J. Phys. I France
Volume 5, Numéro 7, July 1995
Page(s) 847 - 876
DOI: 10.1051/jp1:1995171
J. Phys. I France 5 (1995) 847-876

Magnetoconductance of Ballistic Chaotic Quantum Dots: A Brownian Motion Approach For the S-Matrix

Klaus Frahm and Jean-Louis Pichard

Service de Physique de l'État Condensé, CEA Saclay, 91191 Gif-sur-Yvette, France

(Received 14 December 1994, accepted 7 March 1995)

Using the Fokker-Planck equation describing the evolution of the transmission eigenvalues for Dyson's Brownian motion ensemble, we calculate the magnetoconductance of a ballistic chaotic dot in the crossover regime from the orthogonal to the unitary symmetry. The correlation functions of the transmission eigenvalues are expressed in terms of quaternion determinants for arbitrary number N of scattering channels. The corresponding average, variance and autocorrelation function of the magnetoconductance are given as a function of the Brownian motion time t. A microscopic derivation of this S-Brownian motion approach is discussed and t is related to the applied flux. This exactly solvable random matrix model yields the right expression for the suppression of the weak localization corrections in the large N-limit and for small applied fluxes. An appropriate rescaling of t could extend its validity to larger magnetic fluxes for the averages, but not for the correlation functions.

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