Alladi Ramakrishnan Hall

Nonlinear Dynamics of Heisenberg Ferromagnetic Spin Chain

Prof. M Lakshmanan

Centre for Nonlinear Dynamics, Bharathidasan University, Tiruchirapalli

The dynamics of Heisenberg ferromagnetic spin system is surprisingly an unending source of nonlinear integrable and nonintegrable systems, having
connections with a wide variety of nonlinear evolution equations through geometric, gauge equivalent and other transformations. I will try to point out some of them. The isotropic chain in its continuum limit is a completely integrable solitonic system and is equivalent to the nonlinear Schrödinger equation. Several extensions of this integrable case can be identified. Integrable XY and XYZ spin maps will be pointed out. Special solutions of certain nonintegrable anisotropic spin chains and localized internal modes will be discussed. The evolution equation under stereographic projection shows some remarkable properties. Connection with spin transfer torque effect and the associated Landau-Lifshitz- Gilbert-Slonczewski equation will be pointed out. The associated notions of bifurcation, chaos and syncrhonization to enhance power in a spin transfer oscillator will be indicated.