Quantum Cellular Automaton Model for the Generalized Dirac Equation
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2016
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866915529080438784 |
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| author | Song, Xingyou |
| author_facet | Song, Xingyou |
| contents | This study presents a unitary quantum cellular automaton (QCA) that, in the continuum limit, converges to the (1+1)-dimensional Generalized Dirac Equation (GDE). We outline the construction of the unitary, discrete-time evolution and derive the model's exact dispersion relation from its eigenvalue spectrum, showing it possesses the correct relativistic limit. We then explore its dynamics through numerical simulations. While the total probability density is shown to be insensitive to the chiral angle parameter $(ρ)$ of the GDE, we demonstrate that this parameter has a profound and directly observable effect on the particle's local spin polarization. By measuring this quantity, we reveal the hidden internal dynamics of the spinor, providing a clear, visual confirmation of the physical consequences of the chiral mass term. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1610_02425 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | Quantum Cellular Automaton Model for the Generalized Dirac Equation Song, Xingyou Quantum Physics This study presents a unitary quantum cellular automaton (QCA) that, in the continuum limit, converges to the (1+1)-dimensional Generalized Dirac Equation (GDE). We outline the construction of the unitary, discrete-time evolution and derive the model's exact dispersion relation from its eigenvalue spectrum, showing it possesses the correct relativistic limit. We then explore its dynamics through numerical simulations. While the total probability density is shown to be insensitive to the chiral angle parameter $(ρ)$ of the GDE, we demonstrate that this parameter has a profound and directly observable effect on the particle's local spin polarization. By measuring this quantity, we reveal the hidden internal dynamics of the spinor, providing a clear, visual confirmation of the physical consequences of the chiral mass term. |
| title | Quantum Cellular Automaton Model for the Generalized Dirac Equation |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/1610.02425 |