Ballistic transport through chaotic cavities: Parametric correlations and the weak localization peak in a Brownian-motion model

A Brownian-motion model is devised on the manifold of S matrices, and applied to the calculation of conductance-conductance correlations and of the weak localization peak. The model predicts that (i) the correlation function in B has the same shape and width as the weak localization peak; (ii) the functions behave as ∝1-O(${\mathit{B}}^2$), thus excluding a linear line shape; and (iii) their width increases as the square root of the number of channels in the leads. Some of these predictions do not agree with experiment and with other calculations.