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

TL;DR

This paper investigates how initial coherent states evolve in the Dicke model, revealing distinct behaviors in regular versus chaotic regimes, with implications for quantum state stability and energy distribution structures.

Contribution

It provides analytical expressions for survival probability in regular regimes and compares quantum dynamics between regular and chaotic states in the Dicke model.

Findings

Regular states have longer equilibration times.

Energy components in regular states are Gaussian-distributed.

Chaotic states involve more energy levels with complex structures.

Abstract

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