Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9518069 | Advances in Mathematics | 2005 | 40 Pages |
Abstract
The analyses of compactness and condition (P) boil down to the asymptotic behavior of the lowest eigenvalues of two related sequences of Schrödinger operators, one with a magnetic field and one without, parametrized by a Fourier variable resulting from the Hartogs symmetry. The nonsmooth example is based on the Aharonov-Bohm phenomenon of quantum physics. For smooth domains not satisfying (P), we prove that there always exists an exceptional sequence of Fourier variables for which the Aharonov-Bohm effect is weak and thence that compactness fails to hold. This sequence can be very sparse, so that the lack of compactness is due to a rather subtle effect.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Michael Christ, Siqi Fu,