MAGNETOCONDUCTANCE OF BALLISTIC CHAOTIC QUANTUM DOTS - A BROWNIAN-MOTION APPROACH FOR THE S-MATRIX

Using the Fokker-Planck equation describing the evolution of the trans mission eigenvalues for Dyson's Brownian motion ensemble, we calculate the magnetoconductance of a ballistic chaotic dot in in the crossover regime from the orthogonal to the unitary symmetry. The correlation f unctions of the transmission eigenvalues are expressed in terms of qua ternion determinants for arbitrary number N of scattering channels. Th e 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 dis cussed and t is related to the applied flux. This exactly solvable ran dom matrix model yields the right expression for the suppression of th e weak localization corrections in the large N-limit and for small app lied fluxes. An appropriate rescaling of t could extend its validity t o larger magnetic fluxes for the averages, but not for the correlation functions.