Chaotic Driven Tunneling in Rectangular Double-Well (Communications in Computational Physics, 2018)
We consider a charged particle confined in a one-dimensional rectangular double-wellpotential, driven by an external periodic excitation at frequency Ω and with amplitudeA. We find that there is the regime of the parametric resonance due to the modulation of theamplitude A at the frequency ωprm, which results in the change in the population dynamicsof the energy levels. The analysis relies on the Dirac system of Hamiltonian equations thatare equivalent to the Schrödinger equation. Considering a finite dimensional approximationto the Dirac system, we construct the foliation of its phase space by subsets Fab given byconstraints a ≤ N0 ≤ b on the occupation probabilities N0 of the ground state, and describethe tunneling by frequencies νab of the system's visiting subsets Fab. The frequencies νab determine the probability density and thus the Shannon entropy, which has the maximumvalue at the resonant frequency ω = ωprm. The reconstruction of the state-space of thesystem's dynamics with the help of the Shaw-Takens method indicates that the quasi-periodicmotion breaks down at the resonant value ωprm.