bluuebunny/crossref_metadata_2025 huggingface dataset:
Electron–hole pair excitation in molecule–surface collisions
Authors: Billing Gert D.
Published: July 2002

We investigate the role of electron–hole pair excitation in molecule–surface collisions by using a semiclassical model which incorporates coupling to phonons and electrons in the substrate. The model treats the dynamics of the incoming molecule by classical mechanics but quantizes the phonons and electrons using second quantization techniques. We find that neither phonons nor electron–hole pair excitation can be neglected for an accurate description of molecule–surface collisions.
Resonant two-photon ionization spectroscopy of jet-cooled PtSi
Authors: Shao Lian , Sickafoose Shane M. , Langenberg Jon D. , Brugh Dale J. , Morse Michael D.
Published: July 2002

Jet-cooled diatomic PtSi, produced in a laser ablation supersonic expansion source, has been spectroscopically investigated between 17 400 and 24 000 cm−1 by resonant two-photon ionization spectroscopy. Two vibrational progressions are observed and identified as the [15.7]Ω′=1←X 1Σ+ and [18.5]Ω′=1←X 1Σ+ band systems. Three bands in the former system and six bands in the latter system were rotationally resolved and analyzed, leading to bond lengths of re′=2.1905(13) Å and re′=2.2354(3) Å for the [15.7]Ω′=1 and [18.5]Ω′=1 states, respectively. The Ω″=0 ground state of PtSi is assigned as a 1Σ+ state, in agreement with previous work and with the assigned ground states of the isovalent NiC, PdC, PtC, and NiSi molecules. The ground state bond length of PtSi is given by r0″=2.0629(2) Å. A Rydberg–Klein–Rees analysis of the ground and excited state potential energy curves is presented, along with a discussion of the chemical bonding and a comparison to the isoelectronic molecule, AlAu. Evidence is presented for a double bond in PtSi, as opposed to a single bond in AlAu.
Competition between photochemistry and energy transfer in ultraviolet-excited diazabenzenes. I. Photofragmentation studies of pyrazine at 248 nm and 266 nm
Authors: Sevy Eric T. , Muyskens Mark A. , Rubin Seth M. , Flynn George W. , Muckerman James T.
Published: July 2002

The quantum yield for the formation of HCN from the photodissociation of pyrazine excited at 248 nm and 266 nm is determined by IR diode probing of the HCN photoproduct. HCN photoproducts from excited pyrazine are produced via three different dissociation channels, one that is extremely “prompt” and two others that are “late.” The total quantum yield from all reaction channels obtained at low quencher gas pressures, φ=1.3±0.2 for 248 nm and 0.5±0.3 for 266 nm, is in agreement with preliminary studies of this process as well as recent molecular beam studies. To investigate if HCN production is the result of pyrazine multiphoton absorption, this photodissociation process has been further studied by observing the HCN quantum yield as a function of total quencher gas pressure (10 mTorr pyrazine, balance SF6) and as a function of 248 nm laser fluence from 2.8 to 82 mJ/cm2. At the highest SF6 pressures, the HCN quantum yield shows strong positive correlation with laser fluence, indicating that the “prompt” channel is the result of multiphoton absorption; however, at low pressure, the HCN quantum yield is affected little by changing laser fluence, indicating that the majority of the HCN photoproducts at low pressure are produced from pyrazine which has absorbed only one UV photon. At the lowest pressures sampled, HCN produced from the one-photon “late” process accounts for more than 95% of all HCN formed (at low laser fluence). At high pressures the single photon “late” pyrazine dissociation is quenched, and HCN produced at high quencher gas pressures comes only from the multiphoton absorption channel, which can be clearly observed to depend on laser fluence. The HCN quantum yield as a function of laser intensity at high pressure has been fit to a quadratic function that can be used to determine the amount of “prompt” “unquenched” HCN produced from multiphoton photodissociation. Additionally, the information theoretic prior functions for energy disposal in the 248 nm photodissociation of pyrazine to form HCN have also been developed. Prior functions for one, two, and three-photon absorption indicate that only HCN with near room temperature translational energy comes from the one-photon process and that all HCN molecules with large amounts of translational energy are produced by multiphoton processes. Finally, analysis of the quenching data within the context of a strong collision model allows an estimate of the rate constant for HCN production from pyrazine for the major “late” channel, kd1s=1.69×105 s−1, for 248 nm excitation, and kd1s=1.33×104 s−1 for 266 nm excitation. After 266 nm excitation, pyrazine produced by the major one-photon channel lives for almost an order of magnitude longer than after 248 nm excitation.
Electron transfer via interaction with a polar medium: Modulation and solvation
Authors: Tibbets David A. , Dakhnovskii Yuri
Published: July 2002

