Diana Barseghyan and Pavel Exner
Magnetic field influence on the discrete spectrum of locally deformed leaky wires
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ABSTRACT. We consider magnetic Schr\"odinger operator $H=(i
abla +A)^2-lpha \delta_\Gamma$ 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 $[-rac14lpha^2,\infty)$, as for the non-magnetic operator with a straight $\Gamma$, and demonstrate a sufficient condition for the discrete spectrum of $H$ to be empty.