Stokes Phenomenon in Chaotic Systems: Pruning Trees of Complex Paths with Principle of Exponential Dominance

Abstract

Stokes phenomenon is investigated in the complex semiclassical theory of chaotic tunneling, and a rule for locating contributing complex paths out of a complicated set of candidates is proposed. The proposal is based upon discovery of a tree structure hidden in entangled tunneling paths: The candidates are ordered along the tree, and the principle of exponential dominance (PED) is extended to prune noncontributing paths. This rule enables construction of semiclassical tunneling wave functions systematically. A phenomenon for which PED plays a crucial role is also demonstrated.