On resonances and bound states of Smilansky Hamiltonian

Pavel Exner Vladimir Lotoreichik Milo Tater

Analysis of PDEs mathscidoc:1910.43195

: , , , 7, (5), 2016
We consider the self-adjoint Smilansky Hamiltonian H in L2 R2) associated with the formal differential expression -x2-1/2(y2+y2)-2y(x) in the sub-critical regime, (0, 1). We demonstrate the existence of resonances for H on a countable subfamily of sheets of the underlying Riemann surface whose distance from the physical sheet is finite. On such sheets, we find resonance free regions and characterize resonances for small > 0. In addition, we refine the previously known results on the bound states of H in the weak coupling regime (0+). In the proofs we use Birman-Schwinger principle for H, elements of spectral theory for Jacobi matrices, and the analytic implicit function theorem.
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@inproceedings{pavel2016on,
  title={On resonances and bound states of Smilansky Hamiltonian},
  author={Pavel Exner, Vladimir Lotoreichik, and Milo Tater},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020132926620619724},
  booktitle={: , , },
  volume={7},
  number={5},
  year={2016},
}
Pavel Exner, Vladimir Lotoreichik, and Milo Tater. On resonances and bound states of Smilansky Hamiltonian. 2016. Vol. 7. In : , , . http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020132926620619724.
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