Quasienergy states of a flat rotator in the field of a circularly polarized wave

Exact solution of the spectrum of quasienergy $(\mathscr E_k)$ problem is obtained and complete set of the quasienergy states (steady states) is constructed for the flat rotator with the constant dipole moment $\mathbf p_0$ rotating in the plane of the electric vector of circular polarized wave. Presence of discontinuities of the jump type in the frequency dependence $\mathscr E_k=\mathscr E_k(\Omega)$ at resonance values of the field frequency $\Omega $ is shown, the discontinuities being similar to those in the functional dependence of the electron energy on the quasimomentum $\mathbf k$ in a crystal!. Limiting cases of the weak and strong field are investigated. Some general properties of quasienergy solutions are considered, such as the connection of quasienergy with the mean energy in the steady states, qualitative behaviour of the system in resonance field, and changing of quantum number of the state with adiabatic variation of field frequency.