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Title: Systematic approach to statistics of conductance and shot-noise in chaotic cavities
Authors: Khoruzhenko, BA
Savin, DV
Sommers, H-J
Keywords: Random matrix theory;Chaotic cavities;Conductance;Shot-noise
Issue Date: 2009
Publisher: American Physical Society
Citation: Physical Review B, 80(12): Article no. 125301, 2009
Abstract: Applying random matrix theory to quantum transport in chaotic cavities, we develop a powerful method for computing the moments of the conductance and shot-noise (including their joint moments) of arbitrary order and at any number of open channels. Our approach is based on the Selberg integral theory combined with the theory of symmetric functions and is applicable equally well for systems with and without time-reversal symmetry. We also compute higher-order cumulants and perform their detailed analysis. In particular, we establish an explicit form of the leading asymptotic of the cumulants in the limit of the large channel numbers. We derive further a general Pfaffian representation for the corresponding distribution functions. The Edgeworth expansion based on the first four cumulants is found to reproduce fairly accurately the distribution functions in the bulk even for a small number of channels. As the latter increases, the distributions become Gaussian-like in the bulk but are always characterized by a power-law dependence near their edges of support. Such asymptotics are determined exactly up to linear order in distances from the edges, including the corresponding constants.
Description: Copyright © 2009 The American Physical Society.
ISSN: 1098-0121
Appears in Collections:Dept of Mathematics Research Papers
Mathematical Sciences

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