  An $N$-level quantum system is coupled to a bosonic heat reservoir at
positive temperature. We analyze the system-reservoir dynamics in the following
regime: The strength $\lambda$ of the system-reservoir coupling is fixed and
small, but larger than the spacing $\sigma$ of system energy levels. For
vanishing $\sigma$ there is a manifold of invariant system-reservoir states and
for $\sigma>0$ the only invariant state is the joint equilibrium. The manifold
is invariant for $\sigma=0$ but becomes quasi-invariant for $\sigma>0$. Namely,
on a first time-scale of the order $1/\lambda^2$, initial states approach the
manifold. Then they converge to the joint equilibrium state on a much larger
time-scale of the order $\lambda^2/\sigma^2$. We give a detailed expansion of
the system-reservoir evolution showing the above scenario.