Electron transfer is studied in a solvent having two independent sets of polar modes. One set modulates the transition matrix element, Δ0, the other changes the energy at the donor and acceptor sites. The formal solution for the transition probability, P(t), is found in the framework of a modified spin-boson approach when arbitrary driving forces modulate both the transition matrix element and the bias. The general formal solution is analyzed within the noninteracting blip approximation for both types of modes. The transition probability difference is governed by an integro-differential equation with the time-dependent transition matrix element. In the absence of the driving forces, the rate constant increases, decreases, or is independent of temperature at different values of the reaction heat. For small Δ0, the reaction rate is due to the interaction with modulation vibrations. Depending on the values of the parameters, Γ(ε) exhibits: (a) a four-maxima dependence: or (b) complete insensitivity of ε in a broad range of biases. When strong electron-modulation mode interaction occurs, the equilibrium constant reveals the Gibbs’ behavior with an effective reaction heat, εeff=ε+ℏω0, where ω0 is the frequency of the local modulation mode. The theory is applied to two different types of the modulation modes: (a) a polar modes Debye spectrum; (b) a quantum (or classical) local vibration with strong dissipation.
Correspondence between the pressure expressions and van der Waals theory for a curved surface
Authors: Blokhuis Edgar M. , Lekkerkerker H. N. W. , Szleifer Igal
Published: July 2002

We investigate the apparent contradiction between the pressure expressions, or “mechanical expressions,” and the van der Waals squared-gradient expressions for the curvature coefficients k/R0, k, and k̄. We show that, in the context of the mean-field theory discussed, both types of expression are indeed equivalent, with the differences only being caused by the thermodynamic conditions used to vary the curvature.
One way to characterize the compact structures of lattice protein model
Authors: Wang Bin , Yu Zu-Guo
Published: July 2002

In the study of protein folding, our understanding of the protein structures is limited. In this paper we find one way to characterize the compact structures of lattice protein model. A quantity called “Partnum” is given to each compact structure. The Partnum is compared with the “Designability” of protein structures. It is shown that the highly designable structures have, on average, an atypical number of local degree of freedom. The statistical property of Partnum and its dependence on sequence length is also studied.
Vibrational motions of hydrogen bonds from the short time relative pair dynamics
Authors: De Santis Alberto , Ercoli Alessandro , Rocca Dario
Published: July 2002

The short time dynamics of pairs of water molecules, initially lying in the first coordination shell, is investigated via molecular dynamics simulation. The introduction of the generalized time-dependent pair distribution function allows to obtain a relationship between the dynamics and the local structure. The relationship explains the different short time behaviors between the hydrogen-bonded molecules and the structural defects, and the lack of the free flight time dependence of the mean-square distance. The centers of mass vibrational motion of hydrogen-bonded molecules influences the relative pair dynamics beyond the short time expansion. An approach, based on the instantaneous normal modes theory, is proposed to derive the vibrational motion of the hydrogen bonds. Its general applicability is stressed and the particular relevance for studying systems whose dynamics is determined by strong oriented interactions is suggested.
On the importance of an accurate representation of the initial state of the system in classical dynamics simulations
Authors: Garcı́a-Vela A.
Published: July 2002

A definition of a quantum-type phase-space distribution is proposed in order to represent the initial state of the system in a classical dynamics simulation. The central idea is to define an initial quantum phase-space state of the system as the direct product of the coordinate and momentum representations of the quantum initial state. The phase-space distribution is then obtained as the square modulus of this phase-space state. The resulting phase-space distribution closely resembles the quantum nature of the system initial state. The initial conditions are sampled with the distribution, using a grid technique in phase space. With this type of sampling the distribution of initial conditions reproduces more faithfully the shape of the original phase-space distribution. The method is applied to generate initial conditions describing the three-dimensional state of the Ar–HCl cluster prepared by ultraviolet excitation. The photodissociation dynamics is simulated by classical trajectories, and the results are compared with those of a wave packet calculation. The classical and quantum descriptions are found in good agreement for those dynamical events less subject to quantum effects. The classical result fails to reproduce the quantum mechanical one for the more strongly quantum features of the dynamics. The properties and applicability of the phase-space distribution and the sampling technique proposed are discussed.
Ionic-to-metallic layer transition in Cs adsorption on Si(111)-(7×7): Charge-state selective detection of the adsorbates by Cs+ reactive ion scattering
Authors: Han Seung-Jin , Park Seong Chan , Lee Jong-Gyu , Kang Heon
Published: July 2002

We examined the adsorption of Cs on a Si(111)-(7×7) surface by reactive ion scattering (RIS) of hyperthermal Cs+ beams. The RIS from a Cs-adsorbed surface gives rise to Cs2+, representing pickup of a surface Cs by a Cs+ projectile. The Cs2+ intensity is proportional to the surface coverage of Cs at a high substrate temperature (473 K), while it varies anomalously with the coverage at low temperatures (130–170 K). This observation indicates that RIS selectively detects metallic Cs on the surface, but discriminates ionic Cs. The transition from an ionic to metallic Cs adlayer is driven by the thermal diffusion of Cs and their clustering process.
Localization of random copolymers at an interface
Authors: Chen Zheng Yu
Published: July 2002

A trial-potential approach, which avoids the potential pitfalls of a replica method, is introduced to understand the essential mechanism that leads to the localization of randomly sequenced polymers at an interface. Localization of polymers with an evenly distributed randomness is shown to always occur, and the localization transition of polymers with an unevenly distributed randomness is identified as a second order phase transition. The results agree with numerical simulation data and are compared with previous theories.
Studies on carbon/sulfur cluster anions produced by laser vaporization: Experiment (collision-induced dissociation) and theory (ab initio calculation). I. C2Sm− (1⩽m⩽11)
Authors: Chen Hong , Huang Rong-bin , Lu Xin , Tang Zi-chao , Xu Xin , Zheng Lan-sun
Published: July 2002

