Phonons and periodons in IV–VI semiconductor superlattices

We have calculated the phonon and periodon dispersion relations in IV–VI semi-conducting bulk PbTe and SnTe and their superlattice structure. The model used here is a one-dimensional lattice which includes harmonic interactions up to second neighbours as well as on-site nonlinear electron-ion interactions at the anion site. We calculate the phonon and periodon dispersion relations in bulk and PbTe-SnTe superlattice for the transverse optic and acoustic modes using the transfer matrix method. Our analysis has predicted correct nature of the folding of acoustic and confinement of optical phonons at various frequency intervals corresponding to pass and stop bands of the superlattices.     

Analysis of Low-energy α-4He Elastic Scattering Process in Direct Channel Regge-Pole Formalism

The elastic scattering of low-energy α-particles by a ⁴He target has been analysed within the frame-work of a modified Regge-Pole model which reproduces the partial wave phaseshifts in an elegant and simple way and describes all other relevant features of the scattering phenomena.     

Loop Algebra of Lie symmetries for a short-wave equation

It is demonstrated that Lie point symmetries associated with a nonlinear equation for short waves in three dimensions generate an infinite-dimensional Lie algebra—a loop Algebra. Classification of the independent sets of the subalgebra is done through the adjoint action of the corresponding generators. Different forms of similarity solutions are discussed.     

Painleve Analysis and the Yang-Mills Equation in Two Specific Cases

Two important configurations of Yang-Mills fields are discussed applying to them the Painleve test of Ablowitz. The case with a constant electric E-field does not admit an exact solution while the cylindrically symmetric self-dual system admits an inverse scattering approach for instanton solution.     

Mean-field theories of spin glasses

Different kinds of mean-field theories (MFT) of spin glasses (SG) are reviewed. A brief introductory review of major experimental results, which have to be explained theoretically, is presented in the beginning. Marshall-Klein-Brout type random local field theories are described qualitatively. Edwards-Anderson MFT of SG transition is introduced after defining the various relevant order parameters. Almost all the static and dynamic approaches to the solution of the Sherrington-Kirkpatrick model are reviewed in detail. The existence of mixed phase(s) in the MFT of vector SG is examined critically in the light of recent theories and experiments. The existence of macroscopic anisotropy energy in SG and their microscopic origin are mentioned. The upper and lower critical dimensionalities obtained by different authors are enlisted. The concept of frustration and its deeper connection with other branches of human knowledge are indicated. Nonlinear susceptibilities, spin wave and relaxational modes in SG are also reviewed. The two-level-system picture of SG, its physical basis and important consequences are presented. The Tholence-Tournier-Wohlfarth phenomenological cluster model of SG is discussed with a stress on the role of measurement time. SG transition has been described as percolation and localization-delocalization problems. Some special features of the local field distribution in SG are mentioned. Some results of computer simulation on the various models of SG are summarized. The theories of the transport properties of SG are enlisted. Recent trends in the theory of SG are indicated at the end.     

Representation of supercharges over the scattering data for super-sine-Gordon system

We determine the form of the superchargesQ ₁ andQ ₂ in terms of the scattering data for the super-sine-Gordon equation. The technique is to ascertain the effect of supertranslation on the scattering data used in the inverse scattering transform. The same result was obtained by Kulish and Tsypleyv from the Riccatti equation by expanding in A.     

Anharmonic oxygen vibration and mode softening in Tl2Ba2Ca2Cu3O10 superconductor

The softening of the IR active 300 cm⁻¹ phonon mode in Tl-2223 superconductor, aroundT _c has been explained by considering a sixth order polarization potential at the off-center oxygen ion site in the Tl-O plane, and by using a nonlinear lattice dynamical theory. The present theory explains, more or less satisfactorily, the unusual temperature dependence of oxygen ion vibration and frequency shifts at higher temperature. The existence of strong nonlinear electron-phonon interaction atT _c has been emphasized.     

Effect of temperature on the validity of the einstein relation in heavily doped semiconductors

An analytical expression of the modified form of the Einstein relation in heavily doped semiconductors in which Gaussian band tails are formed near the lower limit of heavy doping is derived for studying the temperature dependence of the diffusivity-mobility ratio of the carriers in such semiconductors. It is found that, with increasing temperature from relatively low values, the ratio first increases in a nonlinear manner and then decreases till, at high temperatures, it approaches its value corresponding to the non-degenerate condition resulting in a peak over a narrow range of temperatures.