Nodal sets for the groundstate of the Schroedinger operator with zero magnetic field in a non simply connected domain
Helffer, B. ; Hoffmann-Ostenhof, M. ; Hoffmann-Ostenhof, T. ; Owen, M. P.
arXiv, 9807064 / Harvested from arXiv
Text on arXiv
We investigate nodal sets of magnetic Schroedinger operators with zero magnetic field, acting on a non simply connected domain in $\r^2$. 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.
Publié le : 1998-07-13
Classification:  Mathematics - Spectral Theory,  Mathematical Physics,  Mathematics - Analysis of PDEs,  Mathematics - Differential Geometry,  58G25,  53C21 
@article{9807064,
     author = {Helffer, B. and Hoffmann-Ostenhof, M. and Hoffmann-Ostenhof, T. and Owen, M. P.},
     title = {Nodal sets for the groundstate of the Schroedinger operator with zero
  magnetic field in a non simply connected domain},
     journal = {arXiv},
     volume = {1998},
     number = {0},
     year = {1998},
     language = {en},
     url = {http://dml.mathdoc.fr/item/9807064}
}

Helffer, B.; Hoffmann-Ostenhof, M.; Hoffmann-Ostenhof, T.; Owen, M. P. Nodal sets for the groundstate of the Schroedinger operator with zero
  magnetic field in a non simply connected domain. arXiv, Tome 1998 (1998) no. 0, . http://gdmltest.u-ga.fr/item/9807064/