Waves in chaotic cavities: dispersion and delocalization

Stéphane Nonnenmacher
Université Paris-Sud, LMO, Orsay 91400, France

Linear (scalar) waves propagating inside a closed cavity resonate a certain frequencies, determined by the shape of the cavity: at these frequencies the waves exhibit stationary modes (eigenmodes of the Laplacian in the cavity). At high frequencies the structure of these eigenmodes may be complicated and diverse; it is strongly influenced by the properties of the ray dynamics inside the cavity (billiard dynamics).

We will address the situations where this ray dynamics is chaotic, which defines the realm of Wave (or Quantum) Chaos. I will explain how the two main ingredients of chaos (instability of trajectories, and infinite recurrence of the trajectories) lead to a fast dispersion of the waves, and the impossibility for the stationary modes to localize (concentrate) on a small region of the cavity; most eigenmodes rather spread uniformly all over the cavity.

This fast wave dispersion is also at work when "open" the chaotic cavity. The stationary modes are then replaced by metastable (or resonant) modes with finite lifetimes. We will show how the dispersion induced by the chaotic ray dynamics influences the distribution of the lifetimes, and thereby the behaviour of the waves at large times.