We analyze the stability under time evolution of complexifier coherent states (CCS) in one-dimensional mechanical systems. A system of coherent states is called stable if it evolves into another coherent state. It turns out that a system can only possess stable CCS if the classical evolution of the variable $\mathbf{z}=e^{-i{\mathcal{L}}_{{\chi }_C}}\mathbf{q}$ for a given complexifier $C$ depends only on $\mathbf{z}$ itself and not on its complex conjugate. This condition is very restrictive in general so that only a few systems exist that obey this condition. However, it is possible to access a wider class of models that in principle may allow for stable coherent states associated with certain regions in the phase space by introducing action-angle coordinates.

• Received 11 February 2016

DOI:https://doi.org/10.1103/PhysRevD.93.084030