Binary cluster anions composed of carbon and sulfur atoms have been produced from laser vaporization of a sample mixed with sulfur and carbon powders in a 20:1 ratio. They were mass-selected and their molecular formula was determined by collision-induced dissociation. The clusters consist of even carbon atoms only and their number of clustering sulfur atoms equals or exceeds that of carbon atoms. Ab initio calculations at the ROHF/6-31G* level have been performed for the cluster anions containing two carbon atoms, C2Sm− (1⩽m⩽10). Geometries of various isomeric structures of the clusters were optimized and their energies were compared to find the most stable isomers. For the singly charged anions, attachment of an additional electron leads to break their sulfur rings, and the isomers with two dangling sulfur atoms and a closed ring have the lowest energy. According to the experimental and theoretical investigations, the two carbon atoms form the bone of the clusters, and ejection of two sulfur atoms is the most competitive dissociation pathway of the cluster anions.
Linear and centrosymmetric N2⋯Ar+⋯N2
Authors: Linnartz H. , Verdes D. , Knowles P. J. , Lakin N. M. , Rosmus P. , Maier J. P.
Published: July 2002

A high resolution infrared absorption spectrum of the ionic complex N2⋯Ar+⋯N2 has been observed by tunable diode laser spectroscopy through a supersonic planar plasma. Seventy-six rovibrational transitions were measured involving excitation of the antisymmetric NN (ν3) stretching fundamental. The band origin is at 2288.7272(2) cm−1 and the ground state rotational constant is determined as B0=0.034 296(7) cm−1. The spectrum shows a clear spin-statistical intensity alternation and is consistent with a linear and centrosymmetric equilibrium geometry and a ground state with Σu+2 symmetry. The charge is predominantly located on the argon atom. The assignment is supported by high level ab initio calculations carried out. The best estimate for the equilibrium geometry is Re(NN)=1.1014 Å and re(Ar⋯N)=2.3602 Å, yielding Be=0.034 297 cm−1. The equilibrium dissociation energy De for fragmentation into N2 and [ArN2]+ is calculated to be ∼1.7 eV.
Spectral concentration for the Laplace operator in the exterior of a resonator
Authors: Fernández Claudio
Published: July 2002

We consider the Laplace operator defined in the exterior of a resonator and we provide explicit estimates for the spectral concentration, in the sense of Kato, in terms of the width of the channel connecting the cavity with the exterior.
Three-dimensional inverse scattering: High-frequency analysis of Newton’s Marchenko equation
Authors: Cheney Margaret , Rose James H.
Published: July 2002

We obtain a high-frequency asymptotic expansion of Newton’s Marchenko equation for three-dimensional inverse scattering. We find that the inhomogeneous term contains the same high-frequency information as does the Born approximation. We show that recovery of the potential via Newton’s Marchenko equation plus the ‘‘miracle’’ depends on low-frequency information.
The gravitational field of a charged, magnetized, accelerating, and rotating mass
Authors: García Díaz Alberto , Bretón Baez Nora
Published: July 2002

The explicit expression of a Petrov type G solution to the Einstein–Maxwell equations is given. This new solution is endowed with eight arbitrary parameters; mass, Newman–Unti–Tamburino (NUT) parameter, angular momentum, acceleration, electric and magnetic charges, and electric and magnetic field parameters.
Functions of infinite generalized cyclic matrices
Authors: Audit Philippe
Published: July 2002

Analytic expressions are derived for the elements or the trace of generalized cyclic matrix functions. Application to the representation of the linear difference operators with constant coefficients and periodic boundary conditions is considered, in order to express functions of such operators in closed form.
Collision-free gases in spatially homogeneous space-times
Authors: Maartens R. , Maharaj S. D.
Published: July 2002

The kinematical and dynamical properties of one-component collision-free gases in spatially homogeneous, locally rotationally symmetric (LRS) space-times are analyzed. Following Ray and Zimmerman [Nuovo Cimento B 42, 183 (1977)], it is assumed that the distribution function f of the gas inherits the symmetry of space-time, in order to construct solutions of Liouville’s equation. The redundancy of their further assumption that f  be based on Killing vector constants of the motion is shown. The Ray and Zimmerman results for Kantowski–Sachs space-time are extended to all spatially homogeneous LRS space-times. It is shown that in all these space-times the kinematic average four-velocity ui can be tilted relative to the homogeneous hypersurfaces. This differs from the perfect fluid case, in which only one space-time admits tilted ui, as shown by King and Ellis [Commun. Math. Phys. 31, 209 (1973)]. As a consequence, it is shown that all space-times admit nonzero acceleration and heat flow, while a subclass admits nonzero vorticity. The stress πij is proportional to the shear σij by virtue of the invariance of the distribution function. The evolution of tilt and the existence of perfect fluid solutions is also discussed.
General Lorentz transformations and applications
Authors: van Wyk C. B.
Published: July 2002

