Eur. Phys. J. B (2018) 91: 52
https://doi.org/10.1140/epjb/e2018-80542-x

Regular Article

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

¹ Department of Physics, Bilkent University, 06800 Çankaya, Ankara, Turkey
² S.N. Bose National Centre for Basic Sciences, JD Block, Sector III, Salt Lake, Kolkata 700106, India

^a e-mail: kumar.abhinav@bilkent.edu.tr

Received: 25 September 2017
Received in final form: 5 December 2017
Published online: 26 March 2018

Abstract

Through 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.