The coherent propagation of elastic waves in a solid filled with a random distribution of pinned dislocation segments is studied to all orders in perturbation theory. It is shown that, within the independent scattering approximation, the perturbation series that generates the mass operator is a geometric series that can thus be formally summed. A divergent quantity is shown to be renormalizable to zero at low frequencies. At higher frequencies said quantity can be expressed in terms of a cut-off with dimensions of length, related to the dislocation length, and physical quantities can be computed in terms of two parameters, to be determined by experiment. The approach used in this problem is compared and contrasted with the scattering of de Broglie waves by delta-function potentials as described by the Schrödinger equation.

We establish the dominant effect of anisotropic weak localization ͑WL͒ in three dimensions ͑3D͒ associated with a propagative Fermi surface on the conductivity correction in heavily nitrogen-doped ultrananocrystalline diamond ͑UNCD͒ films based on magnetoresistance studies at low temperatures. Also, low-temperature electrical conductivity can show weakly localized transport in 3D combined with the effect of electron-electron interactions in these materials, which is remarkably different from the conductivity in two-dimensional WL or strong localization regime. The corresponding dephasing time of electronic wave functions in these systems described as ϳT −p with p Ͻ 1, follows a relatively weak temperature dependence compared to the generally expected nature for bulk dirty metals having p Ն 1. The temperature dependence of Hall ͑electron͒ mobility together with an enhanced electron density has been used to interpret the unusual magnetotransport features and show delocalized electronic transport in these n-type UNCD films, which can be described as lowdimensional superlattice structures.

We study the diffusion of anti-plane elastic waves in a two dimensional continuum by many, randomly placed, screw dislocations. Building on a previously developed theory for coherent prop-

Abstract. In the framework of strong field QED, the generation of a residual alternating polarization current is demonstrated, which remains after switching off an external field pulse. This effect is stipulated by inertial properties of the physical vacuum. In the standard vacuum D = 2 + 1 QED, this current is rapidly damped fast but can be available, apparently, for observation in the graphene, where the Fermi velocity v F c plays an analogous role as the light velocity.

Resonant tunneling features through impurity clusters embedded in an insulating matrix have been examined through the inter-play between the size of the clusters and the inter-cluster distance. Constructive interference phenomena were tuned through a systematic study of different geometrical configurations, thereby controlling confinement in quasi-bound states. Gaussian trap potentials have been used to simulate the imperfect barrier-well interface associated with disordered materials. Strongly localized states can be formed successfully despite weak disorder as illustrated by breaking the symmetry in the horizontal configuration. To this end, triangular cluster configurations were investigated under a variety of conditions including various shapes and orientations. The effects of disorder created effectively by the arbitary configurations destroy the Fano resonance, which is previlent in conductance spectra and consequently reduce the peak to valley ratio of the resonant peak in current vs. voltage curves. However the formation of two quasi-bound states is demonstrated, suggesting possible applications for disordered naturally grown systems of impurity clusters. This work addresses the controlled lifetime of quasi-bound states and can inform the design of fast switching devices based on high band gap materials by the astute incorporation of impurity clusters with specific geometrical configurations.

Manipulating the electrical properties of carbon nanotubes through semi-metal or semiconductor filling is of paramount importance in the realization of nano-electronic devices based on one dimensional composite materials. From low temperature electrical conductivity measurements of a network, of empty and filled double-walled carbon nanotubes (DWNT’s), we report a transition in electrical transport features from hopping to weakly activated conduction by HgTe filling and also semi-metallic conduction in selenium (Se) filled DWNT’s. Magneto-resistance (MR) studies of the filled DWNT’s show suppression of the hopping conduction and a signature of 3D weak localization for Se@DWNT’s at low temperatures and high magnetic fields. These results are discussed on the basis of strength of interaction between the filler material and the inner-walls of the host DWNT’s, which enhances the electronic density of states (DOS) in the material as well as the change in the property of the filler material due to constrained encapsulation.

A realistic transport model showing the interplay of the hopping transport between the outer shells of iron filled entangled multi-walled carbon nanotubes (MWNT) and the diffusive transport through the inner part of the tubes, as a function of the filling percentage, is developed. This model is based on low-temperature electrical resistivity and magneto-resistance (MR) measurements. The conductivity at low temperatures showed a crossover from Efros-Shklovski (E-S) variable range hopping (VRH) to Mott VRH in 3 dimensions (3D) between the neighboring tubes as the iron weight percentage is increased from 11% to 19% in the MWNTs. The MR in the hopping regime is strongly dependent on temperature as well as magnetic field and shows both positive and negative signs, which are discussed in terms of wave function shrinkage and quantum interference effects, respectively. A further increase of the iron percentage from 19% to 31% gives a conductivity crossover from Mott VRH to 3D weak localization (WL). This change is ascribed to the formation of long iron nanowires at the core of the nanotubes, which yields a long dephasing length (e.g. 30 nm) at the lowest measured temperature. Although the overall transport in this network is described by a 3D WL model, the weak temperature dependence of inelastic scattering length expressed as L ~T -0.3 suggests the possibility for the presence of one-dimensional channels in the network due to the formation of long Fe nanowires inside the tubes, which might introduce an alignment in the random structure. _______________________________________________________________________________________________________ *Somnath.Bhattacharyya@wits.ac.za

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