Resonant eigenstates in quantum chaotic scattering
摘要
We study the spectrum of quantized open maps, as a model for the resonance spectrum of quantum scattering systems. We are particularly interested in open maps admitting a fractal repeller. Using the ``open baker's map'' as an example, we numerically investigate the exponent appearing in the Fractal Weyl law for the density of resonances; we show that this exponent is not related with the ``information dimension'', but rather the Hausdorff dimension of the repeller. We then consider the semiclassical measures associated with the eigenstates: we prove that these measures are conditionally invariant with respect to the classical dynamics. We then address the problem of classifying semiclassical measures among conditionally invariant ones. For a solvable model, the ``Walsh-quantized'' open baker's map, we manage to exhibit a family of semiclassical measures with simple self-similar properties.
引用
@article{arxiv.nlin/0608069,
title = {Resonant eigenstates in quantum chaotic scattering},
author = {Stéphane Nonnenmacher and Mathieu Rubin},
journal= {arXiv preprint arXiv:nlin/0608069},
year = {2007}
}
备注
39 pages, 10 figures Compared with the previous version, we generalized the correspondence between semiclassical measures and eigenmeasures to arbitrary quantized open maps. We added some comments and results concerning the Walsh baker