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

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  • Oliveira, Adélcio C.

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.

Suggested Citation

  • Oliveira, Adélcio C., 2021. "Continuum reset dynamics as a pathway to Newtonian classical limit of Quantum Mechanics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 579(C).
    • Handle: RePEc:eee:phsmap:v:579:y:2021:i:c:s0378437121003721
    DOI: 10.1016/j.physa.2021.126099
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