Matrix elements of U(2n) generators in a multishell spin-orbit basis. I. The del-operator MEs in a two-shell composite Gelfand-Paldus basis

This is the first in a series of three articles which aimed to derive the matrix elements of the U(2n) generators in a multishell spin-orbit basis. This is a basis appropriate to many-electron systems which have a natural partitioning of the orbital space and where also spin-dependent terms are included in the Hamiltonian. The method is based on a new spin-dependent unitary group approach to the many-electron correlation problem due to Gould and Paldus [M. D. Gould and J. Paldus, J. Chem. Phys. 92, 7394, (1990)]. In this approach, the matrix elements of the U(2n) generators in the U(n) x U(2)-adapted electronic Gelfand basis are determined by the matrix elements of a single Ll(n) adjoint tensor operator called the del-operator, denoted by Delta(j)(i) (1 less than or equal to i, j less than or equal to n). Delta or del is a polynomial of degree two in the U(n) matrix E = [E-j(i)]. The approach of Gould and Paldus is based on the transformation properties of the U(2n) generators as an adjoint tensor operator of U(n) x U(2) and application of the Wigner-Eckart theorem. Hence, to generalize this approach, we need to obtain formulas for the complete set of adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis. The nonzero shift coefficients are uniquely determined and may he evaluated by the methods of Gould et al. [see the above reference]. In this article, we define zero-shift adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis which are appropriate to the many-electron problem. By definition, these are proportional to the corresponding two-shell del-operator matrix elements, and it is shown that the Racah factorization lemma applies. Formulas for these coefficients are then obtained by application of the Racah factorization lemma. The zero-shift adjoint reduced Wigner coefficients required for this procedure are evaluated first. All these coefficients are needed later for the multishell case, which leads directly to the two-shell del-operator matrix elements. Finally, we discuss an application to charge and spin densities in a two-shell molecular system. (C) 1998 John Wiley & Sons.

Matrix elements of U(2n) generators in a multishell spin-orbit basis. II. The two-shell nonzero shift ACCs and U(2n) generator MEs

This is the second in a series of articles whose ultimate goal is the evaluation of the matrix elements (MEs) of the U(2n) generators in a multishell spin-orbit basis. This extends the existing unitary group approach to spin-dependent configuration interaction (CI) and many-body perturbation theory calculations on molecules to systems where there is a natural partitioning of the electronic orbital space. As a necessary preliminary to obtaining the U(2n) generator MEs in a multishell spin-orbit basis, we must obtain a complete set of adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis. The zero-shift coefficients were obtained in the first article of the series. in this article, we evaluate the nonzero shift adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis. We then demonstrate that the one-shell versions of these coefficients may be obtained by taking the Gelfand-Tsetlin limit of the two-shell formulas. These coefficients,together with the zero-shift types, then enable us to write down formulas for the U(2n) generator matrix elements in a two-shell spin-orbit basis. Ultimately, the results of the series may be used to determine the many-electron density matrices for a partitioned system. (C) 1998 John Wiley & Sons, Inc.

Long-range automaton models of earthquakes: Power-law accelerations, correlation evolution, and mode-switching

We introduce a conceptual model for the in-plane physics of an earthquake fault. The model employs cellular automaton techniques to simulate tectonic loading, earthquake rupture, and strain redistribution. The impact of a hypothetical crustal elastodynamic Green's function is approximated by a long-range strain redistribution law with a r(-p) dependance. We investigate the influence of the effective elastodynamic interaction range upon the dynamical behaviour of the model by conducting experiments with different values of the exponent (p). The results indicate that this model has two distinct, stable modes of behaviour. The first mode produces a characteristic earthquake distribution with moderate to large events preceeded by an interval of time in which the rate of energy release accelerates. A correlation function analysis reveals that accelerating sequences are associated with a systematic, global evolution of strain energy correlations within the system. The second stable mode produces Gutenberg-Richter statistics, with near-linear energy release and no significant global correlation evolution. A model with effectively short-range interactions preferentially displays Gutenberg-Richter behaviour. However, models with long-range interactions appear to switch between the characteristic and GR modes. As the range of elastodynamic interactions is increased, characteristic behaviour begins to dominate GR behaviour. These models demonstrate that evolution of strain energy correlations may occur within systems with a fixed elastodynamic interaction range. Supposing that similar mode-switching dynamical behaviour occurs within earthquake faults then intermediate-term forecasting of large earthquakes may be feasible for some earthquakes but not for others, in alignment with certain empirical seismological observations. Further numerical investigation of dynamical models of this type may lead to advances in earthquake forecasting research and theoretical seismology.

