On the ground state of quantum graphs with attractive -coupling

Pavel Exner Michal Jex

TBD mathscidoc:1910.43103

Physics Letters A, 376, (5), 713-717, 2012.1
We study relations between the ground-state energy of a quantum graph Hamiltonian with attractive <i></i> coupling at the vertices and the graph geometry. We derive a necessary and sufficient condition under which the energy increases with the increase of graph edge lengths. We show that this is always the case if the graph has no branchings while both energy increase and decrease are possible for graphs with a more complicated topology.
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@inproceedings{pavel2012on,
  title={On the ground state of quantum graphs with attractive -coupling},
  author={Pavel Exner, and Michal Jex},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020125953301194632},
  booktitle={Physics Letters A},
  volume={376},
  number={5},
  pages={713-717},
  year={2012},
}
Pavel Exner, and Michal Jex. On the ground state of quantum graphs with attractive -coupling. 2012. Vol. 376. In Physics Letters A. pp.713-717. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020125953301194632.
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