Weak Nonintegrability and Strongly Directional Tunnel Escape

It is no surprise that emission from optical cavities and other wave problems is a nontrivial problem when the underlying ray dynamics shows a mixture of chaotic and integrable behaviour. It is perhaps more surprising that emission from weakly nonintegrable problems can also be nontrivial (as described for example by Lacey, et al., Phys. Rev. Lett. 91, 033902 (2003)). We outline a calculation based on an application of canonical perturbation theory to complex phase space which can quantitatively explain strong directionality of emission from weakly deformed spherical systems. In a ray-dynamics picture, this directionality is related to a symmetry-breaking in the complex manifold of rays obtained by extending the invariant tori to the forbidden regions