Waveguides coupled through a semitransparent barrier: a BirmanSchwinger analysis

Pavel Exner D Krejik

TBD mathscidoc:1910.43145

Reviews in Mathematical Physics, 13, (3), 307-334, 2001.3
The paper is devoted to a model of a mesoscopic system consisting of a pair of parallel planar waveguides separated by an infinitely thin semitransparent boundary modeled by a transverse interaction. We develop the BirmanSchwinger theory for the corresponding generalized Schrdinger operator. The spectral properties become nontrivial if the barrier coupling is not invariant with respect to longitudinal translations, in particular, there are bound states if the barrier is locally more transparent in the mean and the coupling parameter reaches the same asymptotic value in both directions along the guide axis. We derive the weak-coupling expansion of the ground-state eigenvalue for the cases when the perturbation is small in the supremum and the <b>L</b><sup>1</sup>-norms. The last named result applies to the situation when the support of the leaky part shrinks: the obtained asymptotics differs from that of a double guide divided
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  title={Waveguides coupled through a semitransparent barrier: a BirmanSchwinger analysis},
  author={Pavel Exner, and D Krejik},
  booktitle={Reviews in Mathematical Physics},
Pavel Exner, and D Krejik. Waveguides coupled through a semitransparent barrier: a BirmanSchwinger analysis. 2001. Vol. 13. In Reviews in Mathematical Physics. pp.307-334. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020131420816435674.
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