  A quantum system in contact with a heat bath undergoes quantum transitions
between energy levels upon absorption or emission of energy quanta by the bath.
These transitions remain virtual unless the energy of the system is measured
repeatedly, even continuously in time. Isolating the two indispensable
mechanisms in competition, we describe in a synthetic way the main physical
features of thermally activated quantum jumps. Using classical tools of
stochastic analysis, we compute in the case of a two-level system the complete
statistics of jumps and transition times in the limit when the typical
measurement time is small compared to the thermal relaxation time. The emerging
picture is that quantum trajectories are similar to those of a classical
particle in a noisy environment, subject to transitions a la Kramer in a
multi-well landscape, but with a large multiplicative noise.
