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Peculiar Dynamics of Phase-Space Embedded SU(2) Hamiltonians

Claudia M. Sarris, Angelo Plastino, Miryam Patricia Sassano

Published Jan 4, 2014• 0 citations
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Abstract

The Maximum Entropy Principle is used to analyze a phase-space embedded SU(2) Hamiltonian that exhibits a very complex dynamics. It is seen that the uncertainty principle becomes an invariant of the motion.

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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.