  We derive a semiclassical trace formula for quantized chaotic transformations
of the torus coupled to a two-spinor precessing in a magnetic field. The trace
formula is applied to semiclassical correlation densities of the quantum map,
which, according to the conjecture of Bohigas, Giannoni and Schmit, are
expected to converge to those of the circular symplectic ensemble (CSE) of
random matrices. In particular, we show that the diagonal approximation of the
spectral form factor for small arguments agrees with the CSE prediction. The
results are confirmed by numerical investigations.
