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Using coherent states as initial states, we investigate the quantum dynamicsof the Lipkin-Meshkov-Glick (LMG) and Dicke models in the semi-classical limit.They are representative models of bounded systems with one- and two-degrees offreedom, respectively. The first model is integrable, while the second one hasboth regular and chaotic regimes. Our analysis is based on the survivalprobability. Within the regular regime, the energy distribution of the initialcoherent states consists of quasi-harmonic sub-sequences of energies withGaussian weights. This allows for the derivation of analytical expressions thataccurately describe the entire evolution of the survival probability, from$t=0$ to the saturation of the dynamics. The evolution shows decayingoscillations with a rate that depends on the anharmonicity of the spectrum and,in the case of the Dicke model, on interference terms coming from thesimultaneous excitation of its two-degrees of freedom. As we move away from theregular regime, the complexity of the survival probability is shown to beclosely connected with the properties of the corresponding classical phasespace. Our approach has broad applicability, since its central assumptions arenot particular of the studied models.

Analytical description of the survival probability of coherent states in regular regimes