Poschl-Teller potentials based solution to Hilbert's tenth problem

Hypercomputers compute functions or numbers, or in general solve problems that cannot be computed or solved by a Turing machine. An adaptation of the hypercomputing quantum algorithm proposed by Tien D. Kieu is presented, to the dynamic algebra su (1, 1) performed on the Pöschl-Teller potentials. Th...

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Autores:
Sicard, Andrés
Ospina, Juan
Tipo de recurso:
Fecha de publicación:
2006
Institución:
Universidad EAFIT
Repositorio:
Repositorio EAFIT
Idioma:
eng
OAI Identifier:
oai:repository.eafit.edu.co:10784/14552
Acceso en línea:
http://hdl.handle.net/10784/14552
Palabra clave:
Hypercomputing
Adiabatic Quantum Computing
Hilbert'S Tenth Problem
Hipercomputación
Computación Cuántica Adiabática
Décimo Problema De Hilbert
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License
Copyright (c) 2006 Andrés Sicard, Juan Ospina
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spelling Medellín de: Lat: 06 15 00 N degrees minutes Lat: 6.2500 decimal degrees Long: 075 36 00 W degrees minutes Long: -75.6000 decimal degrees2006-12-012019-11-22T19:18:48Z2006-12-012019-11-22T19:18:48Z2256-43141794-9165http://hdl.handle.net/10784/14552Hypercomputers compute functions or numbers, or in general solve problems that cannot be computed or solved by a Turing machine. An adaptation of the hypercomputing quantum algorithm proposed by Tien D. Kieu is presented, to the dynamic algebra su (1, 1) performed on the Pöschl-Teller potentials. The classically incomputable problem that is solved with this hypercomputing algorithm is Hilbert's tenth problem. It is pointed out that a fundamental mathematical condition for these algorithms is the existence of an irreducible infinite dimensional unit representation of low-dimension algebras that admit the construction of coherent states of the Barut-Girardello type. Additionally, the hypercomputational algorithm on the infinite potential box previously constructed by the authors is presented as a limiting case of the proposed algorithm on the Pöschl-Teller potentials.Los hipercomputadores computan funciones o números, o en general solucionan problemas que no pueden ser computados o solucionados por una máquina de Turing. Se presenta una adaptación del algoritmo cuántico hipercomputacional propuesto por Tien D. Kieu, al álgebra dinámica su(1, 1) realizada en los potenciales Pöschl-Teller. El problema clásicamente incomputable que se resuelve con este algoritmo hipercomputacional es el d´ecimo problema de Hilbert. Se señala que una condición matemática fundamental para estos algoritmos es la existencia de una representación unitaria infinito dimensional irreducible de álgebras de baja dimensión que admitan la construcción de estados coherentes del tipo Barut-Girardello. Adicionalmente se presenta como caso límite del algoritmo propuesto sobre los potenciales Pöschl-Teller, el algoritmo hipercomputacional sobre la caja de potencial infinita construido previamente por los autores.application/pdfengUniversidad EAFIThttp://publicaciones.eafit.edu.co/index.php/ingciencia/article/view/460http://publicaciones.eafit.edu.co/index.php/ingciencia/article/view/460Copyright (c) 2006 Andrés Sicard, Juan OspinaAcceso abiertohttp://purl.org/coar/access_right/c_abf2instname:Universidad EAFITreponame:Repositorio Institucional Universidad EAFITIngeniería y Ciencia; Vol 2, No 4 (2006)Poschl-Teller potentials based solution to Hilbert's tenth problemSolución basada en potenciales de Pöschl-Teller para el décimo problema de Hilbertarticleinfo:eu-repo/semantics/articlepublishedVersioninfo:eu-repo/semantics/publishedVersionArtículohttp://purl.org/coar/version/c_970fb48d4fbd8a85http://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1HypercomputingAdiabatic Quantum ComputingHilbert'S Tenth ProblemHipercomputaciónComputación Cuántica AdiabáticaDécimo Problema De HilbertSicard, AndrésOspina, JuanUniversidad EAFITIngeniería y Ciencia244357ing.cienc.THUMBNAILminaitura-ig_Mesa de trabajo 1.jpgminaitura-ig_Mesa de trabajo 1.jpgimage/jpeg265796https://repository.eafit.edu.co/bitstreams/11bb3ac9-ec31-49b7-ae51-7906dd611b36/downloadda9b21a5c7e00c7f1127cef8e97035e0MD51ORIGINALdocument (3).pdfdocument (3).pdfTexto completo PDFapplication/pdf190238https://repository.eafit.edu.co/bitstreams/b0992795-fc17-421f-b5f9-ac29064fbf04/downloadc973c70e976d8b05241e634b38bab475MD52articulo.htmlarticulo.htmlTexto completo HTMLtext/html373https://repository.eafit.edu.co/bitstreams/c1e9f74d-0303-4475-91d5-8e96a3ff7431/downloada9be33cac712f21fb8651423c417f5fbMD5310784/14552oai:repository.eafit.edu.co:10784/145522020-03-02 23:27:40.571open.accesshttps://repository.eafit.edu.coRepositorio Institucional Universidad EAFITrepositorio@eafit.edu.co
