Seminar

An open system has an essential spectral gap if the corresponding quantum evolution operator has exponential local energy decay in the high frequency régime. Examples of systems with spectral gaps include wave equations with trapped sets which are hyperbolic (such as convex co-compact hyperbolic manifolds or exteriors of several convex obstacles) or normally hyperbolic (such as black holes), as well as classical correlations for Anosov flows (which have normally hyperbolic trapping). I will give a broad overview of several results in spectral gaps from the point of view of microlocal analysis and long time wave propagation, explaining how they can be interpreted in terms of uncertainty principles.