Nonlocal Structure Research Articles

Nonlocal quadratic Poisson algebras, monodromy map, and Bogoyavlensky lattices

A new Lax representation for the Bogoyavlensky lattice is found and its r-matrix interpretation is elaborated. The r-matrix structure turns out to be related to a highly nonlocal quadratic Poisson structure on a direct sum of associative algebras. The theory of such nonlocal structures is developed and the Poisson property of the monodromy map is worked out in the most general situation. Some problems concerning the duality of Lax representations are raised.

Dielectric-matrix calculation of the volume-plasmon dispersion relation for silicon.

Plasmon-band splitting in silicon has been the subject of theoretical interest recently, since reports of its experimental observation using coherent inelastic x-ray scattering. The theoretical plasmon-dispersion relation can be obtained from dielectric-response theory and knowledge of the electronic structure of the solid. In this work the frequency- and wave-vector-dependent dielectric matrix (DM) has been calculated in the random-phase approximation, with a nonlocal empirical pseudopotential (EPM) electronic band structure. We present results for the volume-plasmon dispersion relation along high-symmetry directions in the first Brillouin zone. Contrary to previous local EPM-based DM calculations, this nonlocal EPM band structure results in excellent agreement with the experimental plasmon-dispersion anisotropy. In addition, these dispersion results are in better agreement with experiment than previous local-density-approximation calculations. Evidence for a weak \ensuremath{\approxeq}2-eV band gap is found at the L point. Unlike previous calculations, the presence of two plasmon resonances is directly observable from the calculated loss function in the \ensuremath{\Lambda} direction. \textcopyright{} 1996 The American Physical Society.

Impact ionization rate and high-field transport in ZnS with nonlocal band structure

The impact ionization rate in ZnS is calculated using a nonlocal empirical pseudopotential band structure and compared to previous results using a local calculation. The two resulting rates are then compared and simple fit formulas are presented. These are included in an ensemble Monte Carlo simulation of electron transport in bulk ZnS. The calculated impact ionization rate is then compared to experimental impact ionization coefficient data; reasonable agreement between the experimental data and the calculated impact ionization rate is obtained with an appropriate choice of optical deformation potentials.

Far from equilibrium nonconserved growth under a surface diffusion bias.

We study a generic one-dimensional atomistic model of interface growth under random ballistic deposition in the presence of a surface diffusion bias allowing for surface overhangs and bulk vacancies. We find that various diffusion bias induced surface instabilities recently found in the solid-on-solid approximation of kinetic growth are absent in the generic model with the usual statistically self-affine Kardar-Parisi-Zhang scaling dominating the surface morphology. For strong biases and high temperatures, the growing surface resembles the zero temperature ballistic growth without a diffusion bias. The growth front morphologies show intricate flamelike nonlocal structures not typically present in self-affine surfaces. This indicates that the standard coarse-grained single-variable description of the growing film by its local surface height coordinate misses an important qualitative feature, namely, a novel flamelike roughening behavior along vertical faces of the growth front. \textcopyright{} 1996 The American Physical Society.

Averaging of unsteady flows in heterogeneous media of stationary conductivity

A procedure for deriving equations of average unsteady flows in random media of stationary conductivity is developed. The approach is based on applying perturbation methods in the Fourier-Laplace domain. The main result of the paper is the formulation of an effective Darcy's Law relating the mean velocity to the mean head gradient. In the Fourier-Laplace domain the averaged Darcy's Law is given by a linear local relation. The coefficient of proportionality depends only on the heterogeneity structure and is called the effective conductivity tensor. In the physical domain this relation has a non-local structure and it defines the effective conductivity as an integral operator of convolution type in time and space. The mean head satisfies an unsteady integral-differential equation. The kernel of the integral operator is the inverse Fourier-Laplace transform (FLT) of the effective conductivity tensor. The FLT of the mean head is obtained as a product of two functions: the first describes the FLT of the mean head distribution in a homogeneous medium; the second corrects the solution in a homogeneous medium for the given spatial distribution of heterogeneities. This function is simply related to the effective conductivity tensor and determines the fundamental solution of the governing equation for the mean head. These general results are applied to derive the effective conductivity tensor for small variances of the conductivity. The properties of unsteady average flows in isotropic media are studied by analysing a general structure of the effective Darcy's Law. It is shown that the transverse component of the effective conductivity tensor does not affect the mean flow characteristics. The effective Darcy's Law is obtained as a convolution integral operator whose kernel is the inverse FLT of the effective conductivity longitudinal component. The results of the analysis are illustrated by calculating the effective conductivity for one-, two- and three-dimensional flows. An asymptotic model of the effective Darcy's Law, applicable for distances from the sources of mean flow non-uniformity much larger than the characteristic scale of heterogeneity, is developed. New bounds for the effective conductivity tensor, namely the effective conductivity tensor for steady non-uniform average flow and the arithmetic mean, are proved for weakly heterogeneous media.

