Resonances and resonance expansions for point interactions on the half-space

2024/10/16 by Diego Noja, Noja, Diego, Francesco Raso Stoia +1
Mathematics · Physics and Astronomy · #35P25 #47A40 #58J50 #81U15 #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2410.12998

openalex publication_date 2024/10/16 · openalex created_date 2024/10/20 · openalex updated_date 2026/07/28

Abstract

In this paper we describe the resonances of the singular perturbation of the Laplacian on the half space Ω=\mathbb R³₊ given by the self-adjoint operator named δ-interaction. We will assume Dirichlet or Neumann boundary conditions on ∂ Ω. At variance with the well known case of \mathbb R³, the resonances constitute an infinite set, here completely characterized. Moreover, we prove that resonances have an asymptotic distribution satisfying a modified Weyl law and we give the semiclassical asymptotics. Finally we give applications of the results to the asymptotic behavior of the abstract wave and Schrödinger dynamics generated by the Laplacian with a point interaction on the half-space

Related

• The Schrödinger particle on the half-line with an attractive δ-interaction: bound states and resonances
• Resonances for 1D half-line periodic operators: II. Special case
• Resonances for 1D half-line periodic operators: I. Generic case
• Resonance Point Interactions
• Weyl law for semi-classical resonances with randomly perturbed potentials