It is known that the most general proper orthochronous vector Lorentz (transformation) operator can be generated by a skew-symmetric 4×4 matrix containing an antisymmetric tensor of the second rank. The corresponding Lorentz operator for the two-component spinor is presented and, as can be expected, it contains the same tensor as the vector operator. Since the Pauli matrices of the spinor operator have very simple multiplication properties, the behavior of the tensor under multiplication of spinor operators is easily obtained. By comparison the corresponding properties of the tensor in vector operators can be obtained without multiplying 4×4 matrices. The physical meaning of the tensor contained in a Lorentz operator is discussed. Apart from the usual or regular operator a singular operator is discussed. Still other types of Lorentz operators are possible.
Partial wave decomposition of the Glauber amplitude for the elastic scattering of structureless charged particles by atomic hydrogen
Authors: Thomas Brian K. , Franco Victor
Published: July 2002

The partial wave amplitudes for the conventional Glauber approximation to the elastic scattering of structureless charged particles by hydrogen atoms are evaluated in closed form. The asymptotic behavior of these amplitudes in various limits is described. The large-r asymptotic behavior of the Glauber effective interaction and the logarithmic divergence of the elastic Glauber amplitude as θ → 0 are discussed. Some numerical results for these partial amplitudes are presented.
A Green’s function approach to third-order elastic constants of disordered solids
Authors: Middya T. R. , Basu A. N. , Sengupta S.
Published: July 2002

Starting from a Lippmann–Schwinger-type equation, which is very similar to that of quantum mechanical multiple scattering theory, Zeller and Dederichs [Phys. Status Solidi B 55, 831 (1973)] have developed the effective medium theory. This theory has found wide application in understanding the mechanical behavior of disordered solids. However, unlike the problem in quantum mechanics, this equation of the random elasticity is only approximate since this is a linear response theory. So, it is proposed in this work for the first time to go beyond this approximation to treat nonlinear properties of such solids of which the third-order elastic constant is a generic. Again, so far as the nonlinear elastic behavior of these solids is concerned, no work has been done except the simple Voigt- and Reuss-type averaging. Both are extreme approximations and are, moreover, known to lead to violation of the equilibrium condition. The salient feature of the present calculation is to get an exact formal solution of the problem in terms of an appropriate Green’s function in a closed form. The result obtained is quite general and may be adopted to treat nonlinearity in any tensor property of disordered materials. Finally several approximations, including a self-consistent solution, have been discussed for obtaining the effective nonlinear static mechanical susceptibility.
Inverse scattering for geophysical problems when the background is variable
Authors: Ramm A. G.
Published: July 2002

An exact method for finding an inhomogeneity for a variable background from the knowledge of the scattered field on some manifolds is given.
Short-time nonstationary character of correlation functions in classical equilibrium ensembles
Authors: Chatzidimitriou-Dreismann C. A.
Published: July 2002

Dynamical quantities b(t) are considered that depend on the canonical variables of a small number n of particles of a classical N-particle condensed system being in thermal equilibrium. It is proved that equalities like d2〈b(0)b(t)〉/dt2=−〈ḃ(0)ḃ(t)〉 are in general violated, if the interparticle interactions have a finite range and sufficiently short times t are considered. This violation reflects the continuous-in-time creations and destructions of s-particle correlations n<s≪N, which are due to the thermal motion.
Commutation relations for creation–annihilation operators associated with the quantum nonlinear Schrödinger equation
Authors: Gutkin Eugene
Published: July 2002

Using the method of intertwining operators, commutation relations are rigorously obtained for the creation–annihilation operators associated with the quantum nonlinear Schrödinger equation.
Analytical estimation of critical parameter values for bound states of screened Coulomb potentials
Authors: Rosen Gerald
Published: July 2002

As a consequence of the virial theorem and Hellmann–Feynman relation, the ratio of the kinetic energy to the derivative of the total energy, Λ(λ)≡T(λ)/E′(λ), is stationary and equal to the critical parameter value λc at λ=λc: E(λc)=0↘Λ′(λc)=0 and Λ(λc)=λc. The cubic approximation to the latter equation yields positive roots within 3.02% and 0.33% of the exact λc values for the exponential and exponential-cosine screening functions, respectively. An alternative estimation formula for λc is also presented and shown to give a value within 0.19% of the exact λc value for the exponential screening function.
On the strength of Maxwell’s equations
Authors: Matthews N. F. J.
Published: July 2002

The ‘‘strength’’ of a set of field equations (first defined by Einstein as the number of Taylor coefficients of field variables that could be chosen arbitrarily) is used to show that the amount of initial data required by the electromagnetic formulation of Maxwell’s theory in free space is equal, without approximation, to that required by the potential formulation. In each formulation, the strength is interpreted in terms of the amount of initial data required to provide a solution of the Cauchy initial-value problem and in terms of the invariance properties of the formulation. Equality of the strengths of the two formulations of Maxwell’s theory is used to support the assertion that knowledge of the strengths of other established field theories provides a means for predicting the possible existence of unknown formulations of the theories.
Singular points from Taylor series
Authors: Fernández Francisco M. , Arteca Gustavo A. , Castro Eduardo A.
Published: July 2002

