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arXiv · 1407.4892

Local description of band rearrangements. Comparison of semi-quantum and full quantum approach

Toshihiro Iwai·Boris Zhilinskii
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Abstract

Rearrangement of rotation-vibration energy bands in isolated molecules within semi-quantum approach is characterized by delta-Chern invariants associated to a local 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 $\pm1$ 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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Toshihiro Iwai, Boris Zhilinskii. 2014-07-18. Local description of band rearrangements. Comparison of semi-quantum and full quantum approach. https://arxiv.org/abs/1407.4892

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