Weighted CLR type bounds in two dimensions
Mathematical Physics
2023-03-13 v1 math.MP
Spectral Theory
Abstract
We derive weighted versions of the Cwikel-Lieb-Rozenblum inequality for the Schr\"odinger operator in two dimensions with a nontrivial Aharonov-Bohm magnetic field. Our bounds capture the optimal dependence on the flux and we identify a class of long-range potentials that saturate our bounds in the strong coupling limit. We also extend our analysis to the two-dimensional Schr\"odinger operator acting on antisymmetric functions and obtain similar results.
Cite
@article{arxiv.2303.06104,
title = {Weighted CLR type bounds in two dimensions},
author = {Rupert L. Frank and Ari Laptev and Larry Read},
journal= {arXiv preprint arXiv:2303.06104},
year = {2023}
}
Comments
16 pages