Simplified theory of optical nonlinearities in spin-polarized bulk GaAs

Apart from their intrinsic physical interest, spin-polarized many-body effects are expected to be important to the working of spintronic devices. A vast literature exists on the effects of a spin-unpolarized electron-hole plasma on the optical properties of a semiconductor. Here, we include the spin degree of freedom to model optical absorption of circularly polarized light by spin-polarized bulk GaAs. Our model is easy to implement and does not require elaborate numerics, since it is based on the closed-form analytical pair-equation formula that is valid in 3d. The efficacy of our approach is demonstrated by a comparison with recent experimental data.

Simplified theory of optical nonlinearities in spin-polarized bulk GaAs

Apart from their intrinsic physical interest, spin-polarized many-body effects are expected to be important to the working of spintronic devices. A vast literature exists on the effects of a spin-unpolarized electron-hole plasma on the optical properties of a semiconductor. Here, we include the spin degree of freedom to model optical absorption of circularly polarized light by spin-polarized bulk GaAs. Our model is easy to implement and does not require elaborate numerics, since it is based on the closed-form analytical pair-equation formula that is valid in 3d. The efficacy of our approach is demonstrated by a comparison with recent experimental data.

New Look at Kirchhoff's Theory of Plates

KIRCHHOFF’S theory [1] and the first-order shear deformation theory (FSDT) [2] of plates in bending are simple theories and continuously used to obtain design information. Within the classical small deformation theory of elasticity, the problem consists of determining three displacements, u, v, and w, that satisfy three equilibrium equations in the interior of the plate and three specified surface conditions. FSDT is a sixth-order theory with a provision to satisfy three edge conditions and maintains, unlike in Kirchhoff’s theory, independent linear thicknesswise distribution of tangential displacement even if the lateral deflection, w, is zero along a supported edge. However, each of the in-plane distributions of the transverse shear stresses that are of a lower order is expressed as a sum of higher-order displacement terms. Kirchhoff’s assumption of zero transverse shear strains is, however, not a limitation of the theory as a first approximation to the exact 3-D solution.

An algebraic theory of functional and multivalued dependencies in relational databases

Computation of the dependency basis is the fundamental step in solving the membership problem for functional dependencies (FDs) and multivalued dependencies (MVDs) in relational database theory. We examine this problem from an algebraic perspective. We introduce the notion of the inference basis of a set M of MVDs and show that it contains the maximum information about the logical consequences of M. We propose the notion of a dependency-lattice and develop an algebraic characterization of inference basis using simple notions from lattice theory. We also establish several interesting properties of dependency-lattices related to the implication problem. Founded on our characterization, we synthesize efficient algorithms for (a): computing the inference basis of a given set M of MVDs; (b): computing the dependency basis of a given attribute set w.r.t. M; and (c): solving the membership problem for MVDs. We also show that our results naturally extend to incorporate FDs also in a way that enables the solution of the membership problem for both FDs and MVDs put together. We finally show that our algorithms are more efficient than existing ones, when used to solve what we term the ‘generalized membership problem’.

Gauge theory of a group of diffeomorphisms. II. The conformal and de Sitter groups

The extension of Hehl's Poincaré gauge theory to more general groups that include space-time diffeomorphisms is worked out for two particular examples, one corresponding to the action of the conformal group on Minkowski space, and the other to the action of the de Sitter group on de Sitter space, and the effect of these groups on physical fields.

Is one-parameter scaling theory of localisation consistent? Comment on Schuh's comment

It is maintained that the one-parameter scaling theory is inconsistent with the physics of Anderson localisation.

Gauge theory of a group of diffeomorphisms. I. General principles

Any (N+M)-parameter Lie group G with an N-parameter subgroup H can be realized as a global group of diffeomorphisms on an M-dimensional base space B, with representations in terms of transformation laws of fields on B belonging to linear representations of H. The gauged generalization of the global diffeomorphisms consists of general diffeomorphisms (or coordinate transformations) on a base space together with a local action of H on the fields. The particular applications of the scheme to space-time symmetries is discussed in terms of Lagrangians, field equations, currents, and source identities. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

Theory of the mixed valent state

After briefly discussing the question of a distinct mixed valent state and theoretical models for it, the area of greatest theoretical success, namely the mixed valent impurity, is reviewed. Applications to spectroscopy, energetics and Hall effect are then putlined. The independent impurity approximation is inadequate for many properties of the bulk system, which depend on lattice coherence. A recent auxiliary or slave boson approach with a simple mean field limit and fluctuation corrections is summarized. Finally the mixed valent semiconductor is discussed as an outstanding problem.

