The generalised Langevin equation (GLE), originally developed in the context of Brownian motion, yields a convenient representation for the mobility (generalised susceptibility) in terms of a frequency-dependent friction (memory function). Kubo has shown how two deep consistency conditions, or fluctuation-dissipation theorems, follow from the GLE. The first relates the mobility to the velocity auto-correlation in equilibrium, as is also derivable from linear response theory. The second is a generalised Nyquist theorem, relating the memory function to the auto-correlation of the random force driving the velocity fluctuations. Certain subtle points in the proofs of these theorems have not been dealt with sufficiently carefully hitherto. We discuss the input information required to make the GLE description a complete one, and present concise, systematic proofs starting from the GLE. Care is taken to settle the points of ambiguity in the original version of these proofs. The causality condition imposed is clarified, and Felderhof’s recent criticism of Kubo’s derivation is commented upon. Finally, we demonstrate how the ‘persistence’ of equilibrium can be used to evaluate easily the equilibrium auto-correlation of the ‘driven’ variable (e.g., the velocity) from the transient solution of the corresponding stochastic equation.

X-ray and ultraviolet photoelectron spectroscopy as well as x-ray absorption spectroscopy have been employed to investigate transition metal oxide perovskites of the general formula ABO₃ (A = La or rare-earth ion, B=trivalent transition metal ion). Systematics in the core levels and in the valence bands in the series of LaBO₃ compounds have been discussed. Lanthanum chemical shifts in the x-ray absorption spectra in this series show interesting trends. Photoelectron spectra of the solid solutions, LaNi_1−xCo_xO₃, LaNi_1−xFe_xO₃ and LaFe_1−xCo_xO₃ show that the rigid band model is applicable to these systems. It is shown that x-ray photoelectron spectroscopy can be employed to identify multiple oxidation states of transition metal ions in oxide perovskites.

The positron hydrogen charge-exchange problem has been investigated using the three-particle scattering formulation. 1s and 2s intermediate states of hydrogen atom have been taken into account for calculation of second order matrix elements. The effect of 2s term is to decrease total cross-section as compared to the results involving 1s state only. The total cross-sections results are compared with results of other calculations in the energy region 1.5 to 10 Ry.

It is shown that the fringe shifting technique can increase the sensitivity of speckle photography for sub-speckle size changes. The technique gives time-ordered pattern that can be used for the sign detection of the motion as well.

The optical constants of single crystal GaAs were determined in the range 0.6 to 4.2 eV, using Tomlin’s method and are compared in the light of the earlier results obtained using the Kramers-Krönig analysis method.

New methods involving the manipulation of fundamental wavefronts (e.g., plane and spherical) with simple optical components such as pinholes and spherical lenses have been developed for the fabrication of elliptic, hyperbolic and conical holographic zone plates. Also parabolic zone plates by holographic techniques have been obtained for the first time. The performance behaviour of these zone plates has been studied. Further a phenomenological explanation is offered for the observed improved fringe contrast obtained with a spherical reference wave.

Population densities of HeI and HeII excited states are calculated from a collisional radiative model for non-LTE optically thin helium plasmas. Effect of direct ionisation-excitation of HeI to HeII states on the population density of HeII states is shown. Relaxation times for HeI states calculated from the CR model is reported forT_e from 3 to 18 eV andn_e from 10⁹ to 10¹⁶ cm⁻³.

Experiments performed with a 50 MW — 60 nsec ruby laser to estimate the temperature of the plasma produced on the planar targets of carbon as well as polyethylene are reported. Temperatures were estimated by two foil ratio technique. The temperatures of carbon and polyethylene plasma show aφ^2/9 dependance on flux in the flux regime of 10¹⁰ W/cm² to 5 × 10¹¹ W/cm². The comparatively slower dependance is explained on the basis of purely collisional absorption, the effect being enhanced due to relatively long duration of the laser pulses. Scaling laws of plasma temperature against laser flux obtained by different workers in different flux regimes have been analysed on the basis of collisional and non-collisional absorption.

The production of prompt neutrinos in the beam dump experiment is explained in a cluster model, by postulating the emission of strange clusters in hadron collisions, besides the usual non-strange clusters. The low mass strange clusters can decay only by the weak interaction. The leptonic and semi-leptonic decay modes of these clusters give rise to prompt neutrinos. A prediction of the model is that the ratios <v_e>/π⁺ at PS energies would be the same as SPS energies.

We analyse all the neutral-current phenomena following from the general class of gauge models based on the group SU(2)_L ⊗ SU(2)_R ⊗ U(1). It is found that the neutral-current couplings in these models bear a remarkable similarity to those in the standard Weinberg-Salam gauge model. The parameter which plays the role of sin²ϑ_w is found to lie between 0 and 1/2. Comparison with experimental data shows that even a model with the ratio of the masses of the twoZ bosons as small as 1.9 is not ruled out.

Two alternative U₃(W)-gauge models are presented. Both agree with the recent Abbott-Barnett fits to the neutrino-nucleon neutral-current data, and with the SLAC measurement of the asymmetry parameter for longitudinally polarised electrondeuteron inelastic scattering. Results for$$\sigma \left( {\nu _\mu e} \right),\sigma \left( {\bar \nu _\mu e} \right)$$ are also found in agreement with the latest measurements. The models differ in the parameterQ_W(Z, N) characterising parity-violation in heavy atoms for which, however, the experimental situation is still unclear.