Distribution of resonances for open quantum maps

Details Distribution of resonances for open quantum maps Distribution of resonances for open quantum maps

2005-05-11

arxiv.org/abs/math-ph/0505034v4

Communications in Mathematical Physics 269 (01/2007) 311-365

Physics

Mathematical Physics

60 pages, no figures (numerical results are shown in other references)

Scientific paper

10.1007/s00220-006-0131-0

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. For this model, we can also compute a quantity characterizing the 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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