Spectral theory for Schrödinger operators with $\delta$-interactions supported on curves in ${\mathbb{R}}^3$

Abstract

The main objective of this paper is to systematically develop a spectral and scattering theory for selfadjoint Schrödinger operators with $\delta$-interactions supported on closed curves in ${\mathbb{R}}^3$. We provide bounds for the number of negative eigenvalues depending on the geometry of the curve, prove an isoperimetric inequality for the principal eigenvalue, derive Schatten--von Neumann properties for the resolvent difference with the free Laplacian, and establish an explicit representation for the scattering matrix.

to appear in Annales Henri Poincare

References in corpus (3)

• Spectra of self-adjoint extensions and applications to solvable Schroedinger operators
• Schrödinger operators with delta and delta'-potentials supported on hypersurfaces
• Absolute continuity in periodic thin tubes and strongly coupled leaky wires

Cited by in corpus (4)

• On Nelson-type Hamiltonians and abstract boundary conditions
• The point-interaction approximation for the fields generated by contrasted bubbles at arbitrary fixed frequencies
• Asymptotics of the bound state induced by $\delta$-interaction supported on a weakly deformed plane
• A non-degeneracy theorem for interacting fermions in one dimension