  We show that the mean time, which a quantum particle needs to escape from a
system to the environment, is quantized and independent from most dynamical
details of the system. In particular, we consider a quantum system with a
general Hermitian Hamiltonian $\hat{H}$ and one decay channel, through which
probability dissipates to the environment with rate $\Gamma$. When the system
is initially prepared exactly in the decay state, the mean decay time $\langle
T \rangle$ is quantized and equal to $w/(2\Gamma)$. $w$ is the number of
distinct energy levels, i.e. eigenvalues of $\hat{H}$, that have overlap with
the decay state, and is also the winding number of a transform of the resolvent
in the complex plane. Apart from the integer $w$, $\langle T \rangle$ is
completely independent of the system's dynamics. The complete decay time
distribution can be obtained from an electrostatic analogy and features rare
events of very large dissipation times for parameter choices close to critical
points, where $w$ changes, e.g. when a degeneracy is lifted. Experiments of
insufficient observation time may thus measure a too small value of $w$. We
discuss our findings in a disordered tight-binding model and in the two-level
atom in a continuous-wave field.