A simple and accurate method is developed for calculating singular points from Taylor series. It consists of finding the least-squares deviation of the Taylor coefficients from a proposed asymptotic form. Sequences are obtained that converge quickly to the closest singularity to the origin. Some simple mathematical examples and physically interesting eigenvalue problems are discussed to illustrate the procedure. The branch points of the eigenvalues for the solutions of period 2π of the Mathieu equation and those of the Stark shifts for rigid symmetric-top molecules, which were not obtained before, are shown.
Multiplicative stochastic processes involving the time derivative of a Markov process
Authors: Arnoldus Henk F. , George Thomas F.
Published: July 2002

The characteristic functional of the derivative φ̇(t) of a Markov process φ(t) and the related multiplicative process σ(t), which obeys the stochastic differential equation iσ̇(t)=(A+φ̇(t)B)σ(t), have been studied. Exact equations for the marginal characteristic functional and the marginal average of σ(t) are derived. The first equation is applied to obtain a set of equations for the marginal moments of φ̇(t) in terms of the prescribed properties of φ(t). It is illustrated by an example how these equations can be solved, and it is shown in general that φ̇(t) is delta correlated, with a smooth background. The equation of motion for the marginal average of σ(t) is solved for various cases, and it is shown how closed-form analytical expressions for the average 〈σ(t)〉 can be obtained.
Continuity of scattering data for particles on the line with directed repulsive interactions
Authors: Gutkin Eugene
Published: July 2002

The mapping into the remote future for particles on the line interacting by repulsive directed forces is considered. Under suitable assumptions on the forces, it is proved that the mapping (which assigns the scattering data to the initial data) is continuous on a nonempty open set in the phase space.
Comments on exact solutions for a one-dimensional periodic solid
Authors: Dattoli G. , Gallardo J. C. , Torre A.
Published: July 2002

An alternative method to get exact solutions of the single-band time-dependent Schrödinger equation for an electron in a spatially periodic one-dimensional potential in the presence of a uniform electric field is presented.
Approximate representations of SU(2) ordered exponentials in the adiabatic and stochastic limits
Authors: Brachet M. E. , Fried H. M.
Published: July 2002

Approximate representations for the SU(2) ordered exponential U(t‖E) =(exp[i∫t0dt′ σ⋅E(t′)])+, written as a functional of its input field E(t), are derived in the adiabatic ( ρ≪1) and stochastic ( ρ≫1) limits, where ρ≡‖dÊ/dt‖/E, Ê=E/E, E=+(E2)1/2. An algorithm is set up for the adiabatic case, and fixed-point equations are obtained for situations of possible convergence. In the stochastic regime, ‘‘averaged’’ functions describing U(t‖E) are derived which reproduce its slowly varying dependence of large magnitude while missing, or approximating, rapid oscillations of small magnitude. Several functional integrals, analytic and machine are carried out over these approximate forms, and their results compared with the same functional integrals over the exact U(t‖E).
The anharmonic oscillator driven by Gaussian noise. Comparison between direct perturbation and Markov approximation methods
Authors: Pesquera L. , Blanco R.
Published: July 2002

The anharmonic oscillator driven by Gaussian noise is studied in the limit of weak damping using the direct perturbation (DPM) and Markov approximation (MAM) methods. Mean values are obtained to first order in the anharmonic coupling constant g. From a careful treatment of the high-frequency behavior it is concluded that to first order in g the DPM takes high-frequency contributions into account whereas the MAM does not, while both agree if high-frequency contributions are not important. It is also shown that both methods give the same results to second order in g for the quartic anharmonic oscillator. The spectral density of the noise used in stochastic electrodynamics is considered as a particular example.
Construction of indecomposable representations of inhomogeneous Lie groups
Authors: Cantoni Vittorio
Published: July 2002

Simple methods of construction of indecomposable representations of inhomogeneous Lie groups are considered and applied to the Poincaré group.
The theory of screws: A new geometric representation for the group SU(1,1)
Authors: Simon R. , Mukunda N. , Sudarshan E. C. G.
Published: July 2002

Hamilton’s theory of turns, which gives a geometrical description of the elements and structure of the compact group SU(2), is generalized to a theory of screws for the noncompact group SU(1,1). Group elements are pictured as geometric objects in a three-dimensional Minkowski space, and the composition law is reduced to a geometric operation on them. A new classification of elements of SU(1,1), leading to an interesting structural result about the group manifold, is introduced.
The classical susceptibility and the temperature-dependent susceptibility of a free electron gas
Authors: Long Ming , Lee M. Howard
Published: July 2002

The origin of dimensional independence in the classical susceptibility is studied. This study has led to an integral expression for the finite-temperature susceptibility of a free electron gas, given in terms of the zero-temperature susceptibility. At finite temperatures the susceptibility is regular. The singularity, which exists at twice the Fermi wave vector when T=0, vanishes. Thus the anomalous behavior associated with 2kF is expected to disappear when T≠0.
A geometric formulation of the Higgs mechanism
Authors: Talmadge Andy
Published: July 2002

