 1538 Pavel Exner, Semjon Vugalter
 On the existence of bound states in asymmetric leaky wires}
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May 10, 15

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Abstract. We analyze spectral properties of a leaky wire model with a potential bias. It describes a twodimensional quantum particle exposed to a potential consisting of two parts. One is an attractive $\delta$interaction supported by a nonstraight, piecewise smooth curve $\LL$ dividing the plane into two regions of which one, the `interior', is convex. The other interaction component is a constant positive potential $V_0$ in one of the regions. We show that in the critical case, $V_0=lpha^2$, the discrete spectrum is nonvoid if and only if the bias is supported in the interior. We also analyze the noncritical situations, in particular, we show that in the subcritical case, $V_0<lpha^2$, the system may have any finite number of bound states provided the angle between the asymptotes of $\LL$ is small enough.
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