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The quantum dynamics of initial coherent states is studied in the Dicke modeland correlated with the dynamics, regular or chaotic, of their classical limit.Analytical expressions for the survival probability, i.e. the probability offinding the system in its initial state at time $t$, are provided in theregular regions of the model. The results for regular regimes are compared withthose of the chaotic ones. It is found that initial coherent states in regularregions have a much longer equilibration time than those located in chaoticregions. The properties of the distributions for the initial coherent states inthe Hamiltonian eigenbasis are also studied. It is found that for regularstates the components with no negligible contribution are organized insequences of energy levels distributed according to Gaussian functions. In thecase of chaotic coherent states, the energy components do not have a simplestructure and the number of participating energy levels is larger than in theregular cases.

Dynamics of Coherent States in Regular and Chaotic Regimes of the Non-integrable Dicke Model