On stimulated transitions between the self-trapped states of the nonlinear Schrodinger equation

The studied model describes a particle that obeys a one-dimensional nonlinear Schr\"odinger equation in the potential of a double-well. Transitions between the two lowest self-trapped states of this system under the influence of the external time-dependent perturbation are studied in the two-mode approximation. If the perturbation dependence on time is harmonic with the frequency $\omega$, then transitions between the states become possible if the amplitude of the perturbation $F$ exceeds some threshold value $F_c(\omega)$; above the threshold motion of the system becomes chaotic. If the perturbation is a broadband noise, then transitions between the states are possible at arbitrarily small $F$ and occur in the process of the system's energy diffusion.