Complex WKB method for 3‐level scattering systems

Article type: Research Article

Authors: Joye, Alain | Pfister, Charles‐Edouard

Affiliations: Institut Fourier, Université de Grenoble‐1, BP 74, F‐38402 Saint‐Martin d’Hères Cedex, France E‐mail: joye@fourier.ujf‐grenoble.fr | Département de Mathématiques, Ecole Polytechnique Fédérale de Lausanne, CH‐1015 Lausanne, Switzerland E‐mail: cpfister@eldp.epfl.ch

Abstract: In this note the S‐matrix naturally associated with a singularly perturbed three‐dimensional system of linear differential equations without turning point on the real axis is considered. 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.

Keywords: Singular perturbations, semiclassical analysis, adiabatic approximations, exponential asymptotics, [TeX:] n‐level [TeX:] S‐matrix, turning point theory

Journal: Asymptotic Analysis, vol. 23, no. 2, pp. 91-109, 2000