Relativistic Ermakov–Milne–Pinney Systems and First Integrals
Autor(a) principal: | |
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Data de Publicação: | 2021 |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFRGS |
Texto Completo: | http://hdl.handle.net/10183/219606 |
Resumo: | The Ermakov–Milne–Pinney equation is ubiquitous in many areas of physics that have an explicit time-dependence, including quantum systems with time-dependent Hamiltonian, cosmology, time-dependent harmonic oscillators, accelerator dynamics, etc. The Eliezer and Gray physical interpretation of the Ermakov–Lewis invariant is applied as a guiding principle for the derivation of the special relativistic analog of the Ermakov–Milne–Pinney equation and associated first integral. The special relativistic extension of the Ray–Reid system and invariant is obtained. General properties of the relativistic Ermakov–Milne–Pinney are analyzed. The conservative case of the relativistic Ermakov–Milne–Pinney equation is described in terms of a pseudo-potential, reducing the problem to an effective Newtonian form. The non-relativistic limit is considered to be well. A relativistic nonlinear superposition law for relativistic Ermakov systems is identified. The generalized Ermakov–Milne–Pinney equation has additional nonlinearities, due to the relativistic effects. |
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Haas, Fernando2021-04-08T04:17:32Z20212624-8174http://hdl.handle.net/10183/219606001123312The Ermakov–Milne–Pinney equation is ubiquitous in many areas of physics that have an explicit time-dependence, including quantum systems with time-dependent Hamiltonian, cosmology, time-dependent harmonic oscillators, accelerator dynamics, etc. The Eliezer and Gray physical interpretation of the Ermakov–Lewis invariant is applied as a guiding principle for the derivation of the special relativistic analog of the Ermakov–Milne–Pinney equation and associated first integral. The special relativistic extension of the Ray–Reid system and invariant is obtained. General properties of the relativistic Ermakov–Milne–Pinney are analyzed. The conservative case of the relativistic Ermakov–Milne–Pinney equation is described in terms of a pseudo-potential, reducing the problem to an effective Newtonian form. The non-relativistic limit is considered to be well. A relativistic nonlinear superposition law for relativistic Ermakov systems is identified. The generalized Ermakov–Milne–Pinney equation has additional nonlinearities, due to the relativistic effects.application/pdfengPhysics. Basel. Vol. 3, no. 1 (Mar.2021), p. 59-70Equação de PinneyRelatividadeSistemas quanticosErmakov systemErmakov–Milne–Pinney equationRelativistic Ermakov–Lewis invariantRelativistic Ray–Reid systemNonlinear superposition lawRelativistic Ermakov–Milne–Pinney Systems and First IntegralsEstrangeiroinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFRGSinstname:Universidade Federal do Rio Grande do Sul (UFRGS)instacron:UFRGSTEXT001123312.pdf.txt001123312.pdf.txtExtracted Texttext/plain35436http://www.lume.ufrgs.br/bitstream/10183/219606/2/001123312.pdf.txteca01034b7e0baec21ecdaad0fe26c21MD52ORIGINAL001123312.pdfTexto completo (inglês)application/pdf314417http://www.lume.ufrgs.br/bitstream/10183/219606/1/001123312.pdf5c14dbe74edbadd67be6cabb4fd29e12MD5110183/2196062023-07-20 03:36:22.309803oai:www.lume.ufrgs.br:10183/219606Repositório de PublicaçõesPUBhttps://lume.ufrgs.br/oai/requestopendoar:2023-07-20T06:36:22Repositório Institucional da UFRGS - Universidade Federal do Rio Grande do Sul (UFRGS)false |
dc.title.pt_BR.fl_str_mv |
Relativistic Ermakov–Milne–Pinney Systems and First Integrals |
title |
Relativistic Ermakov–Milne–Pinney Systems and First Integrals |
spellingShingle |
Relativistic Ermakov–Milne–Pinney Systems and First Integrals Haas, Fernando Equação de Pinney Relatividade Sistemas quanticos Ermakov system Ermakov–Milne–Pinney equation Relativistic Ermakov–Lewis invariant Relativistic Ray–Reid system Nonlinear superposition law |
title_short |
Relativistic Ermakov–Milne–Pinney Systems and First Integrals |
title_full |
Relativistic Ermakov–Milne–Pinney Systems and First Integrals |
title_fullStr |
Relativistic Ermakov–Milne–Pinney Systems and First Integrals |
title_full_unstemmed |
Relativistic Ermakov–Milne–Pinney Systems and First Integrals |
title_sort |
Relativistic Ermakov–Milne–Pinney Systems and First Integrals |
author |
Haas, Fernando |
author_facet |
Haas, Fernando |
author_role |
author |
dc.contributor.author.fl_str_mv |
Haas, Fernando |
dc.subject.por.fl_str_mv |
Equação de Pinney Relatividade Sistemas quanticos |
topic |
Equação de Pinney Relatividade Sistemas quanticos Ermakov system Ermakov–Milne–Pinney equation Relativistic Ermakov–Lewis invariant Relativistic Ray–Reid system Nonlinear superposition law |
dc.subject.eng.fl_str_mv |
Ermakov system Ermakov–Milne–Pinney equation Relativistic Ermakov–Lewis invariant Relativistic Ray–Reid system Nonlinear superposition law |
description |
The Ermakov–Milne–Pinney equation is ubiquitous in many areas of physics that have an explicit time-dependence, including quantum systems with time-dependent Hamiltonian, cosmology, time-dependent harmonic oscillators, accelerator dynamics, etc. The Eliezer and Gray physical interpretation of the Ermakov–Lewis invariant is applied as a guiding principle for the derivation of the special relativistic analog of the Ermakov–Milne–Pinney equation and associated first integral. The special relativistic extension of the Ray–Reid system and invariant is obtained. General properties of the relativistic Ermakov–Milne–Pinney are analyzed. The conservative case of the relativistic Ermakov–Milne–Pinney equation is described in terms of a pseudo-potential, reducing the problem to an effective Newtonian form. The non-relativistic limit is considered to be well. A relativistic nonlinear superposition law for relativistic Ermakov systems is identified. The generalized Ermakov–Milne–Pinney equation has additional nonlinearities, due to the relativistic effects. |
publishDate |
2021 |
dc.date.accessioned.fl_str_mv |
2021-04-08T04:17:32Z |
dc.date.issued.fl_str_mv |
2021 |
dc.type.driver.fl_str_mv |
Estrangeiro info:eu-repo/semantics/article |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10183/219606 |
dc.identifier.issn.pt_BR.fl_str_mv |
2624-8174 |
dc.identifier.nrb.pt_BR.fl_str_mv |
001123312 |
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2624-8174 001123312 |
url |
http://hdl.handle.net/10183/219606 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.ispartof.pt_BR.fl_str_mv |
Physics. Basel. Vol. 3, no. 1 (Mar.2021), p. 59-70 |
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info:eu-repo/semantics/openAccess |
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openAccess |
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