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Uncertainty Principle and Bifurcations in the SU(2) Nonlinear Semiquantum Dynamics
Department of Mathematics, Faculty of Engineering, University of Buenos Aires, Buenos Aires, Argentina
Common Basic Cycle, Chair of Physics, University of Buenos Aires, Buenos Aires, Argentina
Institute of Physics of La Plata, CCT-CONICET, National University of La Plata, La Plata, Argentina
Physics Department and IFISC-CSIC, University of the Balearic Island, Palma de Mallorca, Spain
- 1 Department of Mathematics, Faculty of Engineering, University of Buenos Aires, Buenos Aires, Argentina
- 2 Common Basic Cycle, Chair of Physics, University of Buenos Aires, Buenos Aires, Argentina
- 3 Institute of Physics of La Plata, CCT-CONICET, National University of La Plata, La Plata, Argentina
- 4 Physics Department and IFISC-CSIC, University of the Balearic Island, Palma de Mallorca, Spain
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Abstract
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.
KeywordsSemiquantum DynamicsUncertainty PrincipleFixed PointsBifurcation Curves
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