A treatment for the phonoriton problem based on the model introduced by Wang and Birman is proposed. It is shown that the model describes an interacting phonoriton system rather than a free one. The phonoriton spectrum is then calculated by using the Matsubara Green function technique. It is seen from the result that the phonoriton-phonoriton interaction narrows the gap in comparison with the gap in the spectrum of free phonoritons obtained by Wang and Birman. The damping of phonoriton states due to the interaction is explicitly calculated as well.

The effect of the hopping on the magnetic and dielectric properties of the box mode. introduced by A. ZAWXDOWSXl and M. H. COHEN [1] are considered.By symmetry reasoning it is shown that the free energy is ah even funetion of the hopping rateas well as of the external electric field.It is proved that at finite temperature when the hopping is small enough the hopping processes in various ]9oxes are uncorrelated. Based on this the magnetic and dieleetric susceptio bilities are ca]culated up to the second order of the hopping tate.

The dynamical aspects of the phonoriton state in highly-photoexcited semiconductors is studied theoretically. The effect of the exciton–exciton interaction and nonbosonic character of high-density excitons are taken into account. Using Green's function method and within the Random Phase Approximation it is shown that the phonoriton dispersion and damping are very sensitive to the exciton density, characterizing the excitation degree of semiconductors.

The novel method proposed by one of the authors to calculate exactly the response functions of the one-dimensional Tomonaga model is described in more detail. The method is generalized for the case of a system of conpled chains where both the intrachain and interchain interactions have forward scatte¡ components only. The model does not show real phase transition at any finite temperature indicating that the interchain backward scattering or hopping is needed to have ah ordering of the chains at finite temperatnre. lntroductionReeently quasi-one-dimensional (quasi-l-d) conductors attraeted a great deal of interest because of their unusual properties. Fora review of works done in the past few years see [1]-- [3]. These systems are built usually of large, flat molecules which ate relatively closely stacked in one direction to forro ehains, the adj aeent chains being ata relatively larger distante. Thus the motion of electrons is confined predominantly to motion along the chains with rare hoppings between them.Various theoretical models have been worked out to study the properties of these systems. One of these models is the Fermi gas model which has been investigated in the strictly 1-d case in great detail. A review of the properties of this model can be found in [4]. Since a 1-d system may ¡ specific properties of behaviour (such as absence of phase transition at finite temperature) which ate characteristic for 1-d systems but ate not neeessarily true in higher dimensions, any realistic model of quasi-l-d conductors should contain some kind of interaction between the chains. Generalizations of the 1-d Fermi gas model in this direction have indeed been attempted [5]-- [9]. The Fermi gas model is a model with infrared singularities difficult to treat in a satisfactory manner at low temperatures and low energies even in its strietly 1-d version already. The treatment becomes increasingly more complicated when interchain interactions ate taken into account. Therefore any simplified model which can be solved exactly is of great value in finding out what the effect of the interaction terms is.