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We consider dynamics of Dicke models, with and without counterrotating terms,under slow variations of parameters which drive the system through a quantumphase transition. The model without counterrotating terms and sweeped detuningis seen in the contexts of a many-body generalization of the Landau-Zener modeland 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 adiabaticinvariants and mapping to the second Painleve equation (PII), we derive aformula which accurately describes particle distributions in the Hilbert spaceat wide range of parameters and initial conditions of the system. We findstriking universal features in the particle distributions which can be probedin an experiment on Feshbach resonance passage or a cavity QED experiment. Thedynamics is found to be crucially dependent on the direction of the sweep. Themodel with counterrotating terms has been realized recently in an experimentwith ultracold atomic gases in a cavity. Its semiclassical dynamics isdescribed by a Hamiltonian system with two degrees of freedom. Passage througha QPT corresponds to passage through a bifurcation, and can also be describedby PII (after averaging over fast variables), leading to similar universaldistributions. Under certain conditions, the Dicke model is reduced to theLipkin-Meshkov-Glick model.

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