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.
Highlights
Semiquantum Dynamics (SD) may be used to describe systems in which quantum and classical degrees of freedom coexist
A nonlinear semiquantum Hamiltonian associated to the SU(2) Lie algebra is very useful to model the problem of quantum confinement, which is of interest for nanotechnology and solid state physics
We present a dimensionless formulation, and because the uncertainty principle (UP) is an invariant of the motion for the nonlinear semiquantum Hamiltonians associated to the SU(2) Lie algebra [6] [11], we make a change of variables that removes it as external strong constrain to the system’s motion equations
Summary
Semiquantum Dynamics (SD) may be used to describe systems in which quantum and classical degrees of freedom coexist. A nonlinear semiquantum Hamiltonian associated to the SU(2) Lie algebra is very useful to model the problem of quantum confinement, which is of interest for nanotechnology and solid state physics. The authors represent the trajectories for different initial conditions by stroboscopic plots, displaying regular and irregular dynamics This Hamiltonian may be reduced to the one in [2] (taking F = 0 ). We present a dimensionless formulation, and because the uncertainty principle (UP) is an invariant of the motion for the nonlinear semiquantum Hamiltonians associated to the SU(2) Lie algebra [6] [11], we make a change of variables that removes it as external strong constrain to the system’s motion equations. The change of variables offers some advantages which are highlighted in describing our treatment and summarized in the conclusions
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