Mirror symmetry breakdown in the Kardar-Parisi-Zhang universality class
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866910509555515392 |
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| author | Schmidt, Johannes Schadschneider, Andreas |
| author_facet | Schmidt, Johannes Schadschneider, Andreas |
| contents | The current/height fluctuation statistics of Kardar-Parisi-Zhang (KPZ) universality in 1+1 dimensions are sensitive to the initial state. We find that the averages over the initial states exhibit universal and scale-invariant patterns when conditioning on fluctuations. To establish universality of our findings we demonstrate scale invariance at different times and heights using large-scale Monte-Carlo simulations of the totally asymmetric simple exclusion process (TASEP) which belongs to the KPZ universality class. Here we focus on current/height fluctuations in the steady state regime described by the Baik-Rains distribution. The conditioned probability distribution of an initial state order parameter shows a transition from uni- to bimodal. Bimodality occurs for negative