Applied Maths Seminar: Kezmerick -- Resonance states in chaotic scattering

Roland Ketzmerick (TU Dresden) will be visiting us from March 11 to April 7, and will be
giving a talk on Wednesday 19 March at 11am in Carslaw 173.  Afterwards we will go to
lunch (free for students).  

Title: Resonance states in chaotic scattering 

Abstract: Eigenfunctions in closed quantum systems with a chaotic classical limit are
equidistributed following the quantum ergodicity theorem.  In contrast, in open
scattering systems one finds that resonance states have a multifractal structure.  How
is this structure generated from the underlying classical dynamics? We answer this by
generalizing Ulam’s matrix approximation of the Perron-Frobenius operator.  It gives
rise to a conditionally invariant measure describing resonance states in the
semiclassical limit.  Numerical examples are a dielectric cavity and the three-disk
scattering system.