Applied Mathematics

Volume 9, Issue 1 (January 2018)

ISSN Print: 2152-7385   ISSN Online: 2152-7393

Google-based Impact Factor: 0.83  Citations  

Uncertainty Principle and Bifurcations in the SU(2) Nonlinear Semiquantum Dynamics

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DOI: 10.4236/am.2018.91001    632 Downloads   1,169 Views  

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.

Cite this paper

Hansen, R. , Sarris, C. and Plastino, A. (2018) Uncertainty Principle and Bifurcations in the SU(2) Nonlinear Semiquantum Dynamics. Applied Mathematics, 9, 1-16. doi: 10.4236/am.2018.91001.

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