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Brownian motion ensembles and parametric correlations of the transmission eigenvalues: Application to coupled quantum billiards and to disordered wires

Klaus Frahm·Jean-Louis Pichard
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Abstract

The parametric correlations of the transmission eigenvalues $T_i$ of a $N$-channel quantum scatterer are calculated assuming two different Brownian motion ensembles. The first one is the original ensemble introduced by Dyson and assumes an isotropic diffusion for the $S$-matrix. The second Brownian motion ensemble assumes for the transfer matrix $M$ an isotropic diffusion yielded by a multiplicative combination law. We review the qualitative differences between transmission through two weakly coupled quantum dots and through a disordered line and we discuss the mathematical analogies between the Fokker-Planck equations of the two Brownian motion models.

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Klaus Frahm, Jean-Louis Pichard. 1995-04-25. Brownian motion ensembles and parametric correlations of the transmission eigenvalues: Application to coupled quantum billiards and to disordered wires. https://doi.org/10.1051/jp1%3A1995111

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