14 citations · 27 across the 2 of their papers we have counts for
2 papers
math-ph2011★ 14 cited
Trapped modes in finite quantum waveguides
Andrey L. Delitsyn, Binh-Thanh Nguyen, Denis S. Grebenkov
The Laplace operator in infinite quantum waveguides (e.g., a bent strip or a twisted tube) often has a point-like eigenvalue below the essential spectrum that corresponds to a trap…
math-ph2011★ 13 cited
Exponential decay of Laplacian eigenfunctions in domains with branches
Andrey Delitsyn, Binh-Thanh Nguyen, Denis S. Grebenkov
The behavior of Laplacian eigenfunctions in domains with branches is investigated. If an eigenvalue is below a threshold which is determined by the shape of the branch, the associa…