Quantum noise in optical fibers. I. Stochastic equations

We analyze the quantum dynamics of radiation propagating in a single-mode optical fiber with dispersion, nonlinearity, and Raman coupling to thermal phonons. We start from a fundamental Hamiltonian that includes the principal known nonlinear effects and quantum-noise sources, including linear gain and loss. Both Markovian and frequency-dependent, non-Markovian reservoirs are treated. This treatment allows quantum Langevin equations, which have a classical form except for additional quantum-noise terms, to be calculated. In practical calculations, it is more useful to transform to Wigner or 1P quasi-probability operator representations. These transformations result in stochastic equations that can be analyzed by use of perturbation theory or exact numerical techniques. The results have applications to fiber-optics communications, networking, and sensor technology.

Quantum noise limits to terabaud communications

From a general model of fiber optics, we investigate the physical limits of soliton-based terabaud communication systems. In particular we consider Raman and initial quantum noise effects which are often neglected in fiber communications. Simulations of the position diffusion in dark and bright solitons show that these effects become increasingly important at short pulse durations, even over kilometer-scale distances. We also obtain an approximate analytic theory in agreement with numerical simulations, which shows that the Raman effects exceed the Gordon-Haus jitter for sub-picosecond pulses. (C) 1997 Elsevier Science B.V.

The electric field effect on spin injection in tunneling regime

Using the quantum tunneling theory, we investigate the spin-dependent transport properties of the ferromagnetic metal/Schottky barrier/semiconductor heterojunction under the influence of an external electric field. It is shown that increasing the electric field, similar to increasing the electron density in semiconductor, will result in a slight enhancement of spin injection in tunneling regime, and this enhancement is significantly weakened when the tunneling Schottky barrier becomes stronger. Temperature effect on spin injection is also discussed. (C) 2003 Elsevier B.V. All rights reserved.

Application of density functional theory to equilibrium adsorption of argon and nitrogen on amorphous silica surface

We present a new version of non-local density functional theory (NL-DFT) adapted to description of vapor adsorption isotherms on amorphous materials like non-porous silica. The novel feature of this approach is that it accounts for the roughness of adsorbent surface. The solid–fluid interaction is described in the same framework as in the case of fluid–fluid interactions, using the Weeks–Chandler–Andersen (WCA) scheme and the Carnahan–Starling (CS) equation for attractive and repulsive parts of the Helmholtz free energy, respectively. Application to nitrogen and argon adsorption isotherms on non-porous silica LiChrospher Si-1000 at their boiling points, recently published by Jaroniec and co-workers, has shown an excellent correlative ability of our approach over the complete range of pressures, which suggests that the surface roughness is mostly the reason for the observed behavior of adsorption isotherms. From the analysis of these data, we found that in the case of nitrogen adsorption short-range interactions between oxygen atoms on the silica surface and quadrupole of nitrogen molecules play an important role. The approach presented in this paper may be further used in quantitative analysis of adsorption and desorption isotherms in cylindrical pores such as MCM-41 and carbon nanotubes.

Spin-charge conductance in nanoscale electronic devices

We introduce a spin-charge conductance matrix as a unifying concept underlying charge and spin transport within the framework of the Landauer-Buttiker conductance formula. It turns out that the spin-charge conductance matrix provides a natural and gauge covariant description for electron transport through nanoscale electronic devices. We demonstrate that the charge and spin conductances are gauge invariant observables which characterize transport phenomena arising from spin-dependent scattering. Tunnelling through a single magnetic atom is discussed to illustrate our theory.

