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

• URL: http://arxiv.org/abs/2006.03877v1
• Date: Sat, 6 Jun 2020 14:27:41 GMT
• Title: Magnetic field influence on the discrete spectrum of locally deformed leaky wires
• Authors: Diana Barseghyan and Pavel Exner
• Abstract summary: We consider magnetic Schr"odinger operator $H=(i nabla +A)2-alpha delta_Gamma$ with an attractive singular interaction. We show that the essential spectrum is $[-frac14alpha2,infty)$, as for the non-magnetic operator with a straight $Gamma$.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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