  We generalize the standard Born-Oppenheimer approximation to the case of open
quantum systems. We define the zeroth order Born-Oppenheimer approximation of
an open quantum system as the regime in which its effective Hamiltonian can be
diagonalized with fixed slowly changing variables. We then establish validity
and invalidity conditions for this approximation for two kinds of
dissipations--the spin relaxation and the dissipation of center-of-mass motion.
As an example, the Born-Oppenheimer approximation of a two-level open system is
analyzed.
