Volume 1, Issue 1
Chaotic Driven Tunneling in Rectangular Double-well

V. L. Golo & Yu. S. Volkov

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Commun. Comput. Phys., 1 (2006), pp. 81-99.

Published online: 2018-03

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  • Abstract

We consider a charged particle confined in a one-dimensional rectangular doublewell potential, driven by an external periodic excitation at frequency Ω 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 ωprm, 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 νab of the system’s visiting subsets Fab. The frequencies νab determine the probability density and thus the Shannon entropy, which has the maximum value at the resonant frequency ω = ωprm. 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 ωprm.

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@Article{CiCP-1-81, author = {V. L. Golo and Yu. S. Volkov}, title = {Chaotic Driven Tunneling in Rectangular Double-well}, journal = {Communications in Computational Physics}, year = {2018}, volume = {1}, number = {1}, pages = {81--99}, abstract = {

We consider a charged particle confined in a one-dimensional rectangular doublewell potential, driven by an external periodic excitation at frequency Ω 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 ωprm, 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 νab of the system’s visiting subsets Fab. The frequencies νab determine the probability density and thus the Shannon entropy, which has the maximum value at the resonant frequency ω = ωprm. 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 ωprm.

}, issn = {1991-7120}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cicp/10939.html} }
TY - JOUR T1 - Chaotic Driven Tunneling in Rectangular Double-well AU - V. L. Golo & Yu. S. Volkov JO - Communications in Computational Physics VL - 1 SP - 81 EP - 99 PY - 2018 DA - 2018/03 SN - 1 DO - http://dor.org/ UR - https://global-sci.org/intro/cicp/10939.html KW - AB -

We consider a charged particle confined in a one-dimensional rectangular doublewell potential, driven by an external periodic excitation at frequency Ω 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 ωprm, 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 νab of the system’s visiting subsets Fab. The frequencies νab determine the probability density and thus the Shannon entropy, which has the maximum value at the resonant frequency ω = ωprm. 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 ωprm.

V. L. Golo & Yu. S. Volkov. (1970). Chaotic Driven Tunneling in Rectangular Double-well. Communications in Computational Physics. 1 (1). 81-99. doi:
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