Dr. Leonidas Pantelidis – Swarthmore College
“Dynamics of the Heisenberg Model”
I will give a brief general description of the Heisenberg Model (HM). Then, I will immediately digress in order to outline the basic ideas of classical and quantum mechanics! Also, I will introduce the nomenclature that I will be using for the rest of the talk. The study of the HM will be motivated, and the quantum version will be presented as a model of magnetism in materials. Moreover, the passage to its classical counterpart will be explained. At this point, a very brief excursion in the realm of nonlinear dynamics (Arnold theorem, periodic orbits, tori, chaos, stability) will provide us with the necessary tools to investigate the structure of the HM phase space. Finally, if there is time left, the simple, but not so simple, case of a four-spin ring will be tackled.
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