dc.contributor.author
Acosta-Humánez, P.
dc.contributor.author
Lázaro, J.T.
dc.contributor.author
Morales-Ruiz, J.J.
dc.contributor.author
Pantazi, C.
dc.date.accessioned
2024-03-04T11:00:34Z
dc.date.accessioned
2024-09-19T14:29:28Z
dc.date.available
2024-03-04T11:00:34Z
dc.date.available
2024-09-19T14:29:28Z
dc.date.issued
2024-01-24
dc.identifier.uri
http://hdl.handle.net/2072/537453
dc.description.abstract
In this work we explain the relevance of the Differential Galois Theory in the semiclassical (or WKB) quantification of some two degree of freedom potentials. The key point is that the semiclassical path integral quantification around a particular solution depends on the variational equation around that solution: a very well-known object in dynamical systems and variational calculus. Then, as the variational equation is a linear ordinary differential system, it is possible to apply the Differential Galois Theory to study its solvability in closed form. We obtain closed form solutions for the semiclassical quantum fluctuations around constant velocity solutions for some systems like the classical Hermite/Verhulst, Bessel, Legendre, and Lamé potentials. We remark that some of the systems studied are not integrable, in the Liouville-Arnold sense. © 2024 Author(s).
eng
dc.description.sponsorship
Funding text 1: J.J.M.R. has been supported by the Universidad Politécnica de Madrid research group Modelos Matemáticos no lineales. As well as he thanks to the Japan Society for Promotion of the Science and to the hospitality of the Departament of Applied Mathematics and Physics of Kyoto University, where he stayed in the fall of 2022 under the Grant “FY JSPS Invitational Fellowships for Research in Japan” and where part of his contribution to this work was done. ; Funding text 2: C.P. is partially supported by the Ministerio de Ciencia e Innovación Grant (No. PID2019-104658GB-I00); is funded partially by the Grant No. PID-2021-122954NB-100 funded by MCIN/AEI/10.13039/501100011033 and by “ERDF A way of making Europe.” ; Funding text 3: P.A.-H. is partially supported by the Ministerio de Educación Superior, Ciencia y Tecnología (MESCyT) Grant No. FONDOCYT 2022-1D2-091 “Aproximación Semiclásica de Sistemas Hamiltonianos con potenciales Homogéneos de dos grados de libertad y osciladores no autónomos.” ; Funding text 4: J.T.L. has been supported by the Spanish State Research Agency (AEI), through the Severo Ochoa and María de Maeztu Program for Centers and Units of Excellence in R&D (Grant No. CEX2020-001084-M). Moreover, he has been funded by the Spanish Project No. PGC2018-098676-B-100 funded by MCIN/AEI/10.13039/501100011033 “ERDF A way of making Europe;” by the Spanish Project No. PID2021-122954NB-I00 funded by MCIN/AEI/10.13039/501100011033/ and “ERDF A way of making Europe;” and by a grant from the “Ayudas para la recualificación del sistema universitario español para 2021–2023.” He also thanks Laboratorio Subterráneo de Canfranc (LSC), the Instituto de Biología Integrativa de Sistemas (I2Sysbio, CSIC-UV), and the Institut de Mathématiques de Jussieu - Paris Rive Gauche (Sorbonne Université) for their kind hospitality as the hosting institutions of this grant.
dc.format.extent
21 p.
cat
dc.publisher
American Institute of Physics Inc.
cat
dc.relation.ispartof
Journal of Mathematical Physics
cat
dc.rights
Published under an exclusive license by AIP Publishing. https://doi.org/10.1063/5.0169069
dc.source
RECERCAT (Dipòsit de la Recerca de Catalunya)
dc.subject.other
two degree of freedom potentials, differential Galois approach
cat
dc.title
Semiclassical quantification of some two degree of freedom potentials: A differential Galois approach
cat
dc.type
info:eu-repo/semantics/article
cat
dc.type
info:eu-repo/semantics/publishedVersion
cat
dc.identifier.doi
10.1063/5.0169069
cat
dc.rights.accessLevel
info:eu-repo/semantics/openAccess
