The Laplacian with Complex Magnetic Fields
Abstract
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 noncritical complex magnetic fields, a WKB approach is used to construct semiclassical pseudomodes, which do not exist when the magnetic field is real-valued.
Fields of Study & Subjects
Spectral Theory in Mathematical Physics
Numerical methods in inverse problems
Theoretical and Computational Physics
Publication details
- Journal / source
- SIAM Journal on Mathematical Analysis
- Volume
- 58
- Issue
- 1
- Pages
- 66–91
- Publication date
- 2 January 2026
- Language
- EN