  The autocorrelation function $C_{\varphi,\eps}(\Delta\varphi,\,\Delta \eps)=$
$\langle \delta g(\varphi,\,\eps)\, \delta
g(\varphi+\Delta\varphi,\,\eps+\Delta \eps)\rangle$ ($\varphi$ and $\eps$ are
rescaled magnetic flux and energy) for the magnetoconductance of a ballistic
chaotic quantum dot is calculated in the framework of the supersymmetric
non-linear $\sigma$-model. The Hamiltonian of the quantum dot is modelled by a
Gaussian random matrix. The particular form of the symmetry breaking matrix is
found to be relevant for the autocorrelation function but not for the average
conductance. Our results are valid for the complete crossover from orthogonal
to unitary symmetry and their relation with semiclassical theory and an
$S$-matrix Brownian motion ensemble is discussed.
