Spectrum of Dirichlet Laplacian in a conical layer

Abstract

We study spectral properties of Dirichlet Laplacian on the conical layer of the opening angle $\pi -2\theta$ and thickness equal to $\pi$. We demonstrate that below the continuum threshold which is equal to one there is an infinite sequence of isolated eigenvalues and analyze properties of these geometrically induced bound states. By numerical computation we find examples of the eigenfunctions.

With some improvements and a broader range of numerical results, to appear in J. Phys. A: Math. Theor

References in corpus (3)

• Bound States in Curved Quantum Layers
• Topologically non-trivial quantum layers
• Bound States in Mildly Curved Layers

Cited by in corpus (13)

• Little Magnetic Book
• Plane waveguides with corners in the small angle limit
• Quantum waveguides with corners
• Dirichlet spectrum of the Fichera layer
• On the discrete spectrum of Robin Laplacians in conical domains
• Discrete spectrum of interactions concentrated near conical surfaces
• Spectral asymptotics of the Dirichlet Laplacian in a conical layer
• Eigenvalue counting function for Robin Laplacians on conical domains
• Spectral properties of soft quantum waveguides
• Attractive conical surfaces create infinitely many bound states
• Dirac operator spectrum in tubes and layers with a zigzag type boundary
• Spectral asymptotics for $\delta$-interactions on sharp cones
• Existence of the discrete spectrum in the Fichera layers and crosses of arbitrary dimension