  Due to their focalizing properties, elliptic quantum corrals present very
interesting physical behaviors. In this work, we analyze static and dynamical
properties of these systems. Results are presented for realistic values of the
parameters, which might be useful for comparison with experiments. We study
noninteracting corrals and their response to several kinds of external
perturbations, observing that, for realistic values of the Fermi level, the
dynamics involves only a few number of excited states, making the system quite
robust with respect to possible sources of decoherence. We also study the
system in the presence of two S=1/2 impurities located at its foci, which
interact with the electrons of the ellipse via a superexchange interaction J.
This system is diagonalized numerically and properties such as the spin gap and
spin-spin static and dynamical correlations are studied. We find that, for
small J, both spins are locked in a singlet or triplet state, for even or odd
filling, respectively, and its spin dynamics consists mainly of a single peak
above the spin gap. In this limit, we can define an effective Heisenberg
Hamiltonian to describe the low-energy properties. For larger J, more states
are involved and the localized spins decorrelate in a manner similar to the
Ruderman-Kittel-Kasuya-Yosida-Kondo transition for the two-impurity problem.
