An electron fluid model is proposed for the lattice dynamics of metals which satisfies the requirement of translational invariance and the lattice is in equilibrium without recourse to external forces. The model is applied to calculate the phonon dispersion of sodium in the symmetry directions.

Unified study of the different properties of metals clearly reveals the inadequacy of the empty-core Ashcroft pseudopotential even in the case of simple metals. In the present paper we propose a modification of the one-parameter Ashcroft pseudopotential by assuming the parameterr_c to be wave vector-dependent. This introduces a simple modification of the electron-ion pseudopotential in the reciprocal space. The corresponding potential in the configuration space shows that the abrupt change in the Coulomb potential atr=r_c is replaced by a continuous change spread over a small region near the core boundary. The present model has been used to make a unified study of Al and is found to be a significant improvement over the simple Ashcroft model. The agreement between the calculated and experimental values is found to be quite satisfactory.

The extensivity property of entropy is clarified in the light of a critical examination of the entropy formula based on quantum statistics and the relevant thermodynamic requirement. The modern form of the Gibbs paradox, related to the discontinuous jump in entropy due to identity or non-identity of particles, is critically investigated. Qualitative framework of a new resolution of this paradox, which analyses the general effect of distinction mark on the Hamiltonian of a system of identical particles, is outlined.

The elastic properties of polypropylene have been investigated in terms of a phenomenological model, which is a modified form of the Takayanagi’s two-phase model. In the present model both the change of crystallinity and orientation of the crystalline chains have been taken into account. The orientation effect at the drawn state has been considered in a simplified manner. It has been shown that a partially aligned crystalline phase may be considered as a superposition of a perfectly aligned crystalline region in an elastically isotropic randomly oriented crystalline phase. The predicted values of elastic modulus agree with experimental values.

The second order pseudopotential theory suggests the possibility of a break-up of the total energy of simple metals into a purely volume-dependent part and an effective central pairwise interaction between ions. In the present paper finite contributions for these two parts of the energy have been extracted in a form convenient for calculation. Using the local Heine-Abarenkov model potential, a reliable effective ion-ion interaction is generated and the volume-dependent energy is calculated for Al. The relative contributions of the effective interaction and the volume-dependent energy term to various metallic properties are also calculated. The importance of volume dependence on the effective interaction is also discussed.

The interactomic force constants upto eighth neighbour are derived from the effective interaction and it is found that the force constants beyond the third neighbour are negligibly small. This result is also confirmed by the calculation of dispersion curves with force constants obtained from the effective interaction upto the third neighbour which is found to reproduce the results of the full pseudopotential calculations. The force constants obtained are also used to study some finite temperature properties of Al in the quasi-harmonic approximation and the limitations of the theory are pointed out.

It is shown that starting from a Fourier transform relation one can derive, in a surprisingly simple manner, all the well-known results of lattice summation, that have been obtained so far by a complicated use of the Ewald theta transformation. We show that the Ewald transformation follows directly from the Fourier transform relation.

A Unified study of lattice-mechanical properties of lead using energy-dependent pseudopotential is carried out. Energy dependence in pseudopotential is considered through the effective mass approximation; the pseudopotential model chosen is the local Heine-Abarenkov model potential. Properties studied include cohesive energy, equilibrium lattice parameter, second-order elastic constants, pressure derivative of second-order elastic constants, equation of state (atT=0 K), phonon-dispersion and effective two-body interaction. The results show fairly good agreement with experiment especially with a modified Heine-Abarenkov potential.

A very important question in ultrarelativistic heavy ion collisions is that of thermalization of the high energy density quark gluon plasma forud in the central rapidity region. Different approaches have been adopted by various authors to study this thermalization problem. These include phenomenological string and capacitor plate models, perturbative QCD based parton cascade models and the classical non-perturbative approach. In this paper we briefly review the earlier studies and discuss our work which emphasizes the role of non-perturbative collective effects (classical chaos) in the thermalization of the plasma. In particular, using classical equations of motion of a coloured parton in self-consistent colour fields, we have carried out a 1+1 dimensional simulation of coloured partonic matter. We find that in certain parameter domains, the system exhibits chaotic behaviour in non-abelian plasma oscillations, which then leads to thermalization of the plasma.

The classical and quantum physics seem to divide nature into two domains macroscopic and microscopic. It is also certain that they accurately predict experimental results in their respective regions. However, the reduction theory, namely, the general derivation of classical results from the quantum mechanics is still a far cry. The outcome of some recent investigations suggests that there possibly does not exist any universal method for obtaining classical results from quantum mechanics. In the present work we intend to investigate the problem phenomenonwise and address specifically the phenomenon of scattering. We suggest a general approach to obtain the classical limit formula from the phase shiftδ_l, in the limiting value of a suitable parameter on whichδ_l depends. The classical result has been derived for three different potential fields in which the phase shifts are exactly known. Unlike the current wisdom that the classical limit can be reached only in the high energy regime it is found that the classical limit parameter in addition to other factors depends on the details of the potential fields. In the last section we have discussed the implications of the results obtained.