Transporte em nanoestruturas: mÃtodos de movimento Browniano e teoria de circuitos

AUTOR(ES)
DATA DE PUBLICAÇÃO

2006

RESUMO

The results presented in this thesis can be divided into two parts. In the first one we study a class of Brownian motion ensembles (BME) obtained from the general theory of matricial Markovian stochastic processes of random matrix theory. The ensembles are characterized by a Fokker-Planck equation and are closely related to Hamiltonians of Calogero-Sutherland type quantum systems. This connection allows a general classification scheme based on a recent multivariate generalization of classical orthogonal polynomials. We show that, under certain conditions, the BME can be applied to transfer matrix ensembles. Therefore, we developed a unified treatment of polynomial and transfer matrix ensembles that, apart from being used as a classification scheme of diverse symmetry classes, allows eficient calculation techniques. We developed Fokker-Planck methods to calculate ensemble averages of observables represented by linear statistics, and to obtain correlation functions. In this case, we developed an integral tansform method and a biorthogonal polynomial method to calculate the n-point correlation function. The results obtained at this general context are applied to quantum dots and quantum wires. In particular, we present a numerical study of transport properties in quantum dots with chiral symmetry. At the second part, we study an open ballistic chaotic cavity coupled, via barriers of arbitrary transparency, to two semi-infinite waveguides by using both the known circuit theory available in the literature: the scalar and the matricial theories. We show the equivalence between them by obtaining the cumulants of charge counting statistics via the generating function from both approaches and by verifying the agreement of the first 18 cumulants via algebraic computation softwares. We also studied exact distributions of electrical current for some two terminals simple systems, such as a quantum dot with symmetric barriers. These results are important, since they supply a measurable quantity in experiments

ASSUNTO(S)

mesoscopic physics semiclassical regime circuit theory fÃsica mesoscÃpica fokker-planck equation regime semiclÃssico random matrix theory polinÃmios de jack jack polynomials teoria de matrizes aleatÃrias equaÃÃo de fokker-planck calogero-sutherland model teoria de circuitos fisica modelo de calogero-sutherland

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