  We develop a semiclassical theory for spin-dependent quantum transport in
ballistic quantum dots. The theory is based on the semiclassical Landauer
formula, that we generalize to include spin-orbit and Zeeman interaction.
Within this approach, the orbital degrees of freedom are treated
semiclassically, while the spin dynamics is computed quantum mechanically.
Employing this method, we calculate the quantum correction to the conductance
in quantum dots with Rashba and Dresselhaus spin-orbit interaction. We find a
strong sensitivity of the quantum correction to the underlying classical
dynamics of the system. In particular, a suppression of weak antilocalization
in integrable systems is observed. These results are attributed to the
qualitatively different types of spin relaxation in integrable and chaotic
quantum cavities.