The Higgs mechanism employed in the standard model of electroweak interactions (Glashow–Weinberg–Salam) is formulated in terms of equivariant mappings on a principal fiber bundle with values in the space of sesquilinear forms defined on a complex vector space. A classification of symmetry-breaking equivariant maps of this nature is given and compared to the phenomenological results of standard model.
SL(3,R) as the group of symmetry transformations for all one-dimensional linear systems. III. Equivalent Lagrangian formalisms
Authors: Aguirre M. , Friedli C. , Krause J.
Published: July 2002

The SL(3,R) theory of projective transformations of the plane is applied to the Lagrangians of all one-dimensional Newtonian linear systems. Noether and non-Noether equivalent Lagrangians, as well as the associated Noether and non-Noether constants of motion, are thus obtained in a completely general and systematic way. Complete unification is achieved by this group-theoretic approach to Lagrangians of one-dimensional linear systems.
On the topological phases in a planar N-point vortex system
Authors: Wu Yihren
Published: July 2002

A topological phase is given for the planar N-point vortex problem. This phase arises from an element in the pure braid group, and is independent of the evolution equations. It is deduced from a regular representation of the group of diffeomorphisms on the plane. This resulting representation of the pure braid group is the monodromy of the hypergeometric functions in N variables. The relations between this topological phase and the usual geometrical phase are discussed.
Time-domain wave splitting of Maxwell’s equations
Authors: Weston V. H.
Published: July 2002

Wave splitting of the time dependent Maxwell’s equations in three dimensions with and without dispersive terms in the constitutive equation is treated. The procedure is similar to the method developed for the scalar wave equation except as follows. The up- and down-going wave condition is expressed in terms of a linear relation between the tangential components of E and H. The resulting system of differential-integral equations for the up- and down-going waves is directly obtained from Maxwell’s equations. This splitting (arising from the principal part of Maxwell’s equations) is applied to the case where there is dispersion. A formal derivation of the imbedding equation for the reflection operator in a medium with no dispersion is obtained.
Transient wave propagation in reciprocal bi-isotropic media at oblique incidence
Authors: Kristensson Gerhard , Rikte Sten
Published: July 2002

In this paper a new wave splitting is suggested that simplifies the analysis of wave propagation in reciprocal bi-isotropic media. Two different methods to solve the scattering problem are analyzed: the invariant imbedding and the Green function approach. The medium is modeled by constitutive relations in the time domain (time convolutions) and the slab is assumed to be inhomogeneous with respect to the depth. It is shown that the cross-polarized contribution to the reflected field at normal incidence is zero for the general reciprocal inhomogeneous slab. Moreover, the rotation and the attenuation of the wave front are calculated explicitly in the general inhomogeneous slab case. Special attention is paid to normal incidence and to the homogeneous semi-infinite medium.
A generalization of the deformed algebra of quantum group SU(2)q for Hopf algebra
Authors: Ludu Andrei , Gupta Raj K.
Published: July 2002

A generalization of the deformation of Lie algebra of the SU(2) group is established for the Hopf algebra, by modifying the J3 component in all of its defining commutators. The modification is carried out in terms of a polynomial f, of J3, and the q-deformation parameter, which contains the known q-deformation functionals as its particular cases.
Dynamical stability analysis of strong/weak wave collapses
Authors: Bergé Luc
Published: July 2002

The dynamical stability of self-similar wave collapses is investigated in the framework of the radially symmetric nonlinear Schrödinger equation defined at space dimensions exceeding a critical value. The so-called ‘‘strong’’ collapse, for which the mass of a collapsing solution remains concentrated near its central self-similar core, is shown to be characterized by an unstable contraction rate as time reaches the collapse singularity. By contrast with this latter case, a so-called ‘‘weak’’ collapse, whose mass dissipates into an asymptotic tail, is proven to contain a stable attractor from which a physical self-similar collapse may be realized.
Quantum chains with GLq(2) symmetry
Authors: Alimohammadi Masoud
Published: July 2002

Usually quantum chains with quantum group symmetry are associated with representations of quantized universal algebras Uq(g). Here we propose a method for constructing quantum chains with Cq(G) global symmetry, where Cq(G) is the algebra of functions on the quantum group. In particular we will construct a quantum chain with GLq(2) symmetry which interpolates between two classical Ising chains. It is shown that the Hamiltonian of this chain satisfies the generalized braid group algebra.
Left–right asymmetry and minimal coupling
Authors: Marques G. C. , Spehler D.
Published: July 2002

In this paper we deal with an alternative approach to the description of massless particles of arbitrary spin. Within this scheme chiral components of a spinor field are regarded as fundamental quantities and treated as independent field variables. The free field Lagrangian is built up from the requirement of chiral invariance. This formulation is parallel to the neutrino theory and allows for a formulation that generalizes, to particles of arbitrary spin, the two-component neutrino theory. We achieve a spinor formulation of electrodynamics. In the case of the photon, the nonzero helicity components satisfy Weyl’s equations and are associated to observables (electromagnetic fields) whereas the zero helicity components are related to nonobservables (electromagnetic potentials). Within the spinor formulation of electrodynamics the minimal coupling substitution follows as a consequence of the linearity of the interaction and the preference of nature for chiral components, that is, of the left–right asymmetry of nature.
Involutions on the algebra of physical observables from reality conditions
Authors: Mena Marugán Guillermo A.
Published: July 2002

