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

Adélcio C. Oliveira

Physica A: Statistical Mechanics and its Applications, 2021, vol. 579, issue 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.

Keywords: Ehrenfest time; Classical limit; Reset dynamics; Shannon Entropy (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:579:y:2021:i:c:s0378437121003721

DOI: 10.1016/j.physa.2021.126099

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