Title: Inhomogeneous Heisenberg Spin Chain and Quantum Vortex Filament as Non-Holonomically Deformed NLS Systems,
Abstract: Through the Hasimoto map, various dynamical systems can be mapped to
different integrodifferential generalizations of Nonlinear Schrodinger (NLS)
family of equations some of which are known to be integrable. Two such
continuum limits, corresponding to the inhomogeneous XXX Heisenberg spin chain
[Balakrishnan, J. Phys. C 15, L1305 (1982)] and that of a thin vortex filament
moving in a superfluid with drag [Shivamoggi, Eur. Phys. J. B 86, 275 (2013)
86; Van Gorder, 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.