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Quantum tunneling on graphs

Yong Lin Department of Mathematics, Information School, Renmin University of China, Beijing, People’s Republic of China Gábor Lippner Department of Mathematics, Harvard University, Cambridge, MA, 02138, USA Shing-Tung Yau Department of Mathematics, Harvard University, Cambridge, MA, 02138, USA

Combinatorics Mathematical Physics mathscidoc:2207.06002

Communications in Mathematical Physics, 311, 113–132, 2012.2
We explore the tunneling behavior of a quantum particle on a finite graph in the presence of an asymptotically large potential with two or three potential wells. The behavior of the particle is primarily governed by the local spectral symmetry of the graph around the wells. In the case of two wells the behavior is stable in the sense that it can be predicted from a sufficiently large neighborhood of the wells. However in the case of three wells we are able to exhibit examples where the tunneling behavior can be changed significantly by perturbing the graph arbitrarily far from the wells.
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@inproceedings{yong2012quantum,
  title={Quantum tunneling on graphs},
  author={Yong Lin, Gábor Lippner, and Shing-Tung Yau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220707115036668860553},
  booktitle={Communications in Mathematical Physics},
  volume={311},
  pages={113–132},
  year={2012},
}
Yong Lin, Gábor Lippner, and Shing-Tung Yau. Quantum tunneling on graphs. 2012. Vol. 311. In Communications in Mathematical Physics. pp.113–132. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220707115036668860553.
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