Resonance tunneling through a nonstationary potential

In the first order of semiclassical perturbation theory, with allowance for many-quantum transitions, a study is made of resonance tunneling through a two-hump nonstationary potential. The problem is reduced to the solution of a functional equation for the transmission probability amplitude. This equation is solved in general form for the case of nonresonance tunneling. A condition of suppression of resonance by nonstationary effects is obtained. The transmission amplitude is found in the case when the twohump potential oscillates as a whole. Periodic, quasiperiodie, and random nonstationary perturbations are considered.