dc.title.eng.fl_str_mv Poschl-Teller potentials based solution to Hilbert's tenth problem
dc.title.spa.fl_str_mv Solución basada en potenciales de Pöschl-Teller para el décimo problema de Hilbert
title Poschl-Teller potentials based solution to Hilbert's tenth problem
spellingShingle Poschl-Teller potentials based solution to Hilbert's tenth problem
Hypercomputing
Adiabatic Quantum Computing
Hilbert'S Tenth Problem
Hipercomputación
Computación Cuántica Adiabática
Décimo Problema De Hilbert
title_short Poschl-Teller potentials based solution to Hilbert's tenth problem
title_full Poschl-Teller potentials based solution to Hilbert's tenth problem
title_fullStr Poschl-Teller potentials based solution to Hilbert's tenth problem
title_full_unstemmed Poschl-Teller potentials based solution to Hilbert's tenth problem
title_sort Poschl-Teller potentials based solution to Hilbert's tenth problem
dc.creator.fl_str_mv Sicard, Andrés
Ospina, Juan
dc.contributor.author.spa.fl_str_mv Sicard, Andrés
Ospina, Juan
dc.contributor.affiliation.spa.fl_str_mv Universidad EAFIT
dc.subject.keyword.eng.fl_str_mv Hypercomputing
Adiabatic Quantum Computing
Hilbert'S Tenth Problem
topic Hypercomputing
Adiabatic Quantum Computing
Hilbert'S Tenth Problem
Hipercomputación
Computación Cuántica Adiabática
Décimo Problema De Hilbert
dc.subject.keyword.spa.fl_str_mv Hipercomputación
Computación Cuántica Adiabática
Décimo Problema De Hilbert
description Hypercomputers compute functions or numbers, or in general solve problems that cannot be computed or solved by a Turing machine. An adaptation of the hypercomputing quantum algorithm proposed by Tien D. Kieu is presented, to the dynamic algebra su (1, 1) performed on the Pöschl-Teller potentials. The classically incomputable problem that is solved with this hypercomputing algorithm is Hilbert's tenth problem. It is pointed out that a fundamental mathematical condition for these algorithms is the existence of an irreducible infinite dimensional unit representation of low-dimension algebras that admit the construction of coherent states of the Barut-Girardello type. Additionally, the hypercomputational algorithm on the infinite potential box previously constructed by the authors is presented as a limiting case of the proposed algorithm on the Pöschl-Teller potentials.
publishDate 2006
dc.date.issued.none.fl_str_mv 2006-12-01
dc.date.available.none.fl_str_mv 2019-11-22T19:18:48Z
dc.date.accessioned.none.fl_str_mv 2019-11-22T19:18:48Z
dc.date.none.fl_str_mv 2006-12-01
dc.type.eng.fl_str_mv article
info:eu-repo/semantics/article
publishedVersion
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status_str publishedVersion
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1794-9165
dc.identifier.uri.none.fl_str_mv http://hdl.handle.net/10784/14552
identifier_str_mv 2256-4314
1794-9165
url http://hdl.handle.net/10784/14552
dc.language.iso.eng.fl_str_mv eng
language eng
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dc.relation.uri.none.fl_str_mv http://publicaciones.eafit.edu.co/index.php/ingciencia/article/view/460
dc.rights.eng.fl_str_mv Copyright (c) 2006 Andrés Sicard, Juan Ospina
dc.rights.coar.fl_str_mv http://purl.org/coar/access_right/c_abf2
dc.rights.local.spa.fl_str_mv Acceso abierto
rights_invalid_str_mv Copyright (c) 2006 Andrés Sicard, Juan Ospina
Acceso abierto
http://purl.org/coar/access_right/c_abf2
dc.format.none.fl_str_mv application/pdf
dc.coverage.spatial.eng.fl_str_mv Medellín de: Lat: 06 15 00 N degrees minutes Lat: 6.2500 decimal degrees Long: 075 36 00 W degrees minutes Long: -75.6000 decimal degrees
dc.publisher.spa.fl_str_mv Universidad EAFIT
dc.source.none.fl_str_mv instname:Universidad EAFIT
reponame:Repositorio Institucional Universidad EAFIT
dc.source.spa.fl_str_mv Ingeniería y Ciencia; Vol 2, No 4 (2006)
instname_str Universidad EAFIT
institution Universidad EAFIT
reponame_str Repositorio Institucional Universidad EAFIT
collection Repositorio Institucional Universidad EAFIT
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