A semiflexible harmonic chain model with extensible bonds is introduced and applied to the stretching of semiflexible polymers or filaments. The semiflexible harmonic chain model allows to study effects from bending rigidity, bond extension, discrete chain structure, and finite length of a semiflexible polymer in a unified manner. The interplay between bond extension and external force can be described by an effective inextensible chain with increased stretching force, which leads to apparently reduced persistence lengths in force-extension relations. We obtain force-extension relations for strong- and weak-stretching regimes which include the effects of extensible bonds, discrete chain structure, and finite polymer length. We discuss the associated characteristic force scales and calculate the crossover behaviour of the force-extension curves. Strong stretching is governed by the discrete chain structure and the bond extensibility. The linear response for weak stretching depends on the relative size of the contour length and the persistence length which affects the behaviour of very rigid filaments such as F-actin. The results for the force-extension relations are corroborated by transfer matrix and variational calculations.
The density of states (DOS) of electrons in two-dimensional (2D) quantum wells and the broadening of Landau levels (LL's) is evaluated. The electrons are assumed to interact with screened, charged impurities located at random in the material. The random location of the impurities leads to a disordered environment seen by the electrons. The screening of the impurities by the 2D electron gas is evaluated in a simple Thomas-Fermi model which depends on the DOS at the Fermi surface, n (EF). The DOS and screening are evaluated iteratively at each magnetic field value. We find that the self-consistent evaluation of the DOS and screening leads to broadening of the LL's and n (EF) that oscillates with B. The oscillating LL widths and n (EF) are compared with the data of Heitmann et al. , Englert et al. , Wang et al. , and Smith et al. and reproduce all the observed values quite well. The chief adjustable parameter is the impurity concentration.
The density of electron states, p(E), in disordered systems in the band-tail region near band edges is investigated. %'e show that the p(E) of the Halperin and Lax type derived by Sa-yakanit predicts, in three dimensions, an exponential (Urbach) band tail for the correlation lengths found in amorphous Si and within the energy range observed in optical absorption near band edges. The simple exponential behavior is not universal and may not, for example, be observed in heavily doped semiconductors.
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