V. Gasparian

Transmission of waves through one-dimensional random layered systems

A convenient formalism is developed that allows one to express the transmission coefficient of a wave propagating in a one-dimensional disordered structure through the determinant TN= mod DN mod -2, which depends on the amplitudes of reflection of a single scatterer only. It is shown that the density of states averaged over the sample as well as the spectrum of surface and volume waves in such a layered system may also be represented by the determinant DN.

Resistance of one-dimensional chains in Kronig-Penny-like models

Abstract We give the formula for the resistance of one-dimensional chains of arbitrary δ-potentials without finding electron eigenfunctions. We have analyzed the main consequences of this formula, and the distribution functions of resistances are also determined.

Fluctuations of the correlation dimension at metal-insulator transitions

We investigate numerically the inverse participation ratio, P(2), of the 3D Anderson model and of the power-law random banded matrix (PRBM) model at criticality. We found that the variance of lnP(2) scales with system size L as sigma(2)(L) = sigma(2)(infinity)-AL(-D(2)/2d), with D(2) being the correlation dimension and d the system dimension. Therefore the concept of a correlation dimension is well defined in the two models considered. The 3D Anderson transition and the PRBM transition for b = 0.3 (see the text for the definition of b) are fairly similar with respect to all critical magnitudes studied.

Anomalously large critical regions in power-law random matrix ensembles

We investigate numerically the power-law random matrix ensembles. Wave functions are fractal up to a characteristic length whose logarithm diverges asymmetrically with different exponents, 1 in the localized phase and 0.5 in the extended phase. The characteristic length is so anomalously large that for macroscopic samples there exists a finite critical region, in which this length is larger than the system size. The Greens functions decrease with distance as a power law with an exponent related to the correlation dimension.

A solvable three-body model in finite volume

Abstract In this work, we propose an approach to the solution of finite volume three-body problem by considering asymptotic forms and periodicity property of wave function in configuration space. The asymptotic forms of wave function define on-shell physical transition amplitudes that are related to distinct dynamics, therefore, secular equations of finite volume problem in this approach require only physical transition amplitudes. For diffractive spherical part of wave function, it is convenient to map a three-body problem into a higher dimensional two-body problem, thus, spherical part of solutions in finite volume resembles higher spatial dimensional two-body Luschers formula. The idea is demonstrated by an example of two light spinless particles and one heavy particle scattering in one spatial dimension.

Localization length in two-dimensional disordered systems: effects of evanescent modes

We study the influence of evanescent modes on the scaling behavior of the renormalized localization length (RLL) in 2D disordered systems, using the δ-function potential strip model and the multichain tight-binding Anderson model. In the weak disorder regime we have evaluated the RLL for large numbers of modes M. It is shown that RLL shrinks with increasing M which indicates that the electron states will remain localized in an infinitely wide system for an arbitrarily small disorder, in agreement with existing theories. In the thermodynamic limit ([Formula: see text]) for the two models, we obtain the localization length in an infinitely large system. We show that the presence of evanescent modes enhances the RLL with respect to the value obtained when evanescent modes are absent. We also derive an exact relationship between the localization length and its corresponding average mean free path for an M-channel system for the case where propagating as well as evanescent channels are present.

Charge pumping and noise in a one-dimensional wire with weak electron-electron interactions

We consider the adiabatic pumping of charge through a mesoscopic one dimensional wire in the presence of electron-electron interactions. A two-delta potential model is used to describe the wire, which allows to obtain exactly the scattering matrix coefficients, which are renormalized by the interactions. Two periodic drives, shifted one from another, are applied at two locations of the wire in order to drive a current through it in the absence of bias. Analytical expressions are obtained for the pumped charge, current noise, and Fano factor in different regimes. This allows to explore pumping for the whole parameter range of pumping strengths. We show that, working close to a resonance is necessary to have a comfortable window of pumping amplitudes where charge quantization is close to the optimum value: a single electron charge is transferred in one cycle. Interactions can improve the situation, the charge

Potential distribution in a finite 1-D array of arbitrary mesoscopic tunnel junctions

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Large diffusion lengths of excitons in perovskite and TiO2 heterojunction

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1D Conductance in Cetineites: A New Class of Chemically Synthesized Nanoporous Semiconductors

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