S-Matrix Formulation of Mesoscopic Systems and Evanescent Modes

The Landauer-Butikker formalism is an important formalism to study mesoscopic systems. Its validity for linear transport is well established theoretically as well as experimentally. Akkermans et al [Phys. Rev. Lett. {\bf 66}, 76 (1991)] had shown that the formalism can be extended to study thermodynamic properties like persistent currents. It was earlier verified for simple one dimensional systems. We study this formula very carefully and conclude that it requires reinterpretation in quasi one dimension. This is essentially because of the presence of evanescent modes in quasi one dimension.Comment: non

Large diamagnetic persistent currents

In multichannel rings, evanescent modes will always co-exist with propagating modes. The evanescent modes can carry a very large diamagnetic persistent current that can oscillate with energy and are very sensitive to impurity scattering. This provides a natural explanation for the large diamagnetic persistent currents observed in experiments.Comment: 5 figure

Wave propagation in a quasi-periodic waveguide network

We investigate the transport properties of a classical wave propagating through a quasi-periodic Fibonacci array of waveguide segments in the form of loops. The formulation is general, and applicable for electromagnetic or acoustic waves through such structures. We examine the conditions for resonant transmission in a Fibonacci waveguide structure. The local positional correlation between the loops are found to be responsible for the resonance. We also show that, depending on the number of segments attached to a particular loop, the intensity at the nodes displays a perfectly periodic or a self-similar pattern. The former pattern corresponds to a perfectly extended mode of propagation, which is to be contrasted to the electron or phonon characteristics of a pure one dimensional Fibonacci quasi-crystal.Comment: 15 pages, 5 figure

Unusual modes and photonic gaps in a Vicsek waveguide network

We propose a simple model of a waveguide network designed following the growth rule of a Vicsek fractal. We show, within the framework of real space renormalization group (RSRG) method, that such a design may lead to the appearance of unusual electromagnetic modes. Such modes exhibit an extended character in RSRG sense. However, they lead to a power law decay in the end-to-end transmission of light across such a network model as the size of the network increases. This, to our mind, may lead to an observation of power law localization of light in a fractal waveguide network. The general occurence of photonic band gaps and their change as a function of the parameters of the system are also discussed.Comment: 13 pages, 6 figure

Effects of dimerization and spin polarization on the conductance of a molecular wire

We have studied the effects of dimerization on the energy levels of a one-dimensional molecular chain attached between two electrodes. Analytic expressions for the change in energies in the presence of a small perturbing external potential have been obtained for the three limiting cases: (a) uniform, (b) partially dimerized and (c) completely dimerized chains. We find that the presence of dimerization enhances the mixing between low-lying energies in the system resulting in a situation conducive to showing negative differential resistance (NDR) in the current-voltage characteristics. The effect of spin-polarized molecule-electrode couplings on a dimerized chain has also been studied, where both spin-parallel and spin-antiparallel current show NDR behaviour. Strong dimerization however is found to destroy the spin-valve effects that are most essential for spintronic devices