  A Fermi's Golden Rule for population transfer between instantaneous
eigenstates of elliptical quantum billiards with oscillating boundaries is
derived. Thereby, both the occurrence of the recently observed resonant
population transfer between instantaneous eigenstates [F. Lenz et al. New J.
Phys., {\bf 13}, 103019, 2011] and the empirical criterion stating that these
transitions occur when the driving frequency matches the mean difference of the
latter are explained. As a second main result a criterion judging which
resonances are resolvable in a corresponding experiment of certain duration is
provided. Our analysis is complemented by numerical simulations for three
different driving laws. The corresponding resonance spectra are in agreement
with the predictions of both criteria.
