Twisted waveguide with a Neumann window

Philippe Briet (1) , Hiba Hammedi (1)

1 CPT - Centre de Physique Théorique - UMR 7332

This paper is concerned with the study of the existence/non-existence of the discrete spectrum of the Laplace operator on a domain of $\mathbb R ^3$ which consists in a twisted tube. This operator is defined by means of mixed boundary conditions. Here we impose Neumann Boundary conditions on a bounded open subset of the boundary of the domain (the Neumann window) and Dirichlet boundary conditions elsewhere.

Mots clés: mixed boundary conditions; twisting; waveguide

Domaines: Théorie spectrale [math.SP]; Physique mathématique [math-ph]

Philippe Briet, Hiba Hammedi. Twisted waveguide with a Neumann window. 2016. ⟨hal-01264262v2⟩