Phonon relaxation of subgap levels in superconducting quantum point contacts

Superconducting quantum point contacts are known to possess two subgap states per propagating mode. In this note we compute the low-temperature relaxation 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 relaxation time may become much longer than the characteristic lifetime of a bulk quasiparticle. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 11, 847–851 (10 December 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.