Coexistence of spin polarization and pairing correlations in metallic grains

We investigate the competition between magnetic depairing interactions, due to spin-exchange mechanism and∕or to spin-dependent asymmetric bandwidths, and pairing coupling in metallic grains. We present a detailed analysis of the quantum ground state in different regimes arising from the interplay between ferromagnetic and pairing correlations for different fillings. We find out that the occurrence of a ground state with coexisting spin-polarization and pairing correlations is enhanced when the asymmetric spin-dependent distribution of the single-particle energies is considered. The mechanisms leading to such a stable quantum state are finally clarified.

Role of chemical cues from cotton in mediating host selection and oviposition behaviour in Helicoverpa armigera (Hubner) (Lepidoptera : Noctuidae)

We investigated the role of chemoreception in the host selection and oviposition behaviour of Helicoverpa armigera in the laboratory using five cotton genotypes and synthetic volatile terpenes. Female moths oviposited on substrates treated with methanol, ethanol, acetone and pentane extracts of leaves, squares and flowers of the cotton genotypes. Phytochemicals soluble in pentane were the most efficient in eliciting oviposition behaviour. In a two-way bioassay, pentane extracts of leaves or squares of a Multiple Host-plant Resistance genotype (MHR11), Deltapine commercial (DP90), and Smith Red Leaf (SRL) received significantly more eggs than solvent-treated controls. Extracts of squares of the native genotype Gossypium nelsonii did not receive more eggs. Females preferred DP90 and MHR11 to SRL and G. nelsonii. Female moths also laid more eggs on pentane extracts of MHR11 flowers than MHR11 leaves from preflowering, early flowering and peak-flowering plants. In a flight chamber, female moths used olfactory cues at short range to mediate oviposition and discrimination between host plants. Egg-laying, mated females were attracted at a distance (1.5 m) to volatile compounds released by whole plants and odours emanating from filter papers treated with synthetic volatile terpenes. Individually, the terpenes did not stimulate any significant oviposition response. However, there was a significant oviposition response to a mixture of equal volumes of the terpenes (trans-beta-caryophyllene, alpha-pinene, beta-pinene, myrcene, beta-bisabolol, and alpha-humulene). Conversely, antennectomised (moths with transected antennae), egg-laying, mated females did not stimulate any significant oviposition response. The significance of these findings in relation to H. armigera hostplant selection are discussed.

Evolution of stress deficit and changing rates of seismicity in cellular automaton models of earthquake faults

We investigate the internal dynamics of two cellular automaton models with heterogeneous strength fields and differing nearest neighbour laws. One model is a crack-like automaton, transferring ail stress from a rupture zone to the surroundings. The other automaton is a partial stress drop automaton, transferring only a fraction of the stress within a rupture zone to the surroundings. To study evolution of stress, the mean spectral density. f(k(r)) of a stress deficit held is: examined prior to, and immediately following ruptures in both models. Both models display a power-law relationship between f(k(r)) and spatial wavenumber (k(r)) of the form f(k(r)) similar tok(r)(-beta). In the crack model, the evolution of stress deficit is consistent with cyclic approach to, and retreat from a critical state in which large events occur. The approach to criticality is driven by tectonic loading. Short-range stress transfer in the model does not affect the approach to criticality of broad regions in the model. The evolution of stress deficit in the partial stress drop model is consistent with small fluctuations about a mean state of high stress, behaviour indicative of a self-organised critical system. Despite statistics similar to natural earthquakes these simplified models lack a physical basis. physically motivated models of earthquakes also display dynamical complexity similar to that of a critical point system. Studies of dynamical complexity in physical models of earthquakes may lead to advancement towards a physical theory for earthquakes.

