1,720,981 research outputs found
On topological soliton dynamics in multidimensional ferromagnetic continuum
No full textA multidimensional model for a ferromagnetic continuum with hydrodynamical properties, which can be regarded as a modified Landau-Lifshitz equation, is presented. The treatment of some physical examples suggests that the fluid vorticity has to be proportional to the magnetic topological current. The model can be written in the Hirota bilinear form. In two spatial dimensions, the existence of a positive definite energy functional is shown. The Bogomol'nyi inequality leads to the self-dual equations of the model, which can be expressed by the Liouville equation. By using time-dependent gauge transformations, a wide class of solutions can be generated. These are, in general, associated with the linear problem of the modified Kadomtsev-Petviashvili equation. In some particular cases, the isolated vortices can move along arbitrary trajectories on the plane. The quantization problem of the time-dependent vortex configurations is briefly discussed, in relation to the possible evaluation of their energy spectrum
Quantization of planar ferromagnets in the Chern-Simons representation
No full textWe formulate the two-dimensional planar classical continuous Heisenberg spin model as a constrained Chern-Simons gauged nonlinear Schrödinger system. Several physical consequences in the framework of the anyon field theory are discussed. We study the Hamiltonian structure of the model, which is quantized using the gauge invariant approach. A preliminary study of the quantum states is presented
Self-Dual Chern-Simons Solitons in Nonlinear σ-model
No full textA self-dual Chern-Simons system and its Lax pair are derived from the tangent space representation of a two-dimensional nonlinear σ-model, endowed with a gauge field. The related “matter” field density obeys the Liouville equation, whose N-soliton solutions correspond to the magnetic vortices in the static self-dual planar Heisenberg model. It is shown that the topological charge and the total vorticity correspond to the electric charge and the magnetic flux for the Chern-Simons system, respectively. General holomorphic solutions of the system studied generate a large class of static solutions to the Davey-Stewartson and Ishimori equations
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