The Erwin Schrr Odinger International Institute for Mathematical Physics What Are the Quantum Mechanical Lyapunov Exponents What Are the Quantum Mechanical Lyapunov Exponents?

The origin of chaotic behaviour of a dynamical system in the sense of sensitive dependence on initial conditions is the action of a certain group. We are used to the importance of a group from the theory of relativity and in fact this group happens to be a subgroup of the Poincare group. Physical consequences like sensitive dependence on initial conditions or exponential decay of time correlations can be deduced if we add some continuity requirements on the action of this group. This will be illustrated by examples from classical mechanics, quantum mechanics and quantum eld theory.