Cargando…

Dynamical Invariant and Exact Mechanical Analyses for the Caldirola–Kanai Model of Dissipative Three Coupled Oscillators

We study the dynamical invariant for dissipative three coupled oscillators mainly from the quantum mechanical point of view. It is known that there are many advantages of the invariant quantity in elucidating mechanical properties of the system. We use such a property of the invariant operator in qu...

Descripción completa

Detalles Bibliográficos
Autores principales: Medjber, Salim, Menouar, Salah, Choi, Jeong Ryeol
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2021
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8304947/
https://www.ncbi.nlm.nih.gov/pubmed/34208801
http://dx.doi.org/10.3390/e23070837
_version_ 1783727456922894336
author Medjber, Salim
Menouar, Salah
Choi, Jeong Ryeol
author_facet Medjber, Salim
Menouar, Salah
Choi, Jeong Ryeol
author_sort Medjber, Salim
collection PubMed
description We study the dynamical invariant for dissipative three coupled oscillators mainly from the quantum mechanical point of view. It is known that there are many advantages of the invariant quantity in elucidating mechanical properties of the system. We use such a property of the invariant operator in quantizing the system in this work. To this end, we first transform the invariant operator to a simple one by using a unitary operator in order that we can easily manage it. The invariant operator is further simplified through its diagonalization via three-dimensional rotations parameterized by three Euler angles. The coupling terms in the quantum invariant are eventually eliminated thanks to such a diagonalization. As a consequence, transformed quantum invariant is represented in terms of three independent simple harmonic oscillators which have unit masses. Starting from the wave functions in the transformed system, we have derived the full wave functions in the original system with the help of the unitary operators.
format Online
Article
Text
id pubmed-8304947
institution National Center for Biotechnology Information
language English
publishDate 2021
publisher MDPI
record_format MEDLINE/PubMed
spelling pubmed-83049472021-07-25 Dynamical Invariant and Exact Mechanical Analyses for the Caldirola–Kanai Model of Dissipative Three Coupled Oscillators Medjber, Salim Menouar, Salah Choi, Jeong Ryeol Entropy (Basel) Article We study the dynamical invariant for dissipative three coupled oscillators mainly from the quantum mechanical point of view. It is known that there are many advantages of the invariant quantity in elucidating mechanical properties of the system. We use such a property of the invariant operator in quantizing the system in this work. To this end, we first transform the invariant operator to a simple one by using a unitary operator in order that we can easily manage it. The invariant operator is further simplified through its diagonalization via three-dimensional rotations parameterized by three Euler angles. The coupling terms in the quantum invariant are eventually eliminated thanks to such a diagonalization. As a consequence, transformed quantum invariant is represented in terms of three independent simple harmonic oscillators which have unit masses. Starting from the wave functions in the transformed system, we have derived the full wave functions in the original system with the help of the unitary operators. MDPI 2021-06-30 /pmc/articles/PMC8304947/ /pubmed/34208801 http://dx.doi.org/10.3390/e23070837 Text en © 2021 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
Medjber, Salim
Menouar, Salah
Choi, Jeong Ryeol
Dynamical Invariant and Exact Mechanical Analyses for the Caldirola–Kanai Model of Dissipative Three Coupled Oscillators
title Dynamical Invariant and Exact Mechanical Analyses for the Caldirola–Kanai Model of Dissipative Three Coupled Oscillators
title_full Dynamical Invariant and Exact Mechanical Analyses for the Caldirola–Kanai Model of Dissipative Three Coupled Oscillators
title_fullStr Dynamical Invariant and Exact Mechanical Analyses for the Caldirola–Kanai Model of Dissipative Three Coupled Oscillators
title_full_unstemmed Dynamical Invariant and Exact Mechanical Analyses for the Caldirola–Kanai Model of Dissipative Three Coupled Oscillators
title_short Dynamical Invariant and Exact Mechanical Analyses for the Caldirola–Kanai Model of Dissipative Three Coupled Oscillators
title_sort dynamical invariant and exact mechanical analyses for the caldirola–kanai model of dissipative three coupled oscillators
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8304947/
https://www.ncbi.nlm.nih.gov/pubmed/34208801
http://dx.doi.org/10.3390/e23070837
work_keys_str_mv AT medjbersalim dynamicalinvariantandexactmechanicalanalysesforthecaldirolakanaimodelofdissipativethreecoupledoscillators
AT menouarsalah dynamicalinvariantandexactmechanicalanalysesforthecaldirolakanaimodelofdissipativethreecoupledoscillators
AT choijeongryeol dynamicalinvariantandexactmechanicalanalysesforthecaldirolakanaimodelofdissipativethreecoupledoscillators