Quantum-classical transition in nonlinear dynamical systems

The qualitative features of quantum-classical transition in nonlinear-dynamical systems were discussed. It was established that classical evolutions could violate the positive semidefiniteness of the density matrix. The systems were classified on the basis of classical quantum correspondence to identify quantum-classical transitions. The issue of environment induced decoherence in the quantum delta kicked rotor (QDKR) in the context of cold atom optics was also studied. Parametric noise or spontaneous emission was used as the decoherent mechanism and a quantum master equation was presented.