Chaotic Driven Tunneling in Rectangular Double-Wellстатья
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Дата последнего поиска статьи во внешних источниках: 27 мая 2015 г.
Аннотация:
We consider a charged particle confined in a one-dimensional rectangular doublewell
potential, driven by an external periodic excitation at frequency and with amplitude
A. We find that there is the regime of the parametric resonance due to the modulation of the
amplitude A at the frequency !prm, which results in the change in the population dynamics
of the energy levels. The analysis relies on the Dirac system of Hamiltonian equations that
are equivalent to the Schr¨odinger equation. Considering a finite dimensional approximation
to the Dirac system, we construct the foliation of its phase space by subsets Fab given by
constraints a · N0 · b on the occupation probabilities N0 of the ground state, and describe
the tunneling by frequencies ºab of the system’s visiting subsets Fab. The frequencies ºab
determine the probability density and thus the Shannon entropy, which has the maximum
value at the resonant frequency ! = !prm. The reconstruction of the state-space of the
system’s dynamics with the help of the Shaw-Takens method indicates that the quasi-periodic
motion breaks down at the resonant value !prm.