Inhomogeneous heisenberg spin chain and quantum vortex filament as non-holonomically deformed NLS systems

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dc.citation.epage7en_US
dc.citation.issueNumber52en_US
dc.citation.spage1en_US
dc.citation.volumeNumber91en_US
dc.contributor.authorAbhinav, K.en_US
dc.contributor.authorGuha, P.en_US
dc.date.accessioned2019-02-21T16:06:39Z
dc.date.available2019-02-21T16:06:39Z
dc.date.issued2018en_US
dc.departmentDepartment of Physicsen_US
dc.description.abstractThrough the Hasimoto map, various dynamical systems can be mapped to different integrodifferential generalizations of Nonlinear Schrödinger (NLS) family of equations some of which are known to be integrable. Two such continuum limits, corresponding to the inhomogeneous XXX Heisenberg spin chain [J. Phys. C 15, L1305 (1982)] and that of a thin vortex filament moving in a superfluid with drag [Eur. Phys. J. B 86, 275 (2013) 86; Phys. Rev. E 91, 053201 (2015)], are shown to be particular non-holonomic deformations (NHDs) of the standard NLS system involving generalized parameterizations. Crucially, such NHDs of the NLS system are restricted to specific spectral orders that exactly complements NHDs of the original physical systems. The specific non-holonomic constraints associated with these integrodifferential generalizations additionally posses distinct semi-classical signature.
dc.description.provenanceMade available in DSpace on 2019-02-21T16:06:39Z (GMT). No. of bitstreams: 1 Bilkent-research-paper.pdf: 222869 bytes, checksum: 842af2b9bd649e7f548593affdbafbb3 (MD5) Previous issue date: 2018en
dc.description.sponsorshipThe authors are grateful to Professors Luiz. A. Ferreira and Wojtek J. Zakrzewski for their encouragement and useful discussions. The research of KA is supported by the TÜBITAK 2216 grant number 21514107-115.02-124285 of the Turkish government. The research of PG was partially supported by Fig. 1. Schematics of different HSCs corresponding to continuum integrable systems. Here I-XXX stands for inhomogeneous XXX and ID-NLS for integrodifferential NLS systems. The right half represents the present results, whereas the left half summarizes the possibilities regarding anisotropic generalizations. {KdV} includes quantum (modified) KdV systems. The possible connection between Hasimoto map and Bethe ansatz is represented by the dashed line.
dc.identifier.doi10.1140/epjb/e2018-80542-x
dc.identifier.eissn1434-6036
dc.identifier.issn1434-6028
dc.identifier.urihttp://hdl.handle.net/11693/50323
dc.language.isoEnglish
dc.publisherSpringer Heidelberg
dc.relation.isversionofhttps://doi.org/10.1140/epjb/e2018-80542-x
dc.source.titleEuropean Physical Journal Ben_US
dc.subjectStatistical and nonlinear physicsen_US
dc.titleInhomogeneous heisenberg spin chain and quantum vortex filament as non-holonomically deformed NLS systemsen_US
dc.typeArticleen_US

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