Bound of diffusion constants from pole-skipping points: spontaneous symmetry breaking and magnetic field
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| Auteurs principaux: | , , |
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| Format: | Preprint |
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2021
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| _version_ | 1866911935265505280 |
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| author | Jeong, Hyun-Sik Kim, Keun-Young Sun, Ya-Wen |
| author_facet | Jeong, Hyun-Sik Kim, Keun-Young Sun, Ya-Wen |
| contents | We investigate the properties of pole-skipping of the sound channel in which the translational symmetry is broken explicitly or spontaneously. For this purpose, we analyze, in detail, not only the holographic axion model, but also the magnetically charged black holes with two methods: the near-horizon analysis and quasi-normal mode computations. We find that the pole-skipping points are related with the chaotic properties, Lyapunov exponent ($λ_L$) and butterfly velocity ($v_B$), independently of the symmetry breaking patterns. We show that the diffusion constant ($D$) is bounded by $D \,\geqslant\, v_{B}^2/λ_{L}$, where $D$ is the energy diffusion (crystal diffusion) bound for explicit (spontaneous) symmetry breaking. We confirm that the lower bound is obtained by the pole-skipping analysis in the low temperature limit. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2104_13084 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Bound of diffusion constants from pole-skipping points: spontaneous symmetry breaking and magnetic field Jeong, Hyun-Sik Kim, Keun-Young Sun, Ya-Wen High Energy Physics - Theory We investigate the properties of pole-skipping of the sound channel in which the translational symmetry is broken explicitly or spontaneously. For this purpose, we analyze, in detail, not only the holographic axion model, but also the magnetically charged black holes with two methods: the near-horizon analysis and quasi-normal mode computations. We find that the pole-skipping points are related with the chaotic properties, Lyapunov exponent ($λ_L$) and butterfly velocity ($v_B$), independently of the symmetry breaking patterns. We show that the diffusion constant ($D$) is bounded by $D \,\geqslant\, v_{B}^2/λ_{L}$, where $D$ is the energy diffusion (crystal diffusion) bound for explicit (spontaneous) symmetry breaking. We confirm that the lower bound is obtained by the pole-skipping analysis in the low temperature limit. |
| title | Bound of diffusion constants from pole-skipping points: spontaneous symmetry breaking and magnetic field |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2104.13084 |