Adiabtic perturbation theory in quantum dynamics

Separation of scales plays a fundamental role in the understanding of the dynamical behavior of complex systems in physics and other natural sciences. A prominent example is the Born-Oppenheimer approximation in molecular dynamics. In my talk I will present a general scheme for deriving effective equations of motion for the slow degrees of freedom in a quantum mechanical system with two time-scales. As an application I consider higher order corrections to the conventional Born-Oppenheimer approximation in molecular dynamics.