Dynamics of quantum phase transitions in Dicke and Lipkin-Meshkov-Glick models

Understand

We consider dynamics of Dicke models, with and without counterrotating terms, under slow variations of parameters which drive the system through a quantum phase transition.

• The model without counterrotating terms and sweeped detuning is seen in the contexts of a many-body generalization of the Landau-Zener model and the dynamical passage through a second-order quantum phase transition (QPT).
• Adiabaticity is destroyed when the parameter crosses a critical value.
• Applying semiclassical analysis based on concepts of classical adiabatic invariants and mapping to the second Painleve equation (PII), we derive a formula which accurately describes particle distributions in the Hilbert space at wide range of parameters and initial conditions of the system.