in anti-de-Sitter space are constructed. The contraction of OSP (2N,4) supersymmetry to Poincaré supersymmetry with central changes is discussed.
A theorem on essential self-adjointness with application to Hamiltonians in nonrelativistic quantum field theory
Authors: Arai Asao
Published: July 2002

An abstract theorem is given on essential self-adjointness of operators in infinite direct sum of Hilbert spaces and is applied to a class of Hamiltonians in nonrelativistic quantum field theory to prove their essential self-adjointness.
Low-temperature smoothness of the pressure for antiferromagnets and other models
Authors: Klein David , Yang Wei-Shih
Published: July 2002

Under certain conditions on a grandcanonical Hamiltonian, it will be proven that at low temperature the pressure is infinitely differentiable with respect to the inverse temperature and other parameters in the Hamiltonian, when the parameters are chosen so that the number of extremal Gibbs states is at least equal to the number of ground states. Applications are made to antiferromagnets and hard-core gases.
Long-time behavior of an electron interacting with a quantized radiation field
Authors: Arai Asao
Published: July 2002

The long-time behavior of an electron coupled to a quantized radiation field is discussed in the ground state and in equilibrium states at finite temperatures. The electron is not confined in an external potential. The model used is a d-dimensional extension of a standard model (the Pauli–Fierz model) in nonrelativistic quantum electrodynamics: The electron moves in Rd (d≥2) and the radiation field is over Rd. Further, the energy function ω of one free photon is taken to be a general one. In defining the interaction part of the Hamiltonian of the model, an ultraviolet cutoff is introduced for photon momenta with a cutoff function ρ̂ and the dipole approximation is used. It is proved that at each finite temperature T>0, the mean-square displacement of the electron behaves like (kBTd/m)t2 as time t tends to infinity, where kB is the Boltzmann constant and m>0 is a renormalized mass of the electron which should be identified with the observed mass of the electron. The long-time asymptotics of the mean square displacement of the electron in the ground state is different from that at the finite temperatures; it depends on the space dimension d and on the infrared behavior of ω and ρ̂.
Asymptotic hadron spectrum in the M.I.T bag model
Authors: Savatier F.
Published: July 2002

The asymptotic hadron spectrum within the M.I.T. bag model is computed. The influence of color is studied and the quark flavors are taken into account in a simple but realistic manner.
The general symmetry algebra structure of the underdetermined equation u
x=(v
x
x)2
Authors: Kersten Paul H. M.
Published: July 2002

In a recent paper, Anderson, Kamran, and Olver [‘‘Interior, exterior, and generalized symmetries,’’ preprint (1990)] obtained the first- and second-order generalized symmetry algebra for the system ux=(vxx)2, leading to the noncompact real form of the exceptional Lie algebra G2. Here, the structure of the general higher-order symmetry algebra is obtained. Moreover, the Lie algebra G2 is obtained as ordinary symmetry algebra of the associated first-order system. The general symmetry algebra for ux=f(u,v,vx,...,) is established also.
The massive scalar field propagator on finite lattices
Authors: Gibbs Richard L.
Published: July 2002

The propagator for the massive free scalar field is calculated for an arbitrary dimension on a finite lattice. The specific boundary conditions are shown, energy dispersion relation found, and applications to self-interacting fields are made. The weak and strong coupling expansions for self-interacting fields are discussed for the finite lattice. A few comments are made in regard to Monte Carlo simulations on finite lattices.
Unitarizable massless fields of higher order and higher spin
Authors: Heidenreich W. F.
Published: July 2002

Explicit Fock spaces for massless multispinors and tensors satisfying ⧠nΨ=0 are constructed. It is found that they carry indecomposable representations which allow Gupta–Bleuler type quantization. For symmetric tensors and odd n there is a unitary space of physical states.
Multivectorial generalization of the Cartan map
Authors: Keller Jaime , Rodríguez-Romo Suemi
Published: July 2002

