Inhomogeneous Heisenberg spin chain and quantum vortex filament as non-holonomically deformed NLS systems
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.
KeywordsStatistical and Nonlinear Physics
- 4.R.J. Baxter, Exactly solved models in statistical mechanics (Academic Press, London, 1982) Google Scholar
- 13.I.L. Bekarevich, I.M. Khalatnikov, Sov. Phys. J. Exp. Theor. Phys. 13, 643 (1961) Google Scholar
- 16.L D Faddeev, Leon Takhtajan, Hamiltonian methods in the theory of solitons (Springer-Verlag Berlin, Heidelberg, 2007) Google Scholar
- 20.J. Nian, arXiv:1611.04562 [hep-th] (2016)
- 21.K. Abhinav, P. Guha, arXiv:1612.07499 [math-ph] (2016)