Quantum Chaos Triggered by Precursors of a Quantum Phase Transition: The   Dicke Model
  We consider the Dicke Hamiltonian, a simple quantum-optical model which exhibits a zero-temperature quantum phase transition. We present numerical results demonstrating that at this transition the system changes from being quasi-integrable to quantum chaotic. By deriving an exact solution in the thermodynamic limit we relate this phenomenon to a localisation-delocalisation transition in which a macroscopic superposition is generated. We also describe the classical analogues of this behaviour. 
C. Emary, T. Brandes (UMIST, Manchester)