Holonomy-reduced dynamics of triatomic molecules

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dc.authorscopusid23481439700
dc.authorscopusid57203397243
dc.authorwosidCiftci, Unver/B-6108-2013
dc.contributor.authorÇiftçi, Ünver
dc.contributor.authorWaalkens, Holger
dc.date.accessioned2022-05-11T14:31:09Z
dc.date.available2022-05-11T14:31:09Z
dc.date.issued2011
dc.departmentFakülteler, Fen Edebiyat Fakültesi, Matematik Bölümü
dc.description.abstractWhereas it is easy to reduce the translational symmetry of a molecular system using, e. g., Jacobi coordinates, the situation is much more involved for rotational symmetry. In this paper, we address the latter problem using holonomy reduction. We suggest that the configuration space may be considered as the reduced holonomy bundle with a connection induced by the mechanical connection. Using the fact that for the special case of the three-body problem the holonomy group is SO(2) (as opposed to SO(3) like in systems with more than three bodies), we obtain a holonomy-reduced configuration space of topology R(+)(3) x S(1). The dynamics then takes place on the cotangent bundle over the holonomy-reduced configuration space. On this phase space, there is an S(1) symmetry action coming from the conserved reduced angular momentum which can be reduced using the standard symplectic reduction method. Using a theorem by Arnold it follows that the resulting symmetry-reduced phase space is again a natural mechanical phase space, i.e. a cotangent bundle. This is different from what is obtained from the usual approach where symplectic reduction is used from the outset. This difference is discussed in some detail, and a connection between the reduced dynamics of a triatomic molecule and the motion of a charged particle in a magnetic field is established.
dc.identifier.doi10.1088/1751-8113/44/16/165202
dc.identifier.issn1751-8113
dc.identifier.issue16en_US
dc.identifier.scopus2-s2.0-79953682276
dc.identifier.scopusqualityQ2
dc.identifier.urihttps://doi.org/10.1088/1751-8113/44/16/165202
dc.identifier.urihttps://hdl.handle.net/20.500.11776/7342
dc.identifier.volume44
dc.identifier.wosWOS:000288939300007
dc.identifier.wosqualityQ2
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.institutionauthorÇiftçi, Ünver
dc.language.isoen
dc.publisherIop Publishing Ltd
dc.relation.ispartofJournal of Physics A-Mathematical and Theoretical
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccess
dc.subjectInternal Motions
dc.subject3-Body Problem
dc.subjectSystems
dc.subjectSpace
dc.titleHolonomy-reduced dynamics of triatomic molecules
dc.typeArticle

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