A multivectorial generalization of the spinors to vectors Cartan map is constructed, with space-time as a base space, constructed from spinors (Dirac spinors and spinors pairs being particular cases) onto a multivector space with two internal symmetries: one of them is the fundamental space-time Clifford group 𝒞(1,3) and the other an ‘‘isotopic space’’ (in multivectorial representation) related with the more common gauge groups. The algebraic properties of this map and of the operators representing observables are studied. The inversion map is also presented. The quaternion projection of the map is shown as are its properties and its mathematical and physical meaning. The procedure presented here is compared with other spinor-vector maps used in the literature.
Multiresolution properties of the wavelet Galerkin operator
Authors: Lawton Wayne M.
Published: July 2002

This paper extends recent results by the author [J. Math. Phys. 31, 1898 (1990), J. Math. Phys. 32, 57 (1991)] that show a scaling parameter sequence h yields an orthonormal wavelet basis for L2(R) if and only if an associated operator Sh has eigenvalue 1 with multiplicity 1. The operator transforms a sequence a by Sh(a)(k)=2Σm,n∼(h(m))h(n)a(2k+m−n). A correspondence is derived between Sh and Galerkin projection operators related to the multiresolution analysis defined by the orthonormal wavelet basis. The spectrum of Sh is characterized in terms of the Fourier modulus of the (unique) scaling function φ that satisfies φ(x)=2Σnh(n)φ(2x−n). This characterization yields several results including a direct, alternate proof that the eigenvalue 1 of Sh has multiplicity 1.
The Baker–Campbell–Hausdorff formula and nested commutator identities
Authors: Oteo J. A.
Published: July 2002

The coefficients of the Baker–Campbell–Hausdorff expansion are calculated by using various methods. Comparison of the results yields several remarkable identities satisfied by multiple commutators, which, in turn, allow us to greatly simplify the form of the expansion up to order eight.
Analytic solution to the Thomas–Fermi and Thomas–Fermi–Dirac–Weizsäcker equations
Authors: Tu Khiet
Published: July 2002

A novel method for solving the Thomas–Fermi and Thomas–Fermi–Dirac–Weizsäcker equation at zero temperature is explored. The fitting formulas for the effective potential and the electron density derived from this theory can serve as appropriate initial input to various computer codes designed to analyze the statistical model of atoms and molecules. One of the important parametrizations for the Thomas–Fermi–Dirac–Weizsäcker equation is that the density at the center of the atom is finite and proportional to the cube of the atomic number with a constant of proportionality nearly equal to 6.87.
On the geometrical structure of covariant anomalies in Yang–Mills theory
Authors: Kelnhofer Gerald
Published: July 2002

Covariant anomalies are studied in terms of the theory of secondary characteristic classes of the universal bundle of the Yang–Mills theory. A new set of descent equations is derived which contains the covariant current anomaly and the covariant Schwinger term. The counterterms relating consistent and covariant anomalies are determined. A geometrical realization of the Becchi–Rouet–Stora (BRS)/anti-BRS algebra is presented which is used to understand the relationship between covariant anomalies in different approaches.
Projection operator technique for imposing the boundary conditions on a trial wave function
Authors: Brownstein K. R.
Published: July 2002

A projection operator technique is developed for using N linear basis functions which do not satisfy the boundary conditions. If the boundary conditions at M locations on the boundary are invoked via M constraint equations, the method leads to an N-by-N determinantal equation which is of the generalized eigenvalue form. Of the N roots, N−M serve as approximations to the lowest N−M exact energy eigenvalues while the remaining M roots are degenerate at a predetermined value.
Monogenic continuation for vector fields
Authors: Auberson G.
Published: July 2002

Using Clifford analysis, the reproducing kernel leading to the solution of stabilized extrapolation problems for divergenceless, irrotational, vector fields in a ball is constructed.
An intrinsic tensor technique in Minkowski space with applications to boundary value problems
Authors: Borzdov George N.
Published: July 2002

