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Tunneling resonances in systems without a classical trapping

Denis Borisov Pavel Exner Anastasia Golovina

TBD mathscidoc:1910.43153

Journal of Mathematical Physics, 54, (1), 012102, 2013.1
In this paper, we analyze a free quantum particle in a straight Dirichlet waveguide which has at its axis two Dirichlet barriers of lengths separated by a window of length 2a. It is known that if the barriers are semi-infinite, i.e., we have two adjacent waveguides coupled laterally through the boundary window, the system has for any a > 0 a finite number of eigenvalues below the essential spectrum threshold. Here, we demonstrate that for large but finite the system has resonances which converge to the said eigenvalues as , and derive the leading term in the corresponding asymptotic expansion.
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@inproceedings{denis2013tunneling,
  title={Tunneling resonances in systems without a classical trapping},
  author={Denis Borisov, Pavel Exner, and Anastasia Golovina},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020131639694599682},
  booktitle={Journal of Mathematical Physics},
  volume={54},
  number={1},
  pages={012102},
  year={2013},
}
Denis Borisov, Pavel Exner, and Anastasia Golovina. Tunneling resonances in systems without a classical trapping. 2013. Vol. 54. In Journal of Mathematical Physics. pp.012102. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020131639694599682.
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