Hydrogen Bond Energies of Hydrogen Chloride−Carbonyl Complexes

Gas phase hydrogen bonding was studied via infrared spectroscopy in the following systems: methyl acetate−hydrogen chloride, methyl formate−hydrogen chloride, 2-butanone−hydrogen chloride, and acetone−hydrogen chloride. The intensity of the H−Cl stretching vibration was monitored as a function of temperature, and the hydrogen bond energies and enthalpies were determined. The hydrogen bond energy for all four complexes was within 2.0 kJ mol-1 of −18.3 kJ mol-1, indicating that the hydrogen bond energy is only minimally affected by nonlocal molecular structure. The acetone−hydrogen chloride complex was modeled by ab initio methods. The energy of formation of the complex, calculated at the MP2/6-311++G** level of theory, is −20.8 kJ mol-1, in good agreement with the experiment.

Nonlocal time-space coherent structures in dissipative heavy-ion collisions from the analysis of excitation function fluctuations

We study the implications of the correlations between fluctuating S-atrix elements with different spin (and parity0 values in dissipative heavy-ion collisions. We demonstrate the possibility to probe the time-irreversible stage of the collision by analyzing excitation function fluctuations. We interpret the quasiperiodicity of fluctuations, anomalously large coherent angles and strong macrochannel cross correlation observed in dissipative heavy-ion collisions in terms of the formation of nonlocal time-space coherent structures due to the dissipation of spin interference. The rate of quantum spin decoherence is given by the Lyapunov exponent which marks quantum chaos to be the origin of the phenomenon.

Localized discussion of stimulated processes for Rindler observers and accelerated detectors.

We investigate the implications of the presence of Minkowski particles on the Rindler particle content in the accelerated frame as well as on the excitation and deexcitation of an accelerated particle detector. To obtain localized statements, the field quantization is based on wave packets. For bosonic particles, nonempty Minkowski modes imply an amplification of the number of Rindler particles in specific modes. The underlying processes reflect a nonlocal pair structure: specific pairs of modes with trajectories of the wave packet maxima passing different Rindler wedges are correlated. An elementary object of quantum optics in noninertial situations is the accelerated detector. The richer structure of the physics of its excitation and deexcitation is studied in detail. In addition to the generalizations of the inertially known excitation and deexcitation processes there are structurally new processes that are inertially forbidden. These processes reflect the nonlocal pair correlations.

Collective pinning theory for magnetically coupled layered superconductors. First order phase transition between different pinning configurations

We calculate the tilt modulus C 44 and make collective pinning estimates for a vortex lattice in magnetically coupled superconducting layers. The tilt modulus has unusual nonlocal structure which leads to peculiar pinning behavior. Namely, under the certain conditions for the pinning strength and the magnetic coupling transition from a regime of independently pinned 2D vortex lattices in the layers to a state of three dimensional (3D) collective pinning occurs as a first order phase transition.

Collective-pinning theory for magnetically coupled layered superconductors.

We calculate the tilt modulus [ital C][sub 44] and make collective-pinning estimates for a vortex lattice in magnetically coupled superconducting layers. Complete analysis of possible pinning regimes is made. The tilt modulus has unusual nonlocal structure which leads to peculiar pinning behavior. Namely, under certain conditions for the pinning strength and the magnetic coupling, a transition from a regime of independently pinned two-dimensional (2D) vortex lattices in the layers to a state of three-dimensional (3D) collective pinning occurs as a first-order phase transition. The critical current in 3D collective-pinning regime has characteristic nonmonotonic field dependence.

Mean inelastic electron scattering potentials for Si and GaAs from dielectric matrix calculations

A first principles calculation of the inelastic electron mean inner-potential is presented for Si and GaAs as a function of incident energy. This work is based on a dielectric matrix calculation of the frequency and wave-vector dependent loss function determined in the RPA from non-local empirical pseudopotential electronic structure. Comparisons are made with the generalised oscillator strength models and experiment.

Multicomponent Schwarzian KdV hierarchies

We extend recent results of Dorfman [1] and Wilson [2] on the Schwarzian-KdV equation to the coupled KdV and Harry Dym hierarchies isospectral to an energy dependent Schrödinger operator [3, 4]. Whilst the N-component coupled KdV hierarchies posses ( N + 1) differential Hamiltonian structures, their Schwarzian modifications posses ( N + 1) nonlocal Hamiltonian structures whose inverses are purely differential. We present, as examples, the Schwarzian modifications associated with the dispersive water waves (DWW) and the Harry Dym equations.

A neural system as a dynamical model for early vision

A functional formulation of the image reconstruction problem has been developed. Contrary to previous efforts, no optimization is performed. The model contains a grey level intensity process, an edge process, and a noise process. Due to a nontrivial mixture of the intensity process and the edge process, amazingly nonlocal structures evolve in the edge finding process. A ferromagnetic interaction term in the noise process is used for forming connected regions of noise, not suited for reconstruction. The connection to neural systems, where each process is implemented as a particular type of neuron, is demonstrated. The intensity process interacts nonlocally with the original image, but locally with the edge and noise process.

