Speed-of-light pulses in the massless nonlinear Dirac equation with a potential
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2017
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866911256335613952 |
|---|---|
| author | Quintero, Niurka R. Mertens, Franz G. Cooper, Fred Saxena, Avadh Bishop, A. R. |
| author_facet | Quintero, Niurka R. Mertens, Franz G. Cooper, Fred Saxena, Avadh Bishop, A. R. |
| contents | We consider the massless nonlinear Dirac (NLD) equation in $1+1$ dimension with scalar-scalar self-interaction $\frac{g^2}{2} (\barΨ Ψ)^2$ in the presence of three external electromagnetic potentials $V(x)$, a potential barrier, a constant potential, and a potential well. By solving numerically the NLD equation, we find that, for all three cases, after a short transit time, the initial pulse breaks into two pulses which are solutions of the massless linear Dirac equation traveling in opposite directions with the speed of light. During this splitting the charge and the energy are conserved, whereas the momentum is conserved when the solutions possess specific symmetries. For the case of the constant potential, we derive exact analytical solutions of the massless NLD equation that are also solutions of the massless linearized Dirac equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1705_11037 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Speed-of-light pulses in the massless nonlinear Dirac equation with a potential Quintero, Niurka R. Mertens, Franz G. Cooper, Fred Saxena, Avadh Bishop, A. R. Pattern Formation and Solitons Mathematical Physics We consider the massless nonlinear Dirac (NLD) equation in $1+1$ dimension with scalar-scalar self-interaction $\frac{g^2}{2} (\barΨ Ψ)^2$ in the presence of three external electromagnetic potentials $V(x)$, a potential barrier, a constant potential, and a potential well. By solving numerically the NLD equation, we find that, for all three cases, after a short transit time, the initial pulse breaks into two pulses which are solutions of the massless linear Dirac equation traveling in opposite directions with the speed of light. During this splitting the charge and the energy are conserved, whereas the momentum is conserved when the solutions possess specific symmetries. For the case of the constant potential, we derive exact analytical solutions of the massless NLD equation that are also solutions of the massless linearized Dirac equation. |
| title | Speed-of-light pulses in the massless nonlinear Dirac equation with a potential |
| topic | Pattern Formation and Solitons Mathematical Physics |
| url | https://arxiv.org/abs/1705.11037 |