We study the activated longitudinal dynamics of a small single-domain
magnet with uniaxial anisotropy, coupled to quantum noise. The smalles
t finite eigenvalue lambda(1) = Gamma(0)e(-EB/kBT) of the relaxation m
atrix is evaluated in a controlled approximation. For white noise we f
ind To cc T-l at moderate temperatures and T-0 = const at very low T.
Coupling to elastic waves leads to a prefactor that is linear in T or
constant, depending on temperature. At very low T, the discreteness of
the energy spectrum is crucial.