Interacting double-state scattering system

Article type: Research Article

Authors: Abdelmoumen, Boulbeba^a | Baklouti, Hamadi^{a; *} | Abdeljeilil, Slaheddine Ben^b

Affiliations: [a] Sfax University, Tunisia | [b] ElManar University, Tunisia

Correspondence: [*] Corresponding author. E-mail: h.baklouti@gmail.com.

Abstract: In this paper, we describe the asymptotic behavior of the scattering matrix S associated with the 2×2 matrix Schrödinger operator P=−h2d2dx2I2+V(x)+hR(x,hDx) on L2(R)⊕L2(R). We study the situation where the diagonal terms of V cross on the real axis. In particular it is proven that, due to the real crossing, the off-diagonal terms of S are no longer exponentially small with respect to the semi-classical parameter h.

Keywords: Scattering theory, Schrödinger operator, Airy equation, microlocal analysis

DOI: 10.3233/ASY-181485

Journal: Asymptotic Analysis, vol. 111, no. 1, pp. 15-42, 2019