  It is frequently observed that even at very low temperatures the number of
quasiparticles in superconducting materials is higher than predicted by
standard BCS-theory. These quasiparticles can interact with two-level systems,
such as superconducting qubits or two-level systems (TLS) in the amorphous
oxide layer of a Josephson junction. This interaction leads to decay and
decoherence of the TLS, with specific results, such as the time dependence,
depending on the distribution of quasiparticles and the form of the
interaction. We study the resulting decay laws for different experimentally
relevant protocols.
