Quantum Entanglement and fixed point Hopf bifurcation
  We present the qualitative differences in the phase transitions of the mono-mode Dicke model in its integrable and chaotic versions. We show that a first order phase transition occurs in the integrable case whereas a second order in the chaotic one. This difference is also reflected in the classical limit: for the integrable case the stable fixed point in phase space suffers a bifurcation of Hopf type whereas for the second one a pitchfork type bifurcation has been reported. 
M. C. Nemes, K. Furuya, G. Q. Pellegrino, A. C. Oliveira, Mauricio   Reis and L. Sanz