36 research outputs found
Approximated integrability of the Dicke model
A very approximate second integral of motion of the Dicke model is identified
within a broad region above the ground state, and for a wide range of values of
the external parameters. This second integral, obtained from a Born Oppenheimer
approximation, classifies the whole regular part of the spectrum in bands
labelled by its corresponding eigenvalues. Results obtained from this
approximation are compared with exact numerical diagonalization for finite
systems in the superradiant phase, obtaining a remarkable accord. The region of
validity of our approach in the parameter space, which includes the resonant
case, is unveiled. The energy range of validity goes from the ground state up
to a certain upper energy where chaos sets in, and extends far beyond the range
of applicability of a simple harmonic approximation around the minimal energy
configuration. The upper energy validity limit increases for larger values of
the coupling constant and the ratio between the level splitting and the
frequency of the field. These results show that the Dicke model behaves like a
two-degree of freedom integrable model for a wide range of energies and values
of the external parameters.Comment: 6 pages, 3 figures. Second version with added text, references and
some new figure
Dynamics of Coherent States in Regular and Chaotic Regimes of the Non-integrable Dicke Model
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 , 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.Comment: Contribution to the proceedings of the Escuela Latinoamericana de
F\'isica (ELAF) Marcos Moshinsky 2017. (9 pages, 4 figures