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Gap control by singular Schr\" odinger operators in a periodically structured metamaterial

Pavel Exner Andrii Khrabustovskyi

Analysis of PDEs mathscidoc:1910.43264

arXiv preprint arXiv:1802.07522, 2018.2
We consider a family \{\mathcal {H}^arepsilon\} _ {arepsilon> 0} of \{\mathcal {H}^arepsilon\} _ {arepsilon> 0} -periodic Schrdinger operators with \{\mathcal {H}^arepsilon\} _ {arepsilon> 0} -interactions supported on a lattice of closed compact surfaces; within a minimal period cell one has \{\mathcal {H}^arepsilon\} _ {arepsilon> 0} surfaces. We show that in the limit when \{\mathcal {H}^arepsilon\} _ {arepsilon> 0} and the interactions strengths are appropriately scaled, \{\mathcal {H}^arepsilon\} _ {arepsilon> 0} has at most \{\mathcal {H}^arepsilon\} _ {arepsilon> 0} gaps within finite intervals, and moreover, the limiting behavior of the first \{\mathcal {H}^arepsilon\} _ {arepsilon> 0} gaps can be completely controlled through a suitable choice of those surfaces and of the interactions strengths.
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@inproceedings{pavel2018gap,
  title={Gap control by singular Schr\" odinger operators in a periodically structured metamaterial},
  author={Pavel Exner, and Andrii Khrabustovskyi},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020135211827032793},
  booktitle={arXiv preprint arXiv:1802.07522},
  year={2018},
}
Pavel Exner, and Andrii Khrabustovskyi. Gap control by singular Schr\" odinger operators in a periodically structured metamaterial. 2018. In arXiv preprint arXiv:1802.07522. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020135211827032793.
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