Table of contents

A symmetry-adapted linear chain model is presented for the calculation of both the Brillouin zone centre and Brillouin zone boundary modes along the chain direction in high-symmetry layer crystals. The significance of group theoretical analysis for the zone boundary modes is discussed.

It is shown that the kinetic theoretical expression of the memory function of the self-diffusion constant of electron liquids exhibits marked oscillations for intermediate times, together with integrable long-time tails in both three and two dimensions.

It is shown that the averaged Green's function G of a particle in a random potential cannot diverge like (E-E_c)^{- gamma} as a function of the energy E with gamma >1. Thus the conventional critical behaviour of the n=O vector model cannot yield a description of the mobility edge behaviour.

From numerical computations based on the Born-Oppenheimer and the adiabatic approximations for the two-electron diatomic molecules, rigorous upper and lower bounds of the dissociation energy of the exciton-neutral impurity complexes are obtained.

The low-temperature thermodynamic properties of a random antiferromagnetic Heisenberg chain in zero magnetic field are studied approximately by a renormalisation group method. The couplings J obey a probability distribution function P(J) approximately 1/J^alpha , with alpha a constant. It is found that the susceptibility chi and the specific heat C behave like chi approximately T^{- alpha chi} and C approximately T^{1- alpha c} at low temperatures alpha _chi and alpha _c are weakly varying functions of temperature and slowly approach unity as T goes to zero. Comparison of these results with other theoretical analysis as well as experimental results on organic charge transfer compounds is also discussed.

By using the real space renormalisation group method proposed by Reynolds, Klein and Stanley (see J. Phys. A, vol.11, p.L199 (1978)) the authors treat bond percolation on d-dimensional cubic lattices and obtain (through various extrapolation methods): (i) p_c=¹/₂ (exact), nu _p=1.351+0.012(-0.020) and alpha _p=-0.700+0.040(-0.024) for the first-neighbour square lattice; (ii) p_c=0.250+or-0.003 for the first and second-neighbour square lattice; (iii) p_c=0.2526+or-0.0013, nu _p=0.840+or-0.020 and alpha _p=-0.520+or-0.060 for the first-neighbour cubic lattice; (iv) p_c=0.149+or-0.010, nu _p=0.667+or-0.030 and alpha _p=-0.67+or-0.12 for the first-neighbour four-dimensional hypercubic lattice. Whenever comparison is possible these figures agree fairly well with other available results. The 'magnetic' scaling power y_h is discussed for the square lattice. The influence on p_c and nu _p of the symmetry of the cluster and of the 'direction' of percolation is exhibited through several two-dimensional examples.

An asymptotic form for the structure factor S(k), for large values of k, is obtained for a simple liquid whose molecules interact via a Lennard-Jones type of potential. The result is possibly of interest in the handling of truncated experimental data.

A theoretical study is given of the heat conduction in dielectric materials in which the quasi-conservation of wavenumber in the Umklapp process is taken into account. A new expression for the thermal conductivity is derived. Comparison with the experimental data for LiF gives reasonable agreement, if the values of the parameters specifying the relaxation time of the Umklapp process are chosen suitably.

The transcorrelated method is applied to the calculation of the energy and wavefunction of the ground-state of the free-electron gas. It is shown that the results obtained are identical to those obtained by Gaskell (see Proc. Phys. Soc., vol.77, p.1182 (1961)), using the standard variational method when approximations similar to those employed by Gaskell are made.

Results are obtained for energy bands in layer compounds using the KKR method and including an ionic contribution to the lattice potential. These are compared with experimental data on densities of states from optical and photoemission data. The results show favourable agreement. A Fermi surface for NbSe₂ is proposed.

A new method for the calculation of photoionisation cross sections is presented. The complex band structure of the host semiconductor is calculated using the spherical model of Penn. The wavefunctions are then modified to provide a description of the wavefunction associated with an impurity. Use of the complex band dispersion relation provides a simple explanation of the inadequacy of the Lucovsky model (1965) when applied to very deep states.

