The Laplacian with complex magnetic fields
Mathematical Physics
2025-09-18 v2 Functional Analysis
math.MP
Spectral Theory
Abstract
We study the two-dimensional magnetic Laplacian when the magnetic field is allowed to be complex-valued. Under the assumption that the imaginary part of the magnetic potential is relatively form-bounded with respect to the real part of the magnetic Laplacian, we introduce the operator as an m-sectorial operator. In two dimensions, sufficient conditions are established to guarantee that the resolvent is compact. In the case of non-critical complex magnetic fields, a WKB approach is used to construct semiclassical pseudomodes, which do not exist when the magnetic field is real-valued.
Cite
@article{arxiv.2410.01377,
title = {The Laplacian with complex magnetic fields},
author = {David Krejcirik and Tho Nguyen Duc and Nicolas Raymond},
journal= {arXiv preprint arXiv:2410.01377},
year = {2025}
}
Comments
Dedicated to Jussi Behrndt on the occasion of his 50th birthday