In this paper we obtain equations for large-scale fluctuations of a mean field (the field of magnetization and quadrupole moments) in a magnetic system realized by a square (cubic) lattice of atoms with spin s 1 at each site. We use the generalized Heisenberg Hamiltonian with a biquadratic exchange as a quantum model. A quantum thermodynamical averaging gives classical effective models, which are interpreted as Hamiltonian systems on coadjoint orbits of the Lie group SU(3).
Orbits of coadjoint representations of classical compact Lie groups have a
lot of applications. They appear in representation theory, geometrical
quantization, theory of magnetism, quantum optics etc. As geometric objects the
orbits were the subject of much study. However, they remain hard for
calculation and application. We propose simple solutions for the following
problems: an explicit parameterization of the orbit by means of a generalized
stereographic projection, obtaining a K\"{a}hlerian structure on the orbit,
introducing basis two-forms for the cohomology group of the orbit.Comment: 21 pages, 1 figure, submitted to Proceedings of the 9th International
Conference on 'Geometry, Integrability and Quantization', Varna, Bulgaria,
June 8-13, 200
We consider the problem of two-level system dynamics induced by the time-dependent field B = {a(t) cos ωt, a(t) sin ωt, ω0}, with a(t) ∝ cn(νt, k). The problem is exactly analytically solvable and we propose the scheme for constructing the solutions. For all field configurations the resonance conditions are discussed. The explicit solutions for N = 1, 2 we obtained coincide at ω = 0 in the proper parameter domain with predictions of the rotating wave approximation and agree nicely with numerical calculations beyond it.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.