Fermions on wobbling kinks: normal versus quasinormal modes
Abstract The system consisting of a fermion in the background of a wobbling kink is studied in this paper. To investigate the impact of the wobbling on the fermion-kink interaction, we employ the time-dependent perturbation theory formalism in quantum mechanics. To do so, we compute the transition p...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2021-09-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP09(2021)103 |
| _version_ | 1818902297076301824 |
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| author | João G. F. Campos Azadeh Mohammadi |
| author_facet | João G. F. Campos Azadeh Mohammadi |
| author_sort | João G. F. Campos |
| collection | DOAJ |
| description | Abstract The system consisting of a fermion in the background of a wobbling kink is studied in this paper. To investigate the impact of the wobbling on the fermion-kink interaction, we employ the time-dependent perturbation theory formalism in quantum mechanics. To do so, we compute the transition probabilities between states given in terms of the Bogoliubov coefficients. We derive Fermi’s golden rule for the model, which allows the transition to the continuum at a constant rate if the fermion-kink coupling constant is smaller than the wobbling frequency. Moreover, we study the system replacing the shape mode with a quasinormal mode. In this case, the transition rate to continuum decays in time due to the leakage of the mode, and the final transition probability decreases sharply for large coupling constants in a way that is analogous to Fermi’s golden rule. Throughout the paper, we compare the perturbative results with numerical simulations and show that they are in good agreement. |
| first_indexed | 2024-12-19T20:33:24Z |
| format | Article |
| id | doaj.art-f7487d3c4eab4607a8b9b34f1a86c39f |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-19T20:33:24Z |
| publishDate | 2021-09-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-f7487d3c4eab4607a8b9b34f1a86c39f2022-12-21T20:06:38ZengSpringerOpenJournal of High Energy Physics1029-84792021-09-012021911910.1007/JHEP09(2021)103Fermions on wobbling kinks: normal versus quasinormal modesJoão G. F. Campos0Azadeh Mohammadi1Departamento de Física, Universidade Federal de PernambucoDepartamento de Física, Universidade Federal de PernambucoAbstract The system consisting of a fermion in the background of a wobbling kink is studied in this paper. To investigate the impact of the wobbling on the fermion-kink interaction, we employ the time-dependent perturbation theory formalism in quantum mechanics. To do so, we compute the transition probabilities between states given in terms of the Bogoliubov coefficients. We derive Fermi’s golden rule for the model, which allows the transition to the continuum at a constant rate if the fermion-kink coupling constant is smaller than the wobbling frequency. Moreover, we study the system replacing the shape mode with a quasinormal mode. In this case, the transition rate to continuum decays in time due to the leakage of the mode, and the final transition probability decreases sharply for large coupling constants in a way that is analogous to Fermi’s golden rule. Throughout the paper, we compare the perturbative results with numerical simulations and show that they are in good agreement.https://doi.org/10.1007/JHEP09(2021)103Solitons Monopoles and InstantonsField Theories in Lower Dimensions |
| spellingShingle | João G. F. Campos Azadeh Mohammadi Fermions on wobbling kinks: normal versus quasinormal modes Journal of High Energy Physics Solitons Monopoles and Instantons Field Theories in Lower Dimensions |
| title | Fermions on wobbling kinks: normal versus quasinormal modes |
| title_full | Fermions on wobbling kinks: normal versus quasinormal modes |
| title_fullStr | Fermions on wobbling kinks: normal versus quasinormal modes |
| title_full_unstemmed | Fermions on wobbling kinks: normal versus quasinormal modes |
| title_short | Fermions on wobbling kinks: normal versus quasinormal modes |
| title_sort | fermions on wobbling kinks normal versus quasinormal modes |
| topic | Solitons Monopoles and Instantons Field Theories in Lower Dimensions |
| url | https://doi.org/10.1007/JHEP09(2021)103 |
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