The structures of Langmuir-Blodgett films of fatty acids and their salts

Recent advances in several experimental techniques have enabled detailed structural information to be obtained for floating (Langmuir) monolayers and Langmuir-Blodgett films. These techniques are described briefly and their application to the study of films of fatty acids and their salts is discussed. Floating monolayers on aqueous subphases have been shown to possess a complex polymorphism with phases whose structures may be compared to those of smectic mesophases. However, only those phases that exist at high surface pressures are normally used in Langmuir-Blodgett (LB) deposition. In single LB monolayers of fatty acids and fatty acid salts the acyl chains are in the all-cans conformation with their long axes normal to the substrate. The in-plane molecular packing is hexagonal with long-range bond orientational order and short-range positional order: known as the hexatic-B structure. This structure is found irrespective of the phase of the parent floating monolayer. The structures of multilayer LB films are similar to the structures of their bulk crystals, consisting of stacked bilayer lamellae. Each lamella is formed from two monolayers of fatty acid molecules or ions arranged head to head and held together by hydrogen bonding between pairs of acids or ionic bonding through the divalent cations. With acids the acyl chains are tilted with respect to the substrate normal and have a monoclinic structure, whereas the salts with divalent cations may have the chains normal to the substrate or tilted. The in-plane structures are usually centred rectangular with the chains in the trans conformation and packed in a herringbone pattern, Multilayer films of the acids show only a single-step order-disorder transition at the malting point, This temperature tends to rise as the number of layers increases. Complex changes occur when multilayer films of the salts are heated. Disorder of the chains begins at low temperatures but the arrangement of the head groups does not alter until the melting temperature is reached, Slow heating to a temperature just below the melting temperature gives, with some salts, a radical change in phase. The lamellar structure disappears and a new phase consisting of cylindrical rods lying parallel to the substrate surface and stacked in a hexagonal pattern is formed, In each rod the cations are aligned along the central axis surrounded by the disordered acyl chains. (C) 2001 Elsevier Science B,V. All rights reserved.

Exact theory of sedimentation equilibrium made useful

The exact description of the thermodynamics of solutions has been used to describe, without approximation, the distribution of all the components of an incompressible solution in a centrifuge cell at sedimentation equilibrium. Thermodynamic parameters describing the interactions between solute components of known molar mass can be obtained by direct analysis of the experimental data. Interpretation of the measured thermodynamic parameters in terms of molecular interactions requires that an arbitrary distinction be made between nonassociative forces, like hard-sphere volume-exclusion and mean-field electrostatic repulsion or attraction, and specific short-range forces of association that give rise to the formation of molecular aggregates. Provided the former can be accounted for adequately, the effects of the latter can be elucidated in the form of good estimates of the equilibrium constants for the reactions of aggregation.

The strength of concentrated Mg-Zn solid solutions

Solid solution effects on the hardness and flow stress have been studied for zinc contents between 0.2 and 2.4 at% (0.5 and 6.9 wt%) in Mg. The alloys were grain refined with 0.6 wt% zirconium to ensure a similar grain size at all compositions. The hardness increases with the zinc content as Hv(10) (kg mm(-2)) = 9 Zn (at%) + 33. At low solute concentrations the (0.2%) proof strength does not change significantly with concentration. At concentrations above 0.7 at%, within the supersaturated solid solution region, the rate of solid solution hardening is high, following a c(2) rule, where c is the atom fraction of Zn. It is suggested that short-range order may account for most of the observed strengthening in concentrated Mg-Zn alloys.

Ultraviolet signals in birds are special

Recent behavioural experiments have shown that birds use ultraviolet (UV)-reflective and fluorescent plumage as cues in mate choice. It remains controversial, however, whether such UV signals play a special role in sexual communication, or whether they are part of general plumage coloration. We use a comparative approach to test for a general association between sexual signalling and either UV-reflective or fluorescent plumage. Among the species surveyed, 72% have UV colours and there is a significant positive association between UV reflectance and courtship displays. Among parrots (Psittaciformes), 68% of surveyed species have fluorescent plumage, and again there is a strong positive association between courtship displays and fluorescence. These associations are not artefacts of the plumage used in courtship displays, being generally more 'colourful' because there is no association between display and colours lacking UV reflectance or fluorescence. Equally, these associations are not phylogenetic artefacts because all results remain unchanged when families or genera, rather than species, are used as independent data points. We also find that, in parrots, fluorescent plumage is usually found adjacent to UV-reflective plumage. Using a simple visual model to examine one parrot, the budgerigar Melopsittacus undulatus, we show that the juxtaposition of UV-reflective and fluorescent plumage leads to a 25-fold increase in chromatic contrast to the budgerigar's visual system. Taken together, these results suggest that signals based on UV contrast are of special importance in the context of active sexual displays. We review briefly six hypotheses on why this may be the case: suitability for short-range signalling; high contrast with backgrounds; invisibility to predators; exploitation of pre-existing sensory biases; advertisement of feather structure; and amplification of behavioural signals.