Alain Joye, Charles-Edouard Pfister
Complex WKB Method for 3-Level Scattering Systems
(88K, Latex)

ABSTRACT.  In this note, recent developements of the Complex WKB method 
allowing to compute the $S$-matrix naturally associated with a 
singularly perturbed three-dimensional system of linear differential 
equations without turning point on the real axis are reviewed. It is 
shown that for a fairly large class of examples, the complex WKB 
method gives results far better than what is proven under generic 
circumstances. In particular, we show how to compute asymptotically 
all exponentially small off-diagonal elements of the corresponding 
$S$-matrix.