Magnetic field influence on the discrete spectrum of locally deformed leaky wires

Diana Barseghyan; Pavel Exner

doi:10.1016/s0034-4877(21)00055-0

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arXiv · 2006.03877

Magnetic field influence on the discrete spectrum of locally deformed leaky wires

Diana Barseghyan·Pavel Exner

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Abstract

We consider magnetic Schr\"odinger operator $H=(i \nabla +A)^2-\alpha \delta_\Gamma$ with an attractive singular interaction supported by a piecewise smooth curve $\Gamma$ being a local deformation of a straight line. The magnetic field $B$ is supposed to be nonzero and local. We show that the essential spectrum is $[-\frac14\alpha^2,\infty)$, as for the non-magnetic operator with a straight $\Gamma$, and demonstrate a sufficient condition for the discrete spectrum of $H$ to be empty.

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BibTeX RIS

Diana Barseghyan, Pavel Exner. 2020-06-06. Magnetic field influence on the discrete spectrum of locally deformed leaky wires. https://doi.org/10.1016/s0034-4877(21)00055-0

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