Bifurcation in kinetic equation for interacting Fermi systems
  The finite duration of collisions appear as time-nonlocality in the kinetic equation. Analyzing the corresponding quantum kinetic equation for dense interacting Fermi systems a delay differential equation is obtained which combines time derivatives with finite time stepping known from the logistic mapping. The responsible delay time is explicitly calculated and discussed. As a novel feature oscillations in the time evolution of the distribution function itself appear and bifurcations up to chaotic behavior can occur. The temperature and density conditions are presented where such oscillations and bifurcations arise indicating an onset of phase transition. 
Klaus Morawetz