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Integrable vortex dynamics in anisotropic planar spin liquid model

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  • Gurkan, Zeynep Nilhan
  • Pashaev, Oktay

Abstract

The problem of magnetic vortex dynamics in an anisotropic spin liquid model is considered. For incompressible flow the model admits reduction to saturating Bogomolny inequality analytic projections of spin variables, subject the linear holomorphic Schrödinger equation. It allows us to construct N vortex configurations in terms of the complex Hermite polynomials. Using complex Galilean boost transformations, the interaction of the vortices and the vortex chain lattices (vortex crystals) is studied. By the complexified Cole–Hopf transformation, integrable N vortex dynamics is described by the holomorphic Burgers equation. Mapping of the point vortex problem to N-particle problem, the complexified Calogero–Moser system, showing its integrability and the Hamiltonian structure, is given.

Suggested Citation

  • Gurkan, Zeynep Nilhan & Pashaev, Oktay, 2008. "Integrable vortex dynamics in anisotropic planar spin liquid model," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 238-253.
    • Handle: RePEc:eee:chsofr:v:38:y:2008:i:1:p:238-253
    DOI: 10.1016/j.chaos.2006.11.013
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    1. El Naschie, M.S., 2006. "Holographic dimensional reduction: Center manifold theorem and E-infinity," Chaos, Solitons & Fractals, Elsevier, vol. 29(4), pages 816-822.
    2. El Naschie, M. Saladin, 2006. "Nanotechnology for the developing world," Chaos, Solitons & Fractals, Elsevier, vol. 30(4), pages 769-773.
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