Parametric excitation of quasiphonons in antiferromagnets by microwave magnetic field

Parametric excitation of quasiphonons by microwave magnetic field has been investigated in the easy-plane antiferromagnets CoCO 3 and FeBO 3. Instability was observed under all geometric arrangements of microwave and static magnetic fields in the basic plane. The threshold field dependencies on static magnetic field for parallel and perpendicular pumping are found to be different in both material. Quasiphonon linear relaxation rate and non-linear susceptibility are studied. Theoretical consideration in the framework of complete form of magnetoelastic and elastic interactions is in qualitative agreement with the experiment. It is shown that indirect elastic-elastic interaction has a nonlocal structure.

Nonlocal matrix hamiltonian operators, differential geometry, and applications

A study is made of a class of nonlocal Hamiltonian operators that arise naturally as second Hamiltonian structures of the nonlinear Schrodinger equation, the Heisenberg magnet, the Landau-Lifshitz equation, etc. A complete description of these operators is obtained, and it reveals intimate connections with classical differential geometry. A new nonlocal Hamiltonian structure of first order is constructed for the parrly anisotropic (J1=J2) Landau-Lifshitz equation (hitherto, only Hamiltonian structures of zeroth and second orders were known for the Landau-Lifshitz equation).

Forced magnetic reconnection in a plasma sheet with localized resistivity profile excited by lower hybrid drift type instability

A forced magnetic reconnection process with a temporal evolution of resistivity is studied for a plasma sheet with a nonuniform resistivity profile based on the nonlocal mode structure of the lower hybrid drift type instability. The growth rate of the mode found is almost independent of the resistivity at the neutral sheet, but depends on the resistivity of the region of maximum density gradient away from the neutral sheet. We study this by using both a nonlinear numerical MHD simulation and a linear theory. The mode may be relevant to the prevalent theoretical concept of MHD reconnection and the localized anomalous resistivity profile based on the lower hybrid drift instability.

An overview of the tomographic forwnrd/inverse problem

In ocean acoustic tomography, the travel time along a ray path is a weighted average of the propagation speed along the path. Because oceanographers generally have intuition about point measurements or simple averages, it has been necessary to transform travel time data into point values (maps) before communicating the results. The transformation can be done with a variety of methods, ranging from exhaustive Monte Carlo searches to Backus-Gilbert constrained estimation. The transformation converts travel time data with more or less independent errors to point value estimates with correlated errors that may have complicated, nonlocal structure. Since the error bars usually presented with an ocean map do not include the correlations, they do not accurately reflect the information content of a tomographic dataset. In addition, it is no longer possible to distinguish between the data errors and sampling blind spots by examining the error bars (or even the error covariances). Communicating tomographic results thus requires more effort, and more plots. Resolution (or averaging) kernels show how the estimate at a point is a weighted average of the entire field (with the average becoming more local as the number of rays increases). Null space vectors show fields that may be added to the estimated map without changing the data significantly. Given that the goal of ocean observations is to test dynamical hypotheses, it is also reasonable to consider transforming hypotheses into constraints on the travel times, rather than transforming the travel times into constraints on physical space hypotheses. [Work supported by ONR and ONT.]

Analysis of the optical potential with coupled-channel scattering equations: Energy dependence and coordinate-space behavior.

We apply a Sturmian-expansion method we have recently developed to perform an exact multichannel analysis of the optical potential. By combining this method with momentum-space integral-equation techniques we can obtain a finite-rank representation of the nonlocal optical potential in which coupling effects are exactly taken into account. In the framework of this approach we provide also detailed expressions of the various contributions arising when couplings are treated perturbatively. These iterative-perturbative approximation schemes are generally employed in phenomenological optical-potential calculations. Our results do not apply to low-order terms only, but can be extended to any desired order. We find that a proper treatment of inelastic-inelastic couplings may be necessary in order to reproduce the detailed nonlocal structure of the optical potential. We then perform an energy-dependent analysis of the resulting optical potential. To this end, the rapid fluctuations in energy due to compound or quasicompound resonances are subtracted off by means of a direct algebraic procedure. The connection of this subtraction method with Feshbach's general reaction theory is clarified. We analyze the energy dependence of the smooth optical interaction in the light of a dispersion-theoretic approach, by resorting to simple analytic parametrizations of the real and imaginary parts. Both a model multichannel problem and the realistic neutron${\mathrm{\ensuremath{-}}}^{208}$Pb case have been considered.

Bell's theorem and the nature of reality

We rediscuss the Einstein-Podolsky-Rosen paradox in Bohm's spin version and oppose to it Bohr's controversial point of view. Then we explain Bell's theorem, Bell inequalities, and its consequences. We describe the experiment of Aspect, Dalibard, and Roger in detail. Finally we draw attention to the nonlocal structure of the underlying theory.

Covariant calculation of the heterotic string effective action in curved (1,0) superspace

Covariant methods for studying the non-local structure of the effective action for the two-dimensional non-linear heterotic sigma -model are developed in a curved (1,0) superspace. The calculational techniques are based on the suitably generalised (to the case of a curved (1,0) superspace) Schwinger-De Witt-Seely representation for the superpropagator heat kernels (Green functions). The results obtained for the low-energy heterotic string effective action are in agreement with the known ones.