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We use semiconductors as an example to show that quantum chaos manifests itself in the energy spectrum of crystals. We analyze the ab initio band structure of silicon and the tight-binding spectrum of the alloy Al Gaz 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 Suxes threading a torus. They are used in the investigation of the parametric autocorrelator of crystal velocities. We 6nd that our results are in good agreement with the universal curves recently proposed by Simons and co-workers.

Effects of pressure and composition on the gap properties of AlxGa1−xAs randomly disordered alloys are investigated theoretically and experimentally. The analogy between pressure and alloying effects is explored. Special attention is given to the direct-to-indirect gap transition region, where the gap sensitivity to both pressure and composition variations is shown to be strongly enhanced. A 30% decrease in luminescence intensity is produced on a x=0.46 sample under applied pressure of 0.7 kbar, while a similar effect in GaAs would require pressures of several tens of kbar. Calculations are performed within the small crystal approach using 64-, 216-, and 1000-atoms basic cluster sizes, with periodic boundary conditions. Convergence of the calculated properties with the cluster size is discussed.

We study the direct-to-indirect gap crossover in Al Gal, As alloys driven by Al addition, in analogy with temperature-induced phase transitions. The adopted real-space formalism incorporates occupational disorder in a realistic manner: different atomic configurations, accommodated in a supercell, are generated and solved independently.We perform a systematic study of the scaling of calculated gap properties of Al Gal As alloys with the cell size, and consider system sizes ranging from 64 to 8000 atoms. Extrapolation to infinite system size follows scaling laws appropriate for firstorder phase transitions, and allows an accurate determination of the crossover composition x, .The current development of electronic structure calculations allows for large systems to be treated and solved, in particular, taking into account surface effects, impurities, and disorder over relatively extended regions in

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