TITLE:
Uncertainty Principle and Bifurcations in the SU(2) Nonlinear Semiquantum Dynamics
AUTHORS:
Roberta Hansen, Claudia M. Sarris, Angelo Plastino
KEYWORDS:
Semiquantum Dynamics, Uncertainty Principle, Fixed Points, Bifurcation Curves
JOURNAL NAME:
Applied Mathematics,
Vol.9 No.1,
January
11,
2018
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.