This paper presents a theory that is the basis of the steady-state-photocarrier-grating (SSPG) technique, as a means of determining the diffusion length of photocarriers in amorphous semiconductors. Solving the SSPG transport problem, including the formulation of small-signal photocurrent, by a second-order perturbation approach reveals deficiencies in the existing SSPG theory, which is based on first-order perturbation theory. It is also shown that the SSPG data analysis done routinely, assuming a priori that local space-charge neutrality prevails, yields a severe overestimate of the diffusion length when the condition is not met experimentally. An extension of the theory to measure accurately the diffusion length by removing these defects inherent in the original SSPG formulation is demonstrated by its successful application to hydrogenated amorphous silicon. The experiments carried out at various illumination levels show that the correct value of the diffusion length and its light-intensity dependence indeed differ to a significant degree from the results obtained with use of the previous method. A physical interpretation of the measured intensity dependence is also given, assuming a trap-controlled photocarrier transport model.

The exactly soluble Luttinger model can also be analyzed from the point of view of the renormalization group. A perturbation theory of the beta function of the model is derived. We argue that the main terms of the beta function vanish identically if the anomalous dimension is properly treated and if suitable properties of the exact solution are taken into account. Our treatment is purely perturbative and we do not discuss the problems of convergence of the formal series defining the beta function: it has recently been established, however, that the series defining it is convergent.

We extend the Su-Schrieffer-Heeger model of polyacetylene to the cases of C60 and C70 molecules. The results of our numerical calculations of the undoped systems agree well with the known results. When the system (C60 or C70) is doped with one or two electrons (or holes), additional charges accumulate nearly along an equatorial line of the molecule. The dimerization becomes weaker along the same line. Two energy levels intrude deeply into the gap; the intrusion is deeper in C70 than in C60. Therefore, polarons are predicted in doped fullerenes. We calculate the optical-absoprtion coefficient for the C60 fullerene in order to consider how the polarons will be observed. It is predicted that an additional absorption peak appears at an energy lower than the intergap transition peaks of the undoped C60. It is found that the C60 and C70 fullerenes are closely related in their electronic structures as well as lattice geometries.

Scattering resonances in ballistic conduction across a quantum dot in a weak magnetic field are investigated. Due to the special geometry considered, the resonances grow narrower with decreasing B, until at B = 0 they become bound states in the continuum. Whereas previously treated geometries exhibit at most one bound state with energy in the continuum, the number of such states in the present case is limited only by the number of transverse modes that the wire leads can sustain. Furthermore, the present model demonstrates the possibility of quantum-mechanical bound states in the continuum having a classical analog. The energy shifts of the resonances in a magnetic field show paramagnetic as well as diamagnetic behavior, which can be understood in terms of the dominant influence of a particular subband and its distance from the cutoff threshold in the dot region.

We give a microscopic derivation of the speed of light relevant for energy transport in media containing randomly distributed scatterers. A comparison is made with the concept of mass-enhancement in electron transport theory. The consequences for the Thouless criterion for strong localization are discussed. Finally, quantitative results are obtained for simple scatterers, such as semiclassical oscillators and dielectric spheres. We will also introduce some heuristic approaches and discuss the validity.

We consider finite-element methods for the approximation of solutions of the Ginzburg-Landau equations of superconductivity. The methods are based on a discretization of the Euler-Lagrange equations resulting from the minimization of the free-energy functional. The discretization is effected by requiring the approximate solution to be a piecewise polynomial with respect to a grid. The magnetization versus magnetic field curves obtained through the finite-element methods agree well with analogous calculations obtained by other schemes. We demonstrate, both by analyzing the algorithms and through computational experiments, that finite-element methods can be very effective and efficient means for the computational simulation of superconductivity phenomena and therefore could be applied to determine macroscopic properties of inhomogeneous, anisotropic superconductors.