A note on the spectrum of the Neumann Laplacian in periodic waveguides

2016/06/14 by Alessandra A. Verri, Verri, Alessandra A., Carlos R. Mamani +1
Computer Science · Materials Science · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Physical sciences #Mathematical Physics (math-ph) #Quasicrystal Structures and Properties #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1606.04513

openalex publication_date 2016/06/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the Neumann Laplacian -Δ^N restricted to a periodic waveguide. In this situation its spectrum σ(-Δ^N) presents a band structure. Our goal and strategy is to get spectral information from an analysis of the asymptotic behavior of these bands provided that the waveguide is sufficiently thin.

Related

• Influence of the bound states in the Neumann Laplacian in a thin waveguide
• Example of periodic Neumann waveguide with gap in spectrum
• Absolute continuity and band gaps of the spectrum of the Dirichlet Laplacian in periodic waveguides
• Spectrum of a singularly perturbed periodic thin waveguide
• Spectrum of the Dirichlet Laplacian in waveguides with parallel cross-sections