The dynamics of a crystal containing a rigid, isolated substitutional molecular impurity is discussed using the Green’s function method. The dynamical matrix for the problem is set up, and the various constraints on the force constants are pointed out. The application of the matrix partitioning technique is then indicated, and the possibility of a resonance mode arising from molecular librations is pointed out. Comparison is made with the earlier work of Wagner, and finally the relevance of the present formalism to the interpretation of a recent neutron scattering experiment is discussed.

The dynamics of a crystal containing a molecular impurity is discussed with allowance for the effects of internal vibrations of the molecule. Cartesian co-ordinates are introduced to describe internal vibrations, angular oscillations and centre of mass motions of the impurity, and the displacements of the atoms of the host crystal. Next the Hamiltonian is set up and the equations of motion derived. In this process, use is made of Dirac brackets when dealing with coordinates having redundancy and constraints. From the dynamical matrix, some of the familiar results of the crystal-field approximation are recovered. The application of the partitioning technique is then discussed, and finally comparison is made with results of other approaches.

V₃Si exhibits an ultrasonic anomaly when cooled well below its martensitic and superconducting transition temperatures (T_m andT_c), and a magnetic field is applied on to the sample. The anomaly is thought to be due to reorientation of microdomains formed belowT_m, to energetically favourable configurations. The effect disappears when the domains are stabilised in new configurations in the presence of the magnetic field. An analysis of these results is presented in this paper by relating the ultrasonic attenuation coefficient to strain fluctuations, arising here from domain reorientations. The treatment is based on a master equation for the probability matrix whose elements yield the probabilities of transitions between domain configurations, in the presence of both the magnetic field and the stress wave. Arguments for the validity of this master equation, when the oscillatory stress is weak, are given in a longish appendix. The derived results are used to analyse, in qualitative terms, the observed experimental facts. Also, new measurements are suggested which may help interpret the experimental data in a satisfactory manner.

The temperature dependence of the line width and the peak position of theE_g librational mode (of nominal frequency 285 cm⁻¹) and theE_g translational mode (of nominal frequency 155 cm⁻¹) in calcite (CaCO₃) have been studied by laser-Raman spectrometry. The role of orientational relaxation as a possible process contributing to the line width has been evaluated. It is concluded that reorientations do not play a major part in relation to the present observations. It is further shown that the latter can be understood on the basis of cubic and quartic anharmonic processes. The data also suggest that certain phonon interactions earlier considered insignificant for peak shift in calcite, do contribute significantly.

Diffusion with interruptions (arising from localized oscillations, or traps, or mixing between jump diffusion and fluid-like diffusion, etc.) is a very general phenomenon. Its manifestations range from superionic conductance to the behaviour of hydrogen in metals. Based on a continuous-time random walk approach, we present a comprehensive two-state random walk model for the diffusion of a particle on a lattice, incorporating arbitrary holding-time distributions for both localized residence at the sites and inter-site flights, and also the correct first-waiting-time distributions. A synthesis is thus achieved of the two extremes of jump diffusion (zero flight time) and fluid-like diffusion (zero residence time). Various earlier models emerge as special cases of our theory. Among the noteworthy results obtained are: closed-form solutions (ind dimensions, and with arbitrary directional bias) for temporally uncorrelated jump diffusion and for the ‘fluid diffusion’ counterpart; a compact, general formula for the mean square displacement; the effects of a continuous spectrum of time scales in the holding-time distributions, etc. The dynamic mobility and the structure factor for ‘oscillatory diffusion’ are taken up in part 2.

Continuing our study of interrupted diffusion, we consider the problem of a particle executing a random walk interspersed with localized oscillations during its halts (e.g., at lattice sites). Earlier approaches proceedvia approximation schemes for the solution of the Fokker-Planck equation for diffusion in a periodic potential. In contrast, we visualize a two-state random walk in velocity space with the particle alternating between a state of flight and one of localized oscillation. Using simple, physically plausible inputs for the primary quantities characterising the random walk, we employ the powerful continuous-time random walk formalism to derive convenient and tractable closed-form expressions for all the objects of interest: the velocity autocorrelation, generalized diffusion constant, dynamic mobility, mean square displacement, dynamic structure factor (in the Gaussian approximation), etc. The interplay of the three characteristic times in the problem (the mean residence and flight times, and the period of the ‘local mode’) is elucidated. The emergence of a number of striking features of oscillatory diffusion (e.g., the local mode peak in the dynamic mobility and structure factor, and the transition between the oscillatory and diffusive regimes) is demonstrated.

The phase transition behaviour of an amplifier with positive feedback is experimentally studied. The results are interpreted using catastrophe theory language. Zero (in Gilmore’s classification), first and second-order transitions are demonstrated by driving the system along appropriate trajectories in control parameter space and the cusp and the spinodal are mapped. The fluctuations of the order parameter are investigated and their relationship to system response time established. Quench experiments analogous to those familiar in condensed matter have also been performed and with similar results.

Damage produced inα- and fused quartz bombarded with low energy (∼ 100 keV) D⁺, He⁺ and Ar⁺ ions, has been studied by observing the changes in their spectrum. Besides bulk reflectivity, the attenuated total reflection spectrum has also been studied, the latter with a view to obtaining the surface polariton frequencies. It is observed that for the same fluence, the changes following D⁺ irradiation are much higher compared to that for Ar⁺ irradiation. The variation of the surface polariton frequency inα-quartz with the damage energy deposited has the same trend as observed earlier for refractive index. Some annealing studies have also been performed in argon-irradiated samples. These studies indicate that whereas in fused quartz the damaged layer recovers completely, inα-quartz there is a residual amorphization even after annealing. A two-layer model is proposed which gives a reasonable simulation of the observedir properties.

The current status of the controversy relating to melting in two dimensions is surveyed. To begin with, a review is given of the seminal work of Kosterlitz and Thouless. This is followed by a discussion of the modifications introduced by Nelson and Halperin. The search for the continuous transitions and the intermediate hexatic phase predicted by these theories is then described, covering both the laboratory as well as simulation experiments. Alternate viewpoints to thekt theory aired recently in the literature are also briefly examined. The paper concludes with an outlook for the future.

This paper presents an overview of diverse topics that are seemingly different but interrelated, with strong connections to statistical mechanics on the one hand and spin glass physics on the other. Written primarily for an inter-disciplinary audience, we start with a brief recapitulation of the relevant aspects of statistical mechanics, particularly those needed for understanding the recently-popular simulated-annealing technique used in optimization studies. Then follows a survey of the spin glass problem, with particular attention to the consequences of quenched randomness. The travelling-salesman problem is considered next, as also the impact made on it by the spin glass problem. Several examples are then presented of optimization studies wherein the simulated-annealing concept has been profitably used. Attention is also drawn in this context to the lessons provided by the spin glass problem. Finally, a brief survey of neural networks is made, essentially from a physicist’s point of view. The different learning schemes proposed are discussed, and the relevance of spin models and their statistical mechanics is also discussed.