In this paper, a nonlinear semiquantum Hamiltonian associated to the special unitary group SU(2) Lie algebra is studied so as to analyze its dynamics. The treatment here applied allows for a reduction in: 1) the syste...In this paper, a nonlinear semiquantum Hamiltonian associated to the special unitary group SU(2) Lie algebra is studied so as to analyze its dynamics. The treatment here applied allows for a reduction in: 1) the system’s dimension, as well as 2) the number of system’s parameters (to only three). We can now discern clear patterns in: 1) the complete characterization of the system’s fixed points and 2) their stability. It is shown that the parameter associated to the uncertainty principle, which constitutes a very strong constraint, is the key one in determining the presence of fixed points and bifurcation curves in the parameter’s space.展开更多
文摘In this paper, a nonlinear semiquantum Hamiltonian associated to the special unitary group SU(2) Lie algebra is studied so as to analyze its dynamics. The treatment here applied allows for a reduction in: 1) the system’s dimension, as well as 2) the number of system’s parameters (to only three). We can now discern clear patterns in: 1) the complete characterization of the system’s fixed points and 2) their stability. It is shown that the parameter associated to the uncertainty principle, which constitutes a very strong constraint, is the key one in determining the presence of fixed points and bifurcation curves in the parameter’s space.
