1998/07/13 by B. Helffer, Bernard Helffer, M. Hoffmann-Ostenhof +4 · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics #math-ph #math.AP #math.DG #math.MP #math.SP #msc:53C21 #msc:58G25
paper · pdf · doi:10.1007/s002200050599
30 pages, 8 figures
arxiv created 1998/07/13 · crossref issued 1999/05/01 · crossref published 1999/05/01 · crossref published-print 1999/05/01 · openalex publication_date 1999/05/01 · crossref created 2002/08/25 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · crossref deposited 2019/05/24 · crossref indexed 2026/04/02 · openalex updated_date 2026/07/28
We investigate nodal sets of magnetic Schroedinger operators with zero magnetic field, acting on a non simply connected domain in \r2. For the case of circulation 1/2 of the magnetic vector potential around each hole in the region, we obtain a charactisation of the nodal set, and use this to obtain bounds on the multiplicity of the groundstate. For the case of one hole and a fixed electric potential, we show that the first eigenvalue takes its highest value for circulation 1/2.