Exponential decay of Laplacian eigenfunctions in domains with branches
Mathematical Physics
2020-01-03 v1 math.MP
Computational Physics
Quantum Physics
Abstract
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 associated eigenfunction is proved to exponentially decay inside the branch. The decay rate is twice the square root of the difference between the threshold and the eigenvalue. The derived exponential estimate is applicable for arbitrary domains in any spatial dimension. Numerical simulations illustrate and further extend the theoretical estimate.
Keywords
Cite
@article{arxiv.1109.3408,
title = {Exponential decay of Laplacian eigenfunctions in domains with branches},
author = {Andrey Delitsyn and Binh-Thanh Nguyen and Denis S. Grebenkov},
journal= {arXiv preprint arXiv:1109.3408},
year = {2020}
}