DYNAMICS BEYOND THE ADIABATIC APPROXIMATION

We explore the dynamics of mixed classical-quantum Hamiltonians, a cla ss of systems that frequently appears in the study of physical systems characterized by both slow and fast modes. Traditionally such systems are studied within the adiabatic approximation and as a rule they dis play level crossings. We show that level crossings can have peculiar e ffects on the dynamics and, in the regime between the adiabatic and di abatic limits in both classical and quantum approaches, the full dynam ics has a series of non-intuitive features.