Twisted waveguide with a Neumann window

Philippe Briet (1, 2) , Hiba Hammedi (1, 2)

1 CPT - E8 Dynamique quantique et analyse spectrale
2 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; waveguide; twisting

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

Philippe Briet, Hiba Hammedi. Twisted waveguide with a Neumann window. Functional Analysis and Operator Theory for Quantum Physics : The Pavel Exner Anniversary Volume, European Mathematical Society, pp.161-175, 2017, EMS Series of Congress Reports, 978-3-03719-175-0. ⟨10.4171/175-1/8⟩. ⟨hal-01264262v3⟩