Stable coherent states

TL;DR

This paper investigates the conditions under which complexifier coherent states remain stable during time evolution in one-dimensional systems, revealing restrictive criteria and proposing broader classes of models using action-angle coordinates.

Contribution

It identifies the specific condition for stability of complexifier coherent states and extends the analysis to a wider class of models via action-angle coordinates.

Findings

Stability requires classical evolution to depend only on the variable z.

Few systems naturally satisfy the stability condition.

Action-angle coordinates can be used to access more models with potentially stable states.

Abstract

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 poses stable CCS if the classical evolution of the variable for a given complexifier C depends only on z itself and not on its complex conjugate. This condition is very restrictive in general so that only 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 to certain regions in the phase space by introducing action-angle coordinates.