Chaos in a deformed Dicke model
arXiv:2112.01923 · doi:10.1088/1751-8121/ac4b16
Abstract
The critical behavior in an important class of excited state quantum phase transitions is signaled by the presence of a new constant of motion only at one side of the critical energy. We study the impact of this phenomenon in the development of chaos in a modified version of the paradigmatic Dicke model of quantum optics, in which a perturbation is added that breaks the parity symmetry. Two asymmetric energy wells appear in the semiclassical limit of the model, whose consequences are studied both in the classical and in the quantum cases. Classically, Poincaré sections reveal that the degree of chaos not only depends on the energy of the initial condition chosen, but also on the particular energy well structure of the model. In the quantum case, Peres lattices of physical observables show that the appearance of chaos critically depends on the quantum conserved number provided by this constant of motion. The conservation law defined by this constant is shown to allow for the coexistence between chaos and regularity at the same energy. We further analyze the onset of chaos in relation with an additional conserved quantity that the model can exhibit.
11 pages, 4 figures
References in corpus (11)
- Foundation of Statistical Mechanics under experimentally realistic conditions
- Semiclassical Foundation of Universality in Quantum Chaos
- Excited state quantum phase transitions in many-body systems
- Periodic-Orbit Theory of Universality in Quantum Chaos
- Periodic-Orbit Theory of Level Correlations
- Excited-state quantum phase transitions
- Periodic-orbit theory of universal level correlations in quantum chaos
- Approximated integrability of the Dicke model
- Phase Transition in the periodically pulsed Dicke Model
- Effects of Spin-Orbit Coupling on Jaynes-Cummings and Tavis-Cummings Models
- Quantum chaos in the nuclear collective model: II. Peres lattices