Size Effects in Quasiparticle Lifetimes and Phonon Generation in Superconductors

In thin films and granular superconductors, the quantization of the phonon wave vector delimits the phonons which can be emitted in a recombination process. We predict jumps in lifetimes for injected quasiparticles and the disappearance of some emitted phonons at characteristic values of $\frac{\Delta }{\mathrm{kT}}$.