Table of contents

Solutions of the (2 + 1)-dimensional Dirac equation with a Coulomb potential are analytically obtained by studying Tricomi equations obtained from a pair of coupled first-order ones. The eigenvalues and their fine structures are also presented.

The degree of nonclassicality of states of a field mode is analysed considering both phase-space and distance-type measures of nonclassicality. By working out some general examples, it is shown explicitly that the phase-space measure is rather sensitive to superposition of states, with finite superpositions possessing maximum nonclassical depth (the highest degree of nonclassicality) irrespective of the nature of the component states. Mixed states are also discussed and examples with nonclassical depth varying between the minimum and the maximum allowed values are exhibited. For pure Gaussian states, it is demonstrated that distance-type measures based on the Hilbert–Schmidt metric are equivalent to the phase-space measure. Analyzing some examples, it is shown that distance-type measures are efficient to quantify the degree of nonclassicality of non-Gaussian pure states.

The basic thermodynamic quantities are considered from the microscopic point of view; and the relations between these quantities and the relevant macroscopic entities are established. A generalized work-energy equation is derived. This equation is independent of the reference frame and is valid irrespective of the macroscopic motion of the material system. As a consequence, a new formulation of the first law of Thermodynamics is suggested. The effective application of this approach is demonstrated by several examples.

Previously observed positive and negative parity states of ⁹⁵Tc have been interpreted using a particle-rotor model. Experimental energies and transition properties have been compared to those predicted by the calculation. The results show that this simple model with very few parameters can explain successfully most of the structure of ⁹⁵Tc. Four rotational bands have been identified and other rotational features as well.

Previously developed BEB, RBEB, DM and recently developed RDM models are employed for the computation of cross-sections of electron impact single K-shell ionization of atoms with atomic numbers from Z = 19 to 103 to augment the work recently done involving atoms with Z = 6 to 40. The calculated cross-sections are compared with the available experimental data over a wide energy range up to 1000 MeV. The RDM model with simple relativistic factor is found to be at least as good as the DM model with a more complex factor up to about 60 MeV. However, the latter one is found to work satisfactorily up to about 1000 MeV.

A depressed density plasma channel, in the presence of a strong azimuthal magnetic field, supports localized lower hybrid modes of finite azimuthal mode number. A high amplitude laser propagating through the channel undergoes stimulated Raman scattering off a lower hybrid mode producing a back propagating electromagnetic sideband wave. The pump beats with the sideband to exert a ponderomotive force on the electrons driving the lower hybrid wave. The density perturbations associated with the lower hybrid wave couple with the oscillatory velocity due to the pump, producing a nonlinear current, driving the sideband. The radial profile of the sideband and the frequency shift have signatures of magnetic field and can be used as a diagnostics for azimuthal magnetic field.

A classical model for high-harmonic generation from the interaction of a laser pulse and an atomic gas is introduced. The effects of finite pulse width and laser magnetic field are included. The optimum intensity-pulse width relation for high-harmonic emission and the corresponding power spectrum are presented. The existing high-harmonic cutoff law is found to remain valid.

A unified treatment, valid for all the axial quasicrystals exhibiting 5-, 8-, 10-, and 12-fold symmetries, is presented for the linear distribution of atomic sites. The starting point is a cyclotomic integer basis that employs non-crystallographic roots involving Pisot–Vijayaraghavan algebraic integers. The general solution is expressed in the form of a theorem. An explicit method is given for determining the basis vectors that are involved. Both two- and three-dimensional quasicrystals with these axial symmetries are considered.

The calculation of the surface nucleation field H_c3 of a type II superconducting cylinder in a parallel applied magnetic field is revised. The linearized Ginzburg–Landau (G–L) equation for the order parameter is employed in the evaluations of the effects of spatial inhomogeneity of the applied magnetic field. The general profile of the applied magnetic field is that it is parabolic in the radial distance although it can take an arbitrary value at the origin. In general, the universal field-temperature curves are characterized by flux-entry points at each of which the azimuthal quantum number decreases by unity. There are no flux entries, however, in the curve for which the applied magnetic field is zero at the origin. The effects of normal-metal cladding, in particular the suppression of the critical temperature, are also evaluated.

We present a theory of Attenuated Total Reflection (ATR) with grating-coupling (GC) as a single technique for studying surface polaritons in a composite medium. Over the years, the experimental techniques of ATR and GC have been employed as separate techniques for probing surface polaritons. The combined technique of ATR with GC (to be referred to as ATRGC) has substantial advantages over either of the two methods when each is employed on its own. A theory of ATRGC is developed using first order pertubation theory. Dispersion curves due to surface polaritons of the composite medium are plotted and found to be strongly dependent on a filling factor, which is a measure of the volume content of constituents of the composite medium. ATRGC spectra are discussed for two cases: (a) with the grating at the base of the coupling prism and (b) with the grating on the surface of a semi-infinite composite specimen. The ATRGC spectra are modelled on a set up consisting of silicon-vacuum-Ag/KCl composite.

A formulation of the reflection and transmission of electromagnetic waves by a stratified planer structure is demonstrated. This formula uses the so-called elementary symmetric functions that are extensively used in the mathematical theory of polynomials. The reflection and transmission coefficients of any number of quantum wells or barriers can be written in a similar way. Finally, one-dimensional scattering from a series of delta-function barriers (a system that is called Dirac Comb) is investigated. An excellent agreement has been found with the earlier results based on other approaches. This approach is also shown to be a powerful technique and can be easily used for analyzing various complicated mesoscopic structures and devices.

Single crystal EPR studies of VO(II) doped magnesium ammonium phosphate hexahydrate have been carried out at room temperature. The results indicate that the paramagnetic impurity has entered substitutional and interstitial sites in the lattice. The maximum hyperfine coupling value for one site and the minimum hyperfine constant for the other site have occurred at the same angle and vice versa. The spin Hamiltonian parameters obtained from single crystal data for these two sites are: Site 1: g_|| = 1.941; g_⊥ = 1.994, A_|| = 19.23 mT; A_⊥ = 7.14 mT; Site 2: g_|| = 1.946; g_⊥ = 1.997, A_|| = 19.07 mT; A_⊥ = 7.29 mT. From these observations, it has been concluded that the two-vanadyl impurities are located approximately at right angles to each other. Superhyperfine interaction with the protons of ligand water molecules have been noticed at a few orientations. EPR powder spectrum of the sample showed a set of eight parallel and perpendicular features indicating the presence of only one magnetically distinct site and the spin Hamiltonian parameters calculated from this spectrum matched with single crystal data. The admixture coefficients have also been calculated, and agree well with the reported values.

Gap solitons in the case of two mono-inductances lines coupled via linear capacitors are considered analytically by means of the method of perturbation combined with a rotating-wave approximation. We extend the local stability analysis at all points of the phase plane, and numerical experiments are undertaken to explore the space-time evolution of these waves.

We consider a model of an electric circuit, which consists of a primary monoinductance branch shunted (cell to cell) by a nonlinear capacitor and two alternate secondary inductances. The cw spectrum of this circuit exhibits two forbidden bands. By means of the method of multiple scales combined with a quasi-discreteness approximation, we show analytically in a unified way that, the system may support gap solitons, which have their frequencies of oscillation contained within these gaps, as well as intrinsic localized modes (with oscillation frequencies above all the phonon bands). Both kinds of excitations have zero group velocity.