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Local Description of Band Rearrangements

Comparison of Semi-quantum and Full Quantum Approach

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Abstract

Rearrangement of rotation-vibration energy bands in isolated molecules within semi-quantum approach is characterized by delta-Chern invariants, each of which is associated to a locally approximated semi-quantum Hamiltonian valid in a small neighborhood of a degeneracy point for the initial semi-quantum Hamiltonian and also valid in a small neighborhood of a critical point corresponding to the crossing of the boundary between iso-Chern domains in the control parameter space. For a full quantum model, a locally approximated Hamiltonian is assumed to take the form of a Dirac operator together with a specific boundary condition. It is demonstrated that the crossing of the boundary along a path with a delta-Chern invariant equal to ±1 corresponds to the transfer of one quantum level from a subspaces of quantum states to the other subspace associated with respective positive and negative energy eigenvalues of the local Dirac Hamiltonian.

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Acknowledgements

The authors would like to thank Dr. G. Dhont for drawing graphs of eigenvalues as functions of the control parameter.

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Authors and Affiliations

  1. Kyoto University, 606-8501, Kyoto, Japan

    Toshihiro Iwai

  2. Université du Littoral Côte d’Opale, 189A av. M. Schumann, Dunkerque, 59140, France

    Boris Zhilinskii

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  1. Toshihiro Iwai
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  2. Boris Zhilinskii
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Correspondence to Boris Zhilinskii.

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Iwai, T., Zhilinskii, B. Local Description of Band Rearrangements. Acta Appl Math 137, 97–121 (2015). https://doi.org/10.1007/s10440-014-9992-y

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  • DOI: https://doi.org/10.1007/s10440-014-9992-y

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