This article describes an intrinsic tensor technique for solving boundary value problems in electrodynamics of moving media, which entails considerable notational simplification and calculational advantages. On the basis of generalized impedance and characteristic matrix methods, the reflection and transmission operators of a multilayer structure consisting of anisotropic media uniformly moving with different velocities are found. A general solution to the problem of reflection and transmission at the interface between two moving isotropic media is obtained, and explicit expressions for Doppler shifts, Snell’s laws, critical and Brewster angles, reflection and transmission coefficients, and the radiation pressure force are found. The material tensor of a uniformly moving linear medium is expressed through its reflection and transmission operators.
Q rotations and other Q transformations as unitary nonlinear automorphisms of quantum algebras
Authors: Zhedanov A. S.
Published: July 2002

For the quantum algebras with three generators [SUq(2), SUq(1,1), q oscillator and others] the unitary operator U(s;q) is found in terms of q exponents from algebra’s generators. Being the q analog of the linear automorphism for the Lie algebras, the operator U(s;q) is shown to generate nonlinear automorphisms of the quantum algebras (q rotations, q shifts, Bogoliubov q transformations, etc.). The matrix elements Tnn′ of the operator U(s;q) are explicitly expressed in terms of Askey–Wilson polynomials. The operator U(s;q) is shown to give rise the new systems of q-coherent states of the quantum algebras.
Path integrals in N=2 supersymmetric quantum mechanics
Authors: Corns R.
Published: July 2002

By use of path integrals in N=2 supersymmetric quantum mechanics, a formula for the kernel of the supersymmetric time evolution operator is found. Structurally it is similar to the Feynman–Kac formula used in the path integrals of quantum mechanics. Crucial to the development of this formula is a generalization of the Wiener measure based upon the free supercharges rather than the free Hamiltonian.
A theorem on light-front quantum models
Authors: Polyzou Wayne N.
Published: July 2002

A sufficient condition for a relativistic front-form quantum mechanical model to be scattering equivalent to a relativistic front-form quantum model with an interaction-independent front-form spin is given.
Rings, quadratic forms, and complete degeneracy for a subclass of highly overmoded rectangular waveguides
Authors: Overfelt P. L.
Published: July 2002

In this article eigenvalue degeneracy formulas for a subclass of highly overmoded rectangular waveguides are determined. This subclass consists of those rectangular geometries with side length ratio, a/b, equal to the square root of a rational integer, √σ, σ∈Z, and contains an unusual amount of degeneracy even when the side length ratio is irrational. The complete degeneracy for members of this subclass (σ<10) is determined by interpreting its normalized eigenvalue formula as (a) the norm of an associated ring of algebraic integers and (b) a special case of a positive definite binary integral quadratic form.
Fermion mass generation at finite temperature
Authors: Romeo August
Published: July 2002

The finite temperature correction to the electron mass in a quantum electrodynamics framework is computed in the high-temperature regime by Matsubaralike sums. As pointed out by other authors, it is confirmed that the leading term is of the type ΔM∝T, contrary to what one might expect by naïve reasonings.
Two-body Dirac equation with diagonal central potentials
Authors: Semay C. , Ceuleneer R. , Silvestre-Brac B.
Published: July 2002

Solutions of the two-body Dirac equation with diagonal central potentials are investigated, both for particle–particle and particle–antiparticle cases. A detailed study of the symmetry properties of the solutions is carried out for systems composed of identical or massless particles. The Klein paradox is discussed and several solutions relevant to the study of the quarkonium are presented.
Totally vicious space-times
Authors: Kim Jong-Chul , Kim Jin-Hwan
Published: July 2002

The concepts of Δ-symmetry and local reflectability in space-times are introduced which are weaker conditions than the reflecting condition. Using these concepts, some characterizations for total viciousness are given. It is shown that any locally reflecting space-time with a closed timelike curve is totally vicious. Also, it is shown that any compact homogeneous space-time is totally vicious.
Tensor operators and Clebsch–Gordan coefficients of the quantum algebra suq(1,1)
Authors: Aizawa N.
Published: July 2002

