  We consider a time-dependent two-level quantum system interacting with a free
Boson reservoir. The coupling is energy conserving and depends slowly on time,
as does the system Hamiltonian, with a common adiabatic parameter
$\varepsilon$. Assuming that the system and reservoir are initially decoupled,
with the reservoir in equilibrium at temperature $T\ge 0$, we compute the
transition probability from one eigenstate of the two-level system to the other
eigenstate as a function of time, in the regime of small $\varepsilon$ and
small coupling constant $\lambda$. We analyse the deviation from the adiabatic
transition probability obtained in absence of the reservoir.
