 177 Pavel Exner
 On the spectrum of leaky surfaces with a potential bias
(565K, pdf)
Jan 23, 17

Abstract ,
Paper (src),
View paper
(auto. generated pdf),
Index
of related papers

Abstract. We discuss operators of the type $H = \Delta + V(x)  lpha \delta(x\Sigma)$ with an attractive interaction, $lpha>0$, in $L^2(\mathbb{R}^3)$, where $\Sigma$ is an infinite surface, asymptotically planar and smooth outside a compact, dividing the space into two regions, of which one is supposed to be convex, and $V$ is a potential bias being a positive constant $V_0$ in one of the regions and zero in the other. We find the essential spectrum and ask about the existence of the discrete one with a particular attention to the critical case, $V_0=lpha^2$. We show that $\sigma_\mathrm{disc}(H)$ is then empty if the bias is supported in the `exterior' region, while in the opposite case isolated eigenvalues may exist.
 Files:
177.src(
177.comments ,
177.keywords ,
hhfest.pdf.mm )