Resonant eigenstates in quantum chaotic scattering
| dc.creator | Nonnenmacher, Stéphane | |
| dc.creator | Rubin, Mathieu | |
| dc.date | 2006-08-31 | |
| dc.date | 2007-04-23 | |
| dc.date.accessioned | 2026-07-07T07:57:42Z | |
| dc.date.available | 2026-07-07T07:57:42Z | |
| dc.description | 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. | |
| dc.description | 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 | |
| dc.identifier | https://arxiv.org/abs/nlin/0608069 | |
| dc.identifier | http://arxiv.org/abs/nlin/0608069 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/127743 | |
| dc.subject | Chaotic Dynamics | |
| dc.subject | Mathematical Physics | |
| dc.title | Resonant eigenstates in quantum chaotic scattering | |
| dc.type | text |