A plateau structure in the tunnelling spectrum as a manifestation of a new tunnelling mechanism in multi-dimensional barrier systems.

In recent years a new description has been developed for tunnelling in multi-dimensional systems based on complexified stable-unstable manifolds of periodic saddles. The complexified stable-unstable manifolds guide complex-classical tunnelling trajectories over the energetic barrier (Takahashi and Ikeda 2003 J. Phys. A: Math. Gen. 36 7953). In this paper it is claimed, based on theoretical analysis and numerical evidence, that the tunnelling mechanism due to complexified stable-unstable manifolds is associated with a characteristic plateau feature in the tunnelling spectrum. An analysis of a particular two-dimensional barrier tunnelling model shows that the plateau feature is obtained by a fully quantum-mechanical computation, and that the complex-semiclassical theory successfully reproduces this feature. Moreover, an analytical theory based upon Melnikov's method is developed and used to clarify quantitatively how the tunnelling mechanism due to the complexified stable-unstable manifolds leads to the formation of the plateau structure; in particular, it is shown that the classical action along the complexified stable manifold controls the height of the plateau. The analysis presented here is based on a particular model, but the main claims should hold for any system with multi-dimensional barrier tunnelling because of the universality of the underlying mechanism. [ABSTRACT FROM AUTHOR]