Phonon relaxation of subgap levels in superconducting quantum point contacts

Superconducting quantum point contacts are known to possess two subgap stat es per propagating mode. In this note we compute the low-temperature relaxa tion rate of the upper subgap state into the lower one with the emission of an acoustic phonon. If the reflection at the contact is small, the relaxat ion time may become much longer than the characteristic lifetime of a bulk quasiparticle. (C) 1998 American Institute of Physics. [S0021-3640(98)01323 -1].