Stimulated transitions between the self-trapped states of the nonlinear Schrödinger equation

We investigate a particle confined within a double-well potential, its behavior described by a one-dimensional nonlinear Schrödinger equation. Transitions between the two lowest self-trapped states of this system are studied, in the two-mode approximation, under the influence of the external time-dependent perturbation. If the perturbation is harmonic in time, with the frequency $\omega ,$ then transitions between the states become possible if the amplitude of the perturbation F exceeds some threshold value $F_c\left(\omega \right);$ above this threshold motion of the system becomes chaotic. If the perturbation is broadband noise, then transitions between the states are possible at arbitrarily small F and occur in the process of the system’s energy diffusion.