Weakly coupled bound states in quantum waveguides
Weakly coupled bound states in quantum waveguides
We study the eigenvalue spectrum of Dirichlet Laplacians which model quantum waveguides associated with tubular regions outside of a bounded domain. Intuitively, our principal new result in two dimensions asserts that any domain $\Omega$ obtained by adding an arbitrarily small "bump" to the tube $\Omega _{0}=\mathbb {R}\times (0,1)$ (i.e., $\Omega …