The evaluations of the eigenstates and eigenvalues associated with deep impurities have been restricted to either very simple models or large computer calculations. The author presents an analytic method by which impurity properties may be calculated. It depends upon the calculation of the evanescent states, i.e. those non-Bloch states with energies in the band-gap, which match on to the impurity core to produce the complete state. It is shown that the band structure and the symmetry of the impurity determines the type of state required quite explicitly.

A quasi-one-dimensional magnet (CsNiF₃) is discussed with respect to the influence of the interchain-coupling on the IPC peaks above and below the transition temperature. A molecular field theory approach is used which allows the author to express the dynamic structure factors of the system in terms of the interchain interaction and the dynamic structure factors of the isolated chain.

The parallel and perpendicular susceptibility of a single crystal of LiTb_0.5Y_0.5F₄ has been measured in the temperature range 0.32-4.2K. A ferromagnetic transition occurs at T_c=1.119K instead of 2.890K for pure LiTbF₄. The critical behaviour of the parallel susceptibility has been accurately studied in the range 5*10^-4<t<10^-1, where t=(T-T_c)/T_c. A marked effect of dilution by yttrium has been observed. In contrast with pure LiTbF₄ where chi /sub /// is well fitted by the theoretically predicted law for uniaxial dipolar ferromagnets (i.e. the classical law with small logarithmic corrections), the usual power law t^{- gamma} with gamma =1.215 seems to hold in LiTb_0.5Y_0.5F₄. This could be related to a reduction of effective dimensionality with dilution.

A new type of Landau approach for the theory of spin glasses using the replica method is presented. Simple symmetry considerations lead us to find the characteristic 'saddle point' behaviour which has been proposed by Thouless, Anderson and Palmer (see Phil. Mag., vol.35, p.593 (1977)). However, in this case, it is only asymptotically valid near T_c(T<or approximately=T_c). Below T_c, the saddle point breaks into a maximum and a minimum, and both solutions yield negative entropies at T=0. To conclude, various remarks are given on the difficulties of mean-field theories in spin glasses.

A finite negative ground state energy and a non-negative ground state entropy appear to be incompatible unless linear response theory is abandoned in the spin glass phase. Various approaches using the method of broken replica symmetry are discussed. The symmetry-breaking scheme used previously by the authors is generalised to the case of an asymmetric bond distribution and the existence of a new phase, between the ferromagnetic and spin glass phases is noted. For a symmetric bond distribution it is observed that the failure of the Fischer relation chi = beta (1-q) seems to be a general consequence of replica symmetry-breaking. A physical argument for this is given, based on the hypothesis that linear response theory breaks down in the spin glass phase because of the quasi-degeneracy of the spin glass ordering.

The way in which the branch cuts of the Lindhard dielectric tensor are located in the complex-wavenumber plane is shown. Some of its physical implications are discussed.

Pure ionic cubic crystals like alkali halides exhibit a very small birefringence under the influence of an external electric field. The effect, however, increases by several orders of magnitude when substitutional impurities, which give rise to dipole defects alignable by an electric field, are added to the crystal. The quadratic electro-optic constants (Kerr constants) R₁₂₁₂ and (R₁₁₁₁-R₁₁₂₂) of KCl containing Pb²⁺ and Cu⁺ as impurities have been determined for different concentrations of the impurities. A static compensator method has been used for the measurements. The constants are found to be of the order of 10^-14 cm² V^-2, which is about four orders greater than those for pure KCl.

The broad L_{gamma 2,3} emission spectra of ₄₆Pd to ₅₄Xe are calculated from first principles in the framework of a free-atom calculation by using diagrammatic many-body theory. The L_{gamma 2,3} emission spectra are found to be due to breakdown of the quasiparticle picture of the final 4p core hole in these elements by very strong giant Coster-Kronig 4p to or from 4d² dipolar fluctuations and epsilon f decay processes. The calculated spectra are in good agreement with those obtained experimentally.

Recently, contradicting results concerning magnetotransport experiments on n-InSb at liquid helium temperatures have been reported by various authors. The authors' experiments show that the assumption of the existence of a conducting surface layer due to soldering of tin contacts to the samples is not valid. Experiments on samples treated by careful etching procedures have proven the sign change of the Hall effect and the saturation of the transverse magnetoresistance to be bulk effects.