Resonance eigenfunctions in chaotic scattering systems

MARTIN SIEBER

School of Mathematics, University of Bristol, Bristol

BS8 1TW, United Kingdom

E-mail: M.Sieber@bristol.ac.uk

Abstract. We study the semiclassical structure of resonance

eigenstates of open chaotic systems. We obtain semiclassical

estimates for the weight of these states on different regions in

phase space. These results imply that the long-lived right (left)

eigenstates of the non-unitary propagator are concentrated in the

semiclassical limit $\hbar \rightarrow 0$ on the backward (forward)

trapped set of the classical dynamics. On this support the

eigenstates display a self-similar behaviour which depends on the

limiting decay rate.

Keywords. Resonances; semiclassics; quantum chaos.

PACS Nos 05.45.Mt, 03.65.Sq, 05.45.Df