04-134 Tomas Ekholm nad Hynek Kovarik

Stability of the magnetic Schr dinger operator in a waveguide (76K, LaTeX 2e ) Apr 28, 04

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Abstract. The spectrum of the Sch dinger operator in a quantum waveguide is known to be unstable in two and three dimensions. Any 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 Schr dinger 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.

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