Volume 33, Number 6, February III 1996
|Page(s)||417 - 422|
|Published online||01 September 2002|
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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.