Some aspects of the algebraic quantization program proposed by Ashtekar are revisited in this article. It is proven that, for systems with first-class constraints, the involution introduced on the algebra of quantum operators via reality conditions can never be projected unambiguously to the algebra of physical observables, i.e., of quantum observables modulo constraints. It is nevertheless shown that, under sufficiently general assumptions, one can still induce an involution on the algebra of physical observables from reality conditions, though the involution obtained depends on the choice of particular representatives for the equivalence classes of quantum observables.
Transitive symplectic manifolds in 1+2 dimensions
Authors: Grigore D. R.
Published: July 2002

A complete list of all transitive symplectic manifolds of the Poincaré and Galilei group in 1+2 dimensions is given.
On harmonic maps from R1,1 into Hilbert loop groups
Authors: Ding Qing , Lu Bao-Qun
Published: July 2002

Motivated by the works of Gu [Pure Appl. Math. 33, 727 (1980)], Ginibre and Velo [Ann. Phys. 142, 393 (1982)] on classical solutions of a two-dimensional σ model, the global existence of harmonic maps from the Minkowski plane R1,1 into Hilbert loop groups is proved. The construction of the harmonic maps strongly depends on some geometric properties of the loop groups.
A Z3-graded generalization of supermatrices
Authors: Le Roy Bertrand
Published: July 2002

We introduce Z3-graded objects which are the generalization of the more familiar Z2-graded objects that are used in supersymmetric theories and in many models of non-commutative geometry. First, we introduce the Z3-graded Grassmann algebra, and we use this object to construct the Z3-matrices, which are the generalizations of the supermatrices. Then, we generalize the concepts of supertrace and superdeterminant.
Bloch and Wannier functions composed of Gaussian orbitals—analyticity, localization, and expectation values
Authors: Zeiner P. , Dirl R. , Davies B. L.
Published: July 2002

We discuss Bloch and Wannier functions composed of Gaussian orbitals. The fact that the Bloch functions may be expressed in terms of θ-functions is used to discuss them in detail. We study not only their analyticity properties, but also features of expectation values of some specifically chosen Hamiltonians. We also investigate the localization properties of various choices of Wannier functions and compare them with the original Gauss functions. Likewise, we discuss in a more general context the relationship between the analyticity properties of Bloch functions and the localization properties of corresponding Wannier functions.
Rotating dust solutions of Einstein’s equations with 3-dimensional symmetry groups. II. One Killing field spanned on uα and wα
Authors: Krasiński Andrzej
Published: July 2002

This is the second part of a series of 3 papers. Using the same method and the same coordinates as in part 1, rotating dust solutions of Einstein’s equations are investigated that possess 3-dimensional symmetry groups, under the assumption that only one of the Killing fields is spanned on the fields of velocity uα and rotation wα, while the other two define vectors that are linearly independent of uα and wα at every point of the spacetime region under consideration. The Killing fields are found and the Killing equations solved for the components of the metric tensor in every case that arises. The Einstein equations are simplified in a few cases, three (most probably) new solutions are found, and several classes of solutions known earlier are identified in the present scheme. They include those by Ozsváth, Maitra, Ellis, King, and Vishveshwara and Winicour.
Operator formalism for bosonic beta–gamma fields on general algebraic curves
Authors: Ferrari Franco , Sobczyk Jan T.
Published: July 2002

An operator formalism for bosonic β–γ system on arbitrary algebraic curves is introduced. The classical degrees of freedom are identified and their commutation relations are postulated. The explicit realization of the algebra formed by the fields is given in the Hilbert space equipped with a bilinear form. The construction is based on the “Gaussian” representation for β–γ system on the complex sphere [Alvarez-Gaumé et al., Nucl. Phys. B 311, 333 (1988)]. Detailed computations are provided for two- and four-point correlation functions.
Stochastically positive structures on Weyl algebras. The case of quasi-free states
Authors: Gielerak R. , Jakóbczyk L. , Olkiewicz R.
Published: July 2002

We consider quasi-free stochastically positive ground and thermal states on Weyl algebras in the imaginary time formulation. In particular, we obtain a new derivation of a general form of thermal quasi-free state and give conditions when such a state is stochastically positive, i.e., when it defines a periodic stochastic process with respect to imaginary time, a so-called thermal process. Then we show that the thermal process completely determines modular structure canonically associated with the quasi-free thermal state on Weyl algebra. We discuss a variety of examples connected with free quantum field theories on globally hyperbolic stationary space–times and models of quantum statistical mechanics.
Symmetry adapted states for Hubbard clusters
Authors: Tjernberg O.
Published: July 2002

The application of spin, pseudo spin and space group symmetry to find symmetry adapted states for the square planar Hubbard model is discussed. An approach based on pseudo spin configurations and the application of Young tableaux to the permutation group is presented. The method is illustrated for the case of a 4*4 cluster and the complete classification of the states for this cluster is given. It is shown that the linear dimension of the largest matrix block is reduced by three orders of magnitude by application of the above symmetries.
Is there a general area theorem for black holes?
Authors: Giulini Domenico
Published: July 2002

