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Quantum Tunneling on Graphs

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Abstract

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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Authors and Affiliations

  1. Department of Mathematics, Information School, Renmin University of China, Beijing, People’s Republic of China

    Yong Lin

  2. Department of Mathematics, Harvard University, Cambridge, MA, 02138, USA

    Gábor Lippner & Shing-Tung Yau

Authors
  1. Yong Lin
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  2. Gábor Lippner
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  3. Shing-Tung Yau
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Correspondence to Gábor Lippner.

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Communicated by S. Zelditch

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Lin, Y., Lippner, G. & Yau, ST. Quantum Tunneling on Graphs. Commun. Math. Phys. 311, 113–132 (2012). https://doi.org/10.1007/s00220-012-1453-8

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  • DOI: https://doi.org/10.1007/s00220-012-1453-8

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