St phane Nonnenmacher, Maciej Zworski
Distribution of resonances for open quantum maps
(730K, Latex 2e with 11 PS figures, in the archive .tar.gz)

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.