Note on the one-parameter scaling theory of localisation

The necessary and sufficient condition for the existence of the one-parameter scale function, the /Munction, is obtained exactly. The analysis reveals certain inconsistency inherent in the scaling theory, and tends to support Motts’ idea of minimum metallic conductivity.

Note on the one-parameter scaling theory of localisation

The necessary and sufficient condition for the existence of the one-parameter scale function, the /Munction, is obtained exactly. The analysis reveals certain inconsistency inherent in the scaling theory, and tends to support Motts’ idea of minimum metallic conductivity.

Fluctuation Theory Of The Specific-Heat Of Normal Liquid-3He

The measured specific heat of normal liquid 3He shows a plateau for 0.15<1 K; below 0.15 K and above 1 K, it rises linearly with temperature. However, the slope on the high-temperature side is very much reduced compared with the free-Fermi-gas value. We explain these features through a microscopic, thermal spin- and density-fluctuation model. The plateau is due to spin fluctuations which have a low characteristic energy in 3He. Because of the low compressibility, the density fluctuations are highly suppressed; this leads to a reduced slope for CV(T) for high temperatures.

Theory of freezing in simple systems

The transition parameters for the freezing of two one-component liquids into crystalline solids are evaluated by two theoretical approaches. The first system considered is liquid sodium which crystallizes into a body-centered-cubic (bcc) lattice; the second system is the freezing of adhesive hard spheres into a face-centered-cubic (fcc) lattice. Two related theoretical techniques are used in this evaluation: One is based upon a recently developed bifurcation analysis; the other is based upon the theory of freezing developed by Ramakrishnan and Yussouff. For liquid sodium, where experimental information is available, the predictions of the two theories agree well with experiment and each other. The adhesive-hard-sphere system, which displays a triple point and can be used to fit some liquids accurately, shows a temperature dependence of the freezing parameters which is similar to Lennard-Jones systems. At very low temperature, the fractional density change on freezing shows a dramatic increase as a function of temperature indicating the importance of all the contributions due to the triplet direction correlation function. Also, we consider the freezing of a one-component liquid into a simple-cubic (sc) lattice by bifurcation analysis and show that this transition is highly unfavorable, independent of interatomic potential choice. The bifurcation diagrams for the three lattices considered are compared and found to be strikingly different. Finally, a new stability analysis of the bifurcation diagrams is presented.

Coupled amplitude theory of nonlinear surface acoustic waves

The nonlinear propagation characteristics of surface acoustic waves on an isotropic elastic solid have been studied in this paper. The solution of the harmonic boundary value problem for Rayleigh waves is obtained as a generalized Fourier series whose coefficients are proportional to the slowly varying amplitudes of the various harmonics. The infinite set of coupled equations for the amplitudes when solved exhibit an oscillatory slow variation signifying a continuous transfer of energy back and forth among the various harmonics. A conservation relation is derived among all the harmonic amplitudes.

Grid-connected versus stand-alone energy systems for decentralized power-A review of literature

The decentralized power is characterised by generation of power nearer to the demand centers, focusing mainly on meeting local energy needs. A decentralized power system can function either in the presence of grid, where it can feed the surplus power generated to the grid, or as an independent/stand-alone isolated system exclusively meeting the local demands of remote locations. Further, decentralized power is also classified on the basis of type of energy resources used-non-renewable and renewable. These classifications along with a plethora of technological alternatives have made the whole prioritization process of decentralized power quite complicated for decision making. There is abundant literature, which has discussed various approaches that have been used to support decision making under such complex situations. We envisage that summarizing such literature and coming out with a review paper would greatly help the policy/decision makers and researchers in arriving at effective solutions. With such a felt need 102 articles were reviewed and features of several technological alternatives available for decentralized power, the studies on modeling and analysis of economic, environmental and technological asibilities of both grid-connected (GC) and stand-alone (SA) systems as decentralized power options are presented. (C) 2009 Elsevier Ltd. All rights reserved.

A semi-empirical theory of molten salts

A semi-empirical model is presented for describing the interionic interactions in molten salts using the experimentally available structure data. An extension of Bertaut's method of non-overlapping charges is used to estimate the electrostatic interaction energy in ionic melts. It is shown, in agreement with earlier computer simulation studies, that this energy increases when an ionic salt melts. The repulsion between ions is described using a compressible ion theory which uses structure-independent parameters. The van der Waals interactions and the thermal free energy are also included in the total energy, which is minimised with respect to isostructural volume variations to calculate the equilibrium density. Detailed results are presented for three molten systems, NaCl, CaCl2 and ZnCl2, and are shown to be in satisfactory agreement with experiments. With reliable structural data now being reported for several other molten salts, the present study gains relevance.