Tunneling and quantum localization in chaos-driven symmetric triple well potential: An approach using quantum theory of motion

For a symmetric triple well potential, driven by the forces associated with the bifurcation diagram of a logistic map, the tunneling and quantum localization are studied using quantum theory of motion and time-dependent Fourier grid Hamiltonian methods. Detailed analysis reveals that application of only asymmetric or symmetric perturbation results into either quantum localization or over-barrier transition and no tunneling while application of mixed symmetry perturbation gives either tunneling or over-barrier transition, depending on temporal nature and initial position of the particle. For bifurcative and chaotic symmetric-asymmetric perturbation, with truncation of mixed symmetry perturbation, a sudden jump in energy causes a transition from the tunneling phenomenon to the over-barrier transition. With particle located initially near to either of the minima of the unperturbed well, quantum localization, or over-barrier transition is observed, depending on types of perturbation used.