The general validity of the area law for black holes is still an open problem. We first show in detail how to complete the usually incompletely stated textbook proofs under the assumption of piecewise C2-smoothness for the surface of the black hole. Then we prove that a black hole surface necessarily contains points where it is not C1 (called “cusps”) at any time before caustics of the horizon generators show up, like, e.g., in merging processes. This implies that caustics never disappear in the past and that black holes without initial cusps will never develop such. Hence black holes which will undergo any nontrivial processes anywhere in the future will always show cusps. Although this does not yet imply a strict incompatibility with piecewise C2 structures, it indicates that the latter are likely to be physically unnatural. We conclude by calling for a purely measure theoretic proof of the area theorem.
Time-independent bounds on solutions with shocks to the relativistic Euler equations on conformally flat space–times with curvature singularities
Authors: Groah Jeffrey M.
Published: July 2002

We consider the initial value problem of the relativistic Euler equations when the underlying space–time is not flat but conformally flat, and demonstrate existence of solutions with shocks, with time-independent bounds, in some cases from big bang till big crunch. Our theorem requires that the space–time metric satisfy certain bounds, but these do not constrain the curvature of space–time, and hence our theorem may guarantee uniform bounds on solutions until the formation of curvature singularities.
Supersymmetric Kadomtsev–Petviashvili hierarchy: “Ghost” symmetry structure, reductions, and Darboux–Bäcklund solutions
Authors: Aratyn H. , Nissimov E. , Pacheva S.
Published: July 2002

This paper studies Manin–Radul supersymmetric Kadomtsev–Petviashvili hierarchy (MR-SKP) in three related aspects: (i) We find an infinite set of additional (“ghost”) symmetry flows spanning the same (anti)commutation algebra as the ordinary MR-SKP flows. (ii) The latter are used to construct consistent reductions SKPr/2,m/2 of the initial unconstrained MR-SKP hierarchy which involves a nontrivial modification for the fermionic flows. (iii) For the simplest constrained MR-SKP hierarchy SKP12,12 we show that the orbit of Darboux–Bäcklund transformations lies on a supersymmetric Toda lattice being a square root of the standard one-dimensional Toda lattice, and also we find explicit Wronskian-ratio solutions for the super-tau function.
The spectrum of a magnetic Schrödinger operator with randomly located delta impurities
Authors: Pulé J. V. , Scrowston M.
Published: July 2002

We consider a single band approximation to the random Schrödinger operator in an external magnetic field. The spectrum of such an operator has been characterized in the case where delta impurities are located on the sites of a lattice. In this paper we generalize these results by letting the delta impurities have random positions as well as strengths; they are located in squares of a lattice with a general bounded distribution. We characterize the entire spectrum of this operator when the magnetic field is sufficiently high. We show that the whole spectrum is pure point, the energy coinciding with the first Landau level is infinitely degenerate, and that the eigenfunctions corresponding to other Landau band energies are exponentially localized.
Taylor dispersion in the presence of time-periodic convection phenomena. Part I. Local-space periodicity
Authors: Shapiro M. , Brenner H.
Published: July 2002

Generalized Taylor dispersion theory is herein extended to circumstances for which the transport of dissolved or suspended chemically reactive (as well as inert) solutes is affected by carrier-solvent flow fields and/or external forces that are time periodic in both their global and local microscale spaces (and possess commensurate frequencies). The local-space- and time-averaged solute transport process is characterized by three time-independent, but frequency-dependent microscale phenomenological coefficients—K̄*, Ū*, and cf6D*, representing the mean chemical reaction rate, velocity vector, and dispersivity dyadic of the solute, respectively. These macroscale transport coefficients are expressed in terms of time-periodic eigenfunctions and corresponding eigenvalues using a recently developed solution scheme. This scheme permits the analysis of phenomena involving time-periodic transport coefficients on a par with that for the classical case of time-independent microscale phenomenological coefficients.

The analysis generalizes to time-periodic local-space phenomena a previous treatment, in which only the global-space coefficients were allowed to vary periodically with time. This greatly enlarges the scope of potential applications of the analysis. In addition to the time-averaged phenomenological coefficients K̄*, Ū*, and CF6D*, comparable instantaneous coefficients are defined governing the local-space-averaged instantaneous solute concentration. In contrast with their time-averaged counterparts, K̄*, Ū*, and CF6D*, the latter instantaneous transport coefficients are shown to depend upon the initial solute distribution within the local space. Because of coupling between the local- and global-space transport processes in oscillatory flows and/or oscillatory external force fields, all harmonics of the resulting global-space solute velocity field contribute to the mean convective solute transport. This phenomenon may result, for example, in zero solvent–nonzero solute net macroscale transport (or vice versa). The driving frequency of the local-space time-periodic transport process may be used to parametrically control the macroscale solute reactivity rate coefficient, as well as the solute’s mean velocity and dispersivity about that mean. A companion paper (Part II) [Phys. Fluids A 2, 1744 (1990)], provides an example, albeit for the nonreactive case.