Electromagnetic lattice gauge invariance in two-dimensional discrete-time quantum walks
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2018
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| Acceso en línea: | |
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| _version_ | 1866916632115281920 |
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| author | Márquez-Mártin, Iván Arnault, Pablo Di Molfetta, Giuseppe Pérez, Armando |
| author_facet | Márquez-Mártin, Iván Arnault, Pablo Di Molfetta, Giuseppe Pérez, Armando |
| contents | Gauge invariance is one of the more important concepts in physics. We discuss this concept in connection with the unitary evolution of discrete-time quantum walks in one and two spatial dimensions, when they include the interaction with synthetic, external electromagnetic fields. One introduces this interaction as additional phases that play the role of gauge fields. Here, we present a way to incorporate those phases, which differs from previous works. Our proposal allows the discrete derivatives, that appear under a gauge transformation, to treat time and space on the same footing, in a way which is similar to standard lattice gauge theories. By considering two steps of the evolution, we define a density current which is gauge invariant and conserved. In the continuum limit, the dynamics of the particle, under a suitable choice of the parameters, becomes the Dirac equation, and the conserved current satisfies the corresponding conservation equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1808_04488 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Electromagnetic lattice gauge invariance in two-dimensional discrete-time quantum walks Márquez-Mártin, Iván Arnault, Pablo Di Molfetta, Giuseppe Pérez, Armando Quantum Physics Other Condensed Matter High Energy Physics - Lattice Gauge invariance is one of the more important concepts in physics. We discuss this concept in connection with the unitary evolution of discrete-time quantum walks in one and two spatial dimensions, when they include the interaction with synthetic, external electromagnetic fields. One introduces this interaction as additional phases that play the role of gauge fields. Here, we present a way to incorporate those phases, which differs from previous works. Our proposal allows the discrete derivatives, that appear under a gauge transformation, to treat time and space on the same footing, in a way which is similar to standard lattice gauge theories. By considering two steps of the evolution, we define a density current which is gauge invariant and conserved. In the continuum limit, the dynamics of the particle, under a suitable choice of the parameters, becomes the Dirac equation, and the conserved current satisfies the corresponding conservation equation. |
| title | Electromagnetic lattice gauge invariance in two-dimensional discrete-time quantum walks |
| topic | Quantum Physics Other Condensed Matter High Energy Physics - Lattice |
| url | https://arxiv.org/abs/1808.04488 |