A geometrical approach to wave dynamics in billiards
Laboratoire de Physique de la Matière Condensée, CNRS URA 190,
Université de Nice-Sophia Antipolis, Parc Valrose, 06108 Nice Cedex 2,
Accepted: 5 January 1996
A semi-classical time-dependent Green's function for the hyperbolic wave equation is constructed using a summation over quasi-recurrent classical ray trajectories. The finite resolution of the wave problem associated to the smallest wavelength introduces a natural coarse graining which allows us to partition the classical rays into bundles. Our parametrization introduces precursor contributions in the sum, which allow for a very good agreement with the direct numerical integration of the wave equation in integrable as well as chaotic two-dimensional (2D) billiards. These precursors give a new insight in the role of focal points in semi-classical wave dynamics.
PACS: 03.65.Sq – Semiclassical theories and applications / 03.40.Kf – Waves and wave propagation: general mathematical aspects / 05.45.+b – Theory and models of chaotic systems
© EDP Sciences, 1996