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In order to investigate the structure of the charge density waves in nearly quarter-filled one-dimensional electron-photon systems, the ground states of finite chains are studied numerically by using the SSH and Frohlich-type models. The structure factor of the CDW is calculated for the two models with different electron concentrations and different constants. The results are discussed in connection to the X-ray or neutron scattering experiments.

Magnetothermal resistivity of an antiferromagnetic insulator is calculated by assuming that the thermal energy is carried mainly by phonons which are scattered by spin fluctuations. The spin system is treated by the Green function method.

The impurity concentration dependence of the transition temperature into the Peierls phase is discussed in the low concentration region (i.e. in the linear region), assuming a δ-function type potential. The effect of fluctuation is taken account of by the method of Scalapino, Sears and Ferrell. The decrease of the transition temperature per one per cent of impurities is estimated in the case of TTF—TCNQ but found to be one order of magnitude smaller than that observed recently in an experiment.

We discuss the status of the theory of localisation in two dimensions in the presence of a strong perpendicular magnetic field. The model potentials which have been used are described. The importance of the various length scales in the problem is pointed out. A summary of the currently available definitions of localisation is given. The results for the localisation length, the inverse participation number of the states, and their shape, obtained so far are summarised.

Etude du melange entre les etats de bord appartenant a la plus basse (N=0) sousbande de Landeau et les etats etendus de la sousbande de Landau pour laquelle N=1 et entre les etats de bord des sousbandes N=0 et N=1. On montre qu'il depend fortement de la gamme des potentiels et qu'il est considerablement reduit par une diminution du potentiel des impuretes

Eigenvalue problem for an effective Hamiltonian to describe the dynamics of the center coordinates of the cyclotron motion, derived by Tsukada, is explicitly solved in the case of a single Gaussian type potential. The eigen function does not depend on the range of the potential while the eigenergy does. Assuming random distributions of the strength and range of the potentials and of the positions of potential centers, the frequency dependence of the dynamical conductivity due to the tail states is expected to be given by D(EF)2ω2lnω in the low frequency and low temperature limit where D(EF) is the density of states at the Fermi energy EF.

From self-consistent determination of the dynamical diffusion coefficient, the Fermi energy dependence of the localization length, ξ( E F ), is obtained for the case where the Fermi energy, E F , lies near the center of the lowest Landau subb057.tex and. If the energy is measured from the point where the real part of the retarded Green's function vanishes, ξ( E F ) for small | E F | is expected to be proportional to l exp (γ 2 / E F 2 ) with l the cyclotron radius and γ a constant of the order of subband width.

The magnetic field dependence of the mobility edge is examined within the framework of the self-consistent treatment of the Anderson localization. It is seen that the mobility edge is reduced in proportion to \( \sqrt{H}\) where H is the strength of the field.

A self-consistent treatment of Anderson localization by Vollhardt and Wolfle [Phys. Rev. B22 (1980) 4666] is extended to systems without time reversal symmetry. In this paper the method is applied to a system in such a weak magnetic field that the field effect can be treated quasiclassically. It is found that the magnetic field enhances the dynamical conductivity, though the static conductivity remains zero at absolute zero. The present investigation indicates that the one-parameter scaling theory cannot describe systems without the time reversal symmetry.