  In the conventional quantum mechanics (i.e., hermitian QM) the adia- batic
theorem for systems subjected to time periodic fields holds only for bound
systems and not for open ones (where ionization and dissociation take place)
[D. W. Hone, R. Ketzmerik, and W. Kohn, Phys. Rev. A 56, 4045 (1997)]. Here
with the help of the (t,t') formalism combined with the complex scaling method
we derive an adiabatic theorem for open systems and provide an analytical
criteria for the validity of the adiabatic limit. The use of the complex
scaling transformation plays a key role in our derivation. As a numerical
example we apply the adiabatic theorem we derived to a 1D model Hamiltonian of
Xe atom which interacts with strong, monochromatic sine-square laser pulses. We
show that the gener- ation of odd-order harmonics and the absence of
hyper-Raman lines, even when the pulses are extremely short, can be explained
with the help of the adiabatic theorem we derived.
