Stephen CREAGH

Service de Physique Theorique

CEA/Saclay

F91191 Gif-sur-Yvette CEDEX

Tunnelling in KAM systems

Abstract: Formal calculations of quantum mechanical tunnelling effects in weakly nonintegrable systems require the analytic continuation of invariant tori to complex angles.Natural boundaries, formed by dense accumulations of singularities along lines in the complex plane prevent a satisfactory resolution of this problem, and the classical aspect remains essentially ununderstood. One class of problem for which some analysis might be possible are rapidly forced systems such are responsible for exponentially small separatrix splittings. It is hoped that the same techniques as used there might allow determination of the classical structures demanded by semiclassical calculations, at least in restricted cases.