Two kinds of suq(1,1) tensor operators are considered. One of them carries a nonunitary finite dimensional representation of suq(1,1), and the other carries a unitary infinite dimensional representation. Explicit formulas of the former tensor operators are constructed and a useful formula to calculate the matrix elements of rank 1 tensors is derived. By making use of the q analog of the Wigner–Eckart’s theorem, the Clebsch–Gordan coefficient can be extracted from the matrix element of a tensor operator. Explicit formulas of three kinds of the suq(1,1) Clebsch–Gordan coefficients are given, that is, the Clebsch–Gordan coefficient which couples two (non) unitary representations to get the third (non) unitary representation, and the one which couples a nonunitary and a unitary representations to get a new unitary representation. It is shown that these Clebsch–Gordan coefficients and the one of suq(2) can transmute one another by the appropriate replacement of their variables. It is further shown that, by using this property, various recoupling coefficients of suq(1,1), such as 6-j and 9-j symbols, can be directly obtained from the corresponding ones of suq(2).
Coherent states for the quantum complex plane
Authors: Kowalski K. , Rembielinski J.
Published: July 2002

The coherent states for the quantum complex plane are introduced. It is demonstrated that the Bargmann representation corresponding to these states involves both the standard integral with respect to the Gaussian measure and the Berezin integral over Grassmann variables. The quantum generalizations of many constructions developed for classical coherent states are described.
Constrained time-dependent Lagrangian systems and Lagrangian submanifolds
Authors: de León Manuel , Marrero Juan C.
Published: July 2002

In this paper a description, à la Tulczyjew, of constrained time-dependent dynamical systems in terms of special symplectic manifolds is first developed. Next, this description is combined with the constraint algorithm for time-dependent constrained systems.
Non-Abelian solitons in two-dimensional lattice field theories
Authors: Müller V. F.
Published: July 2002

For a class of self-interacting multicomponent scalar field theories with a global discrete non-Abelian symmetry group, mixed order–disorder correlation functions are defined in terms of Euclidean functional integrals. These correlation functions satisfy Osterwalder–Schrader positivity. From a representation of the correlation functions in terms of the transfer matrix, the dual algebra at fixed time is derived. This algebra implies parafermion operators showing non-Abelian braid group statistics. In a pure phase of spontaneous symmetry breaking for a related class of order–disorder correlation functions a convergent polymer representation is developed, emerging from a combined low- and high-temperature-type expansion. The infinite volume correlation functions of this class show exponential clustering in the disorder fields.
The complete reduction of Clifford algebras
Authors: Bergdolt G.
Published: July 2002

The complete reduction of simple Clifford algebras is spanned by matrix bases. Considered as generators of an algebra the basis elements pij satisfy the product relations pijpkl= δjkpil. It follows that subsets of pij with subscript or superscript fixed span minimal left or right ideals. The expression of the basis elements pij in the usual multivector basis is derived from isomorphic matrix algebras. Spinors and Hermitian conjugate spinors are defined as members of minimal left and right ideals. Spinor scalar products are defined, these scalar products are in fact scalar multiples of an idempotent.
Commutator expansion of the self-energy operator for an electron in an external potential
Authors: Hostler Levere
Published: July 2002

Techniques of Erickson and Yennie [Ann. Phys. N.Y. 35, 271 (1965)] are applied in an investigation of a simple Taylor’s series which involves products of commutators and nested commutators and which represents the self-energy operator Σ of an electron in an external potential. A technique of ‘‘moving the parameter integrals to the mass’’ leads to a relatively simple representation of all terms as a one-dimensional integral over a common virtual electron mass squared parameter. Although not a true expansion in powers of the external field, the method provides a window on the higher-order terms in the self-energy operator. Mass eigenfunction expansion concepts are shown to be quite useful in a discussion of infrared divergences.
Even and odd symplectic and Kählerian structures on projective superspaces
Authors: Khudaverdian O. M. , Nersessian A. P.
Published: July 2002

Supergeneralization of CP(N) provided with even and odd Kählerian structures from Hamiltonian reduction are constructed. Operator Δ, which is used in Batalin–Vilkovisky quantization formalism and mechanics, which are bi-Hamiltonian under corresponding even and odd Poisson brackets, are considered.
Kinking number and the Hopf index theorem
Authors: Low Robert J.
Published: July 2002

The various definitions of kinking number that have been used are examined and compared, and a general definition is proposed. A generalization of Hopf’s index theorem is given.