Resolvent expansions and continuity of the scattering matrix at embedded thresholds: the case of quantum waveguides

Serge Richard (1) , Rafael Tiedra de Aldecoa (2)

1 PSPM - Probabilités, statistique, physique mathématique
2 Facultad de Matemáticas [Santiago de Chile]

We present an inversion formula which can be used to obtain resolvent expansions near embedded thresholds. As an application, we prove for a class of quantum waveguides the absence of accumulation of eigenvalues and the continuity of the scattering matrix at all thresholds.

Mots clés: scattering matrix; quantum waveguides.; quantum waveguides; Thresholds; resolvent expansions

Domaines: Physique mathématique [math-ph]

Serge Richard, Rafael Tiedra de Aldecoa. Resolvent expansions and continuity of the scattering matrix at embedded thresholds: the case of quantum waveguides. Bulletin de la société mathématique de France, 2016, 144 (2), pp.251-277. ⟨hal-00941136⟩