- 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.