MANIFESTATION OF QUANTUM CHAOS IN ELECTRONIC BAND STRUCTURES

We use semiconductors as an example to show that quantum chaos manifes ts itself in the energy spectrum of crystals. We analyze the ab initio band structure of silicon and the tight-binding spectrum of the alloy AlxGa1-xAs, and show that some of their statistical properties obey t he universal predictions of quantum chaos derived from the theory of r andom matrices. Also, the Bloch momenta are interpreted as external, t unable, 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 velo cities. We find that our results are in good agreement with the univer sal curves recently proposed by Simons and co-workers.