  We use semiconductors as an example to show that quantum chaos manifests
itself in the energy spectrum of crystals. We analyze the {\it ab initio} band
structure of silicon and the tight-binding spectrum of the alloy
$Al_xGa_{1-x}As$, and show that some of their statistical properties obey the
universal predictions of quantum chaos derived from the theory of random
matrices. Also, the Bloch momenta are interpreted as external, tunable,
parameters, acting on the reduced (unit cell) Hamiltonian, in close analogy to
Aharonov-Bohm fluxes threading a torus. They are used in the investigation of
the parametric autocorrelator of crystal velocities. We find that our results
are in good agreement with the universal curves recently proposed by Simons and
coworkers.
