TITLE:
Gauge Transformation Approach to a Dynamic Description in Dicke Model
AUTHORS:
Ahlem Abidi
KEYWORDS:
Dicke Model, Phase Transition, Entanglement, Fichier Information, Wigner Phase Probability Distribution
JOURNAL NAME:
Open Access Library Journal,
Vol.12 No.11,
November
6,
2025
ABSTRACT: Dynamic analysis can be an efficient tool to understand and characterize some physical systems at different stages of processing. This is the subject of this paper. We derive analytically the scale entropies, Fishier information and Wigner phase probability distribution of the Dicke model in a quantum phase transition. We focus the treatment on the Gauge transformation approach. The Dicke model is considered as two harmonic oscillators. For two different models, the first is two harmonic oscillators with angular frequencies varying for negative and positive time intervals, the second is two harmonic oscillators in a Paul Trap motion with a periodic quadrupole potential. The Gauge transformation approach is a path between classical and quantum such that the choice cosinusoidal form of the classical functions fully reflects the oscillatory behavior of entanglement, Fishier information and the Wigner phase probability distribution. Another interesting result, the time evolution of entanglement, Fishier information and the Wigner phase probability distribution are used to distinguish different quantum phase transitions. It is shown that the oscillations of the normal phase are always in phase advance compared to the critical phase, while the oscillations of the superradiant phase are in phase delay.