05-173 St phane Nonnenmacher, Maciej Zworski
Distribution of resonances for open quantum maps (730K, Latex 2e with 11 PS figures, in the archive .tar.gz) May 11, 05
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Abstract. We analyze simple models of classical chaotic open systems and of their quantizations (open quantum maps on the torus). Our models are similar to models recently studied in atomic and mesoscopic physics. They provide a numerical confirmation of the fractal Weyl law for the density of quantum resonances of such systems. The exponent in that law is related to the dimension of the classical repeller (or trapped set) of the system. In a simplified model, a rigorous argument gives the full resonance spectrum, which satisfies the fractal Weyl law. In this model, we can also compute a quantity characterizing the quantum fluctuations of conductance through the system, namely the shot noise power: the value we obtain is close to the prediction of random matrix theory.

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