Exact sum rules for quantum billiards of arbitrary shape
Mathematical Physics
2017-12-06 v1 math.MP
Abstract
We have derived explicit expressions for the sum rules of order one of the eigenvalues of the negative Laplacian on two dimensional domains of arbitrary shape. Taking into account the leading asymptotic behavior of these eigenvalues, as given from Weyl's law, we show that it is possible to define sum rules that are finite, using different prescriptions. We provide the explicit expressions and test them on a number of non trivial examples, comparing the exact results with precise numerical results.
Cite
@article{arxiv.1707.06574,
title = {Exact sum rules for quantum billiards of arbitrary shape},
author = {Paolo Amore},
journal= {arXiv preprint arXiv:1707.06574},
year = {2017}
}
Comments
19 pages, 2 tables