Publications (3)0 Total impact
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Gabriel A. Cwilich
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ABSTRACT: It is possible to discuss the propagation of an electronic current through certain layered nanostructures modeling them as a collection of random one-dimensional interfaces, through which a coherent signal can be transmitted or reflected while being scattered at each interface. We present a simple model in which a persistent random walk (the "t-r" model in 1-D) is used as a representation of the propagation of a signal in a medium with such random interfaces. In this model all the possible paths through the system leading to transmission or reflection can be enumerated in an expansion in the number of loops described by the path . This expansion allows us to conduct a statistical analysis of the length of the paths for different geometries and boundary conditions and understand their scaling with the size of the system. By tuning the parameters of the model it is possible to interpolate smoothly between the ballistic and the diffusive regimes of propagation. An extension of this model to higher dimensions is presented. We show Monte Carlo simulations that support the theoretical results obtained. Comment: 12 pages, 5 figures
01/2002;
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ABSTRACT: We obtain the statistics of the intensity, transmission and conductance for scalar electromagnetic waves propagating through a disordered collection of scatterers. Our results show that the probability distribution for these quantities, x, follow a universal form x^a Exp(-x^m) . This family of functions includes the Rayleigh distribution (when a=0, m=1) and the Dirac delta function (a -> Infinity), which are the expressions for intensity and transmission in the diffusive regime neglecting correlations. Finally, we find simple analytical expressions for the nth moment of the distributions and for to the ratio of the moments of the intensity and transmission, which generalizes the n! result valid in the above regime.
12/2001;
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ABSTRACT: Waves propagate through disordered systems in a variety of regimes. There is a threshold of disorder beyond which waves become localized and transport becomes restricted. The intensity I of the wave transmitted through a system has a dependence on the length L of the sample that is characteristic of the regime. For example, I decays as 1/L in the diffusive regime. It is of current interest to characterize the transport regime of a wave from statistical studies of the transmittance quantities through it. Studies suggest that the probability distribution of the intensity could be used to characterize the localized regime. There is an ongoing debate on what deviations from the classical Rayleigh distribution are to be expected. In this numerical work, we use scalar waves to obtain the intensity, transmission, and conductance of waves through a disordered system. We calculate the intensity, by setting an incoming plane wave towards the sample from a fixed direction. The outgoing intensity is then calculated at one point in space. This process is repeated for a collection of samples belonging to the same ensemble that characterizes the disorder, and we construct the probability distribution of the intensity. In the case of transmission, we evaluate the field arriving to a series of points distributed in the far field, and repeat the same statistical analysis. For the conductance, we calculate the field at the same series of points for incoming waves in different directions. We analyze the distribution of the transmittance quantities and their change with the degree of disorder.
05/2001;
