Resonant eigenstates in quantum chaotic scattering
Résumé
We study the resonant eigenstates of the quantized "open baker's map'', a simple model for quantum chaotic scattering, in the semiclassical limit. We first investigate the exponent appearing in the Fractal Weyl law for the density of resonances, showing that it is not related with the "information dimension''. In a second step, we consider the semiclassical measures associated with sequences of resonant eigenstates. We show that these measures are conditionally invariant with respect to the classical dynamics, and generally exhibit interesting fractal structures.