Non-stationary quantum phase transitions in hot clusters?

Cluster impact on a hard wall enables us to rapidly heat and compress an initially cold cluster. We start by discussing the theoretical prediction and experimental observation of phase transitions in these hot clusters. We then note that different types of quantum phase transitions have been induced by compression, but under quasi-static conditions. The question is if it might be possible to realize a combined experiment, leading to a quantum phase transition but where the compression is very fast. The theoretical reasons why such an experiment may work and why it may not, are considered with special reference to the choice of cluster composition. Other types of experiments on hot clusters, that have not yet been realized, are also noted.