Spectroscopic and magnetic mirages of impurities in nanoscopic systems with focusing properties

We study the behavior of magnetic impurities in nanoscopic systems with focusing properties. In this paper, we analyze the spectroscopic and magnetic properties of Kondo, intermediate valence and magnetic impurities on a sphere with a metallic surface. Using exact calculations, we obtain important spectroscopic and magnetic mirages at the antipodes of the impurity location. When compared with calculations performed using effective models our results validate previous calculations of spectroscopic mirages. These calculations can be extended to other systems with focusing properties like quantum corrals where a similar behavior is expected.