Multiple Reflections for Classical Particles Moving under the Influence of a Time-Dependent Potential Well

We study the dynamics of classical particles confined in a time-dependent potential well. The dynamics of each particle is described by a two-dimensional nonlinear discrete mapping for the variables energy [Formula: see text] and phase [Formula: see text] of the periodic moving well. We obtain the p...

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Autores principales: Graciano, Flávio Heleno, da Costa, Diogo Ricardo, Leonel, Edson D., de Oliveira, Juliano A.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2022
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9602288/
https://www.ncbi.nlm.nih.gov/pubmed/37420447
http://dx.doi.org/10.3390/e24101427
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author Graciano, Flávio Heleno
da Costa, Diogo Ricardo
Leonel, Edson D.
de Oliveira, Juliano A.
author_facet Graciano, Flávio Heleno
da Costa, Diogo Ricardo
Leonel, Edson D.
de Oliveira, Juliano A.
author_sort Graciano, Flávio Heleno
collection PubMed
description We study the dynamics of classical particles confined in a time-dependent potential well. The dynamics of each particle is described by a two-dimensional nonlinear discrete mapping for the variables energy [Formula: see text] and phase [Formula: see text] of the periodic moving well. We obtain the phase space and show that it contains periodic islands, chaotic sea, and invariant spanning curves. We find the elliptic and hyperbolic fixed points and discuss a numerical method to obtain them. We study the dispersion of the initial conditions after a single iteration. This study allows finding regions where multiple reflections occur. Multiple reflections happen when a particle does not have enough energy to exit the potential well and is trapped inside it, suffering several reflections until it has enough energy to exit. We also show deformations in regions with multiple reflection, but the area remains constant when we change the control parameter [Formula: see text]. Finally, we show some structures that appear in the [Formula: see text] plane by using density plots.
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spelling pubmed-96022882022-10-27 Multiple Reflections for Classical Particles Moving under the Influence of a Time-Dependent Potential Well Graciano, Flávio Heleno da Costa, Diogo Ricardo Leonel, Edson D. de Oliveira, Juliano A. Entropy (Basel) Article We study the dynamics of classical particles confined in a time-dependent potential well. The dynamics of each particle is described by a two-dimensional nonlinear discrete mapping for the variables energy [Formula: see text] and phase [Formula: see text] of the periodic moving well. We obtain the phase space and show that it contains periodic islands, chaotic sea, and invariant spanning curves. We find the elliptic and hyperbolic fixed points and discuss a numerical method to obtain them. We study the dispersion of the initial conditions after a single iteration. This study allows finding regions where multiple reflections occur. Multiple reflections happen when a particle does not have enough energy to exit the potential well and is trapped inside it, suffering several reflections until it has enough energy to exit. We also show deformations in regions with multiple reflection, but the area remains constant when we change the control parameter [Formula: see text]. Finally, we show some structures that appear in the [Formula: see text] plane by using density plots. MDPI 2022-10-07 /pmc/articles/PMC9602288/ /pubmed/37420447 http://dx.doi.org/10.3390/e24101427 Text en © 2022 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Graciano, Flávio Heleno
da Costa, Diogo Ricardo
Leonel, Edson D.
de Oliveira, Juliano A.
Multiple Reflections for Classical Particles Moving under the Influence of a Time-Dependent Potential Well
title Multiple Reflections for Classical Particles Moving under the Influence of a Time-Dependent Potential Well
title_full Multiple Reflections for Classical Particles Moving under the Influence of a Time-Dependent Potential Well
title_fullStr Multiple Reflections for Classical Particles Moving under the Influence of a Time-Dependent Potential Well
title_full_unstemmed Multiple Reflections for Classical Particles Moving under the Influence of a Time-Dependent Potential Well
title_short Multiple Reflections for Classical Particles Moving under the Influence of a Time-Dependent Potential Well
title_sort multiple reflections for classical particles moving under the influence of a time-dependent potential well
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9602288/
https://www.ncbi.nlm.nih.gov/pubmed/37420447
http://dx.doi.org/10.3390/e24101427
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