Continuum reset dynamics as a pathway to Newtonian classical limit of Quantum Mechanics

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Date
2001
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Elsevier
Abstract
The Quantum–Classical transition problem is investigated in a nonlinear oscillator model context. The main issue addressed here is: how quantum mechanics can reproduce Newtonian dynamics for a nonlinear oscillator. The used model is the Gamma Oscillator, and it was solved, in terms of series and semi-classically, in all orders. The Ehrenfest time scale was numerically determined and shown that it decreases as the classical action increases in the small action interval and tends to a smaller and constant value the classical action increases. The Newtonian regime is reaching if a continuum monitoring is considered, i.e., continuum reset dynamics, no matter how strong nonlinearity is. The numerical calculations did not show a correlation between Ehrenfest time and the complexity of the dynamics observed in the quantum phase space and measured by Shannon Entropy.
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Oliveira, Adélcio C. (2001). Continuum reset dynamics as a pathway to Newtonian classical limit of Quantum Mechanics. Physica A: Statistical Mechanics and its Applications, 579(1), 126099,