01-207 DeBievre Stephan

Quantum chaos: a brief first visit (855K, Postscript) Jun 5, 01

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Abstract. These notes contain a slightly expanded version of six lectures I delivered at the Cuernavaca Summer School on Analysis and Mathematical Physics (June 2000). They provide an elementary and self-contained introduction to some aspects of quantum chaos that is adapted -- it is hoped -- to the audience of the school, which consisted of advanced undergraduate and beginning graduate students in mathematics having had little or no exposure to physics in general and to classical or quantum mechanics in particular. The lectures therefore include brief self-contained introductions to the Hamiltonian and quantum mechanics of a point particle. The basic problematics of quantum chaos is first explained using billiards as an example. Chaotic maps on the torus are then treated in some detail and a complete and self-contained proof of the Schnirelman theorem is given in this context.

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