Spectrum of the Magnetic Schrodinger Operator in a Waveguide with Combined Boundary Conditions

Details Spectrum of the Magnetic Schrodinger Operator in a Waveguide with Combined Boundary Conditions Spectrum of the Magnetic Schrodinger Operator in a Waveguide with Combined Boundary Conditions

2004-05-11

arxiv.org/abs/math-ph/0405034v3

Annales Henri Poincare. 2005. V. 6. No. 2. P. 327-342.

Physics

Mathematical Physics

Scientific paper

10.1007/s00023-005-0209-9

We consider the magnetic Schrodinger operator in a two-dimensional strip. On the boundary of the strip the Dirichlet boundary condition is imposed except for a fixed segment (window), where it switches to magnetic Neumann boundary condition (see Section 2, Eq. (2.2) for the definition of this boundary condition}. We deal with a smooth compactly supported field as well as with the Aharonov-Bohm field. We give an estimate on the maximal length of the window, for which the discrete spectrum of the considered operator will be empty. In the case of a compactly supported field we also give a sufficient condition for the presence of eigenvalues below the essential spectrum.

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