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

AM > Vol.9 No.1, January 2018

Applied Mathematics

Volume 9, Issue 1 (January 2018)

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

Google-based Impact Factor: 0.58 Citations

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

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DOI: 10.4236/am.2018.91001 837 Downloads 1,717 Views Citations

Author(s)

Roberta Hansen¹, Claudia M. Sarris^1,2, Angelo Plastino^3,4

Affiliation(s)

¹Department of Mathematics, Faculty of Engineering, University of Buenos Aires, Buenos Aires, Argentina.
²Common Basic Cycle, Chair of Physics, University of Buenos Aires, Buenos Aires, Argentina.
³Institute of Physics of La Plata, CCT-CONICET, National University of La Plata, La Plata, Argentina.
⁴Physics Department and IFISC-CSIC, University of the Balearic Island, Palma de Mallorca, Spain.

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.

KEYWORDS

Semiquantum Dynamics, Uncertainty Principle, Fixed Points, Bifurcation Curves

Share and Cite:

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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