Stability of the Magnetic Schrödinger Operator in a Waveguide
2005 (English)In: Communications in Partial Differential Equations, ISSN 0360-5302, E-ISSN 1532-4133, Vol. 30, no 4-6, 539-565 p.Article in journal (Refereed) Published
The spectrum of the Schrödinger operator in a quantum waveguide is known to be unstable in two and three dimensions. Any local enlargement of the waveguide produces eigenvalues beneath the continuous spectrum. Also, if the waveguide is bent, eigenvalues will arise below the continuous spectrum. In this paper a magnetic field is added into the system. The spectrum of the magnetic Schrödinger operator is proved to be stable under small local deformations and also under small bending of the waveguide. The proof includes a magnetic Hardy-type inequality in the waveguide, which is interesting in its own right.
Place, publisher, year, edition, pages
2005. Vol. 30, no 4-6, 539-565 p.
hardy inequality, magnetic field, Schrödinger operator
Other Physics Topics
IdentifiersURN: urn:nbn:se:kth:diva-6105DOI: 10.1081/PDE-200050113ISI: 000230842900004ScopusID: 2-s2.0-23444462495OAI: oai:DiVA.org:kth-6105DiVA: diva2:10722
QC 201010072005-09-142005-09-142010-10-07Bibliographically approved