  We perform a comparative study of the quantum and classical transport
probabilities of low-energy quasiparticles ballistically traversing normal and
Andreev two-dimensional open cavities with a Sinai-billiard shape. We focus on
the dependence of the transport on the strength of an applied magnetic field
$B$. With increasing field strength the classical dynamics changes from mixed
to regular phase space. Averaging out the quantum fluctuations, we find an
excellent agreement between the quantum and classical transport coefficients in
the complete range of field strengths. This allows an overall description of
the non-monotonic behavior of the average magnetoconductance in terms of the
corresponding classical trajectories, thus, establishing a basic tool useful in
the design and analysis of experiments.
