### Abstract

We consider the dislocation problem for the Dirac operator with a periodic potential on the real line. The dislocation is parameterized by a real parameter. For each parameter value, the absolutely continuous spectrum has a band structure and there are open gaps between spectral bands. We show that in each open gap there exist exactly two distinct 'states' (eigenvalues or resonances) of the dislocated operator, such that they runs clockwise around the gap. These states are separated from each other by the Dirichlet eigenvalue and they make half as many revolutions as the Dirichlet eigenvalue does in unit time. We find asymptotic of this motion for the cases when a state is near the gaps boundary and collides with the Dirichlet eigenvalue.

Original language | English |
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Title of host publication | Proceedings of the International Conference on Days on Diffraction 2019, DD 2019 |

Editors | Oleg V. Motygin, Aleksei P. Kiselev, Leonid I. Goray, A.A. Fedotov, A.Ya. Kazakov, Anna S. Kirpichnikova |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 94-98 |

Number of pages | 5 |

ISBN (Electronic) | 9781728158372 |

DOIs | |

Publication status | Published - Jun 2019 |

Event | 2019 International Conference on Days on Diffraction, DD 2019 - St. Petersburg Duration: 3 Jun 2019 → 7 Jun 2019 |

### Publication series

Name | Proceedings of the International Conference on Days on Diffraction 2019, DD 2019 |
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### Conference

Conference | 2019 International Conference on Days on Diffraction, DD 2019 |
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Country | Russian Federation |

City | St. Petersburg |

Period | 3/06/19 → 7/06/19 |

### Scopus subject areas

- Computational Mathematics
- Mathematical Physics
- Acoustics and Ultrasonics
- Atomic and Molecular Physics, and Optics
- Radiation

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## Cite this

*Proceedings of the International Conference on Days on Diffraction 2019, DD 2019*(pp. 94-98). [9016424] (Proceedings of the International Conference on Days on Diffraction 2019, DD 2019). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/DD46733.2019.9016424