The one‐dimensional Fröhlich model with a nearly half‐filled band is solved in the mean‐field approximation for finite temperatures, extending a recent ground‐state calculation by Brazovski et al. The commensurate–incommensurate phase transition is shown to be continuous, and the corresponding transition temperature is calculated as a function of the chemical potential or the electron density.

The electron density of states and localization length are calculated for weakly disordered dimerized tight‐binding chains. Pure bond disorder causes a singular density of states for small bond gaps, and a singular localization length for zero bond gap, whereas larger bond gaps are transformed into pseudogaps. A site gap for diatomic chains is preserved under bond disorder. Site disorder destroys any gap and does not create singularities in the density of states or localization length. These results are compared with those obtained from the continuum approximation with Gaussian disorder, which is not strictly justified for short‐ranged disorder potentials. However, the continuum results are valid for weakly disordered chains provided the bond and site disorders in the chain correspond to bond‐gap and combined site and site‐gap disorders in the continuum model, respectively.

Quasi-one-dimensional systems with arbitrary disorder that are subject to a Peierls ͑bond͒ or Fröhlich ͑site͒ distortion can be classified in the continuum approximation by five parameters. These are bond and site gap, as well as forward, backward, and umklapp scattering. The averaged one-particle Green's function of the general continuum model is calculated exactly by means of the supersymmetry method. The density of states and the localization length are given by an explicit formula in terms of the hypergeometric function. The results are applied to discuss the tail in the optical conductivity of polyacetylene and to investigate the combined influence of site and bond gaps in diatomic chains. ͓S0163-1829͑96͒50532-1͔

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Magnetic surface states on cylindrical part5 of the Fermi surface and their relation to volume Landau states are discussed. The scattering of the surface states by a rough Burface is calculated quantum mechanically, giving the classical Scattering rate in a certain limiting case. Transitions between surface states give rise to small oscillations of the surface impedance, which are calculated for arbitrary orientations of the cylinder and the magnetic field, starting with the electric field distribution in the case of anomalous skin effect. The results are compared with experimental data in indium. More elaborate numerical calculations of the transition matrix elements and the surface scattering rate are required to determine the parameters of surface scattering unambiguously.Magnetische Oberfliichenzustiinde von Elektronen auf zylindrischen Teilen der Fermifliiche und ihr Zusammenhang mit den Landau-Volumenzustiinden werden diskutiert. Die Streuung von OberfIichenzustiinden an einer rauhen Oberfliiche wird quantenmechanisch berechnet, wobei sich in einem gewissen Grenzfall die klassische Streurate ergibt. Ubergiinge zwischen Oberfliichenzustiinden fiihren zu schwachen Oszillationen der Oberflichenimpedanz, die unter Zugrundelegung der Feldverteilung des anomalen Skineffektes fur beliebige Orientierung des Zylinders und des Magnetfeldes berechnet werden. Die Ergebnisse werden mit gemessenen Impedanzkurven fur Indium verglichen. Weitere numerische Berecbnungen der ubergangs-Matrixelemente sowie der Oberfliichenstreurate sind erforderlich, um den Parameter der Oberfliichenstreuung eindeutig zu bestimmen.