AnÃlise diagramÃtica para cavidades caÃticas de barreira dupla : equivalÃncia com teoria quÃntica de circuitos

AUTOR(ES)
DATA DE PUBLICAÇÃO

2005

RESUMO

In this work we derive a set of coupled non-linear algebraic equations for the asymptotics of the Poisson kernel distribution, describing the statistical properties of a two-terminal double-barrier chaotic billiar (or ballistic quantum dot). The equations are calculated from a diagrammatic technique [P. W. Brouwer e C. W. Beenakker, J. Math. Phys. 37, 4904 (1996)] for performing averages over the unitary group. Nazarovâs circuit theory does not allow for a direct comparison with the diagrammatic approach for arbitrary values of the barriesâs transparencies, because of the intrisicic difficulty to determine the averge pseudo-current-voltage characteristics of an arbitrary circuit element. This difficulty was recently removed by a novel systematic treatment presented in [A. M. S. MacËedo, Phys. Rev. B 66, 033306 (2002)], in which circuit theory is combined with the supersymmetric non-linear Â-model. The problem was reduced to a comparison between a pair ofcoupled non-linear algebraic equations (diagramatic technique) and a polynomial equation of fourth order (circuit theory. Exact agreement was found for a variety of quantities, such as the first four cumulants of the full counting statistics and the average trasmission eigenvalue density for symmetric barriers and tunnel junctions. The complete equivalence of these approaches is a non-trivial result, because the semiclassical concatenation priciple, used to derive circuit theory equations, has no obvious counterpart in the diagrammatic method. We expect our result to help establishing a direct connection between several recent independent developments of both approaches, such as those in magnetoelectronics end normal-superconducting hybrid systems

ASSUNTO(S)

teoria de matrizes aleatorias fisica analise diagramatica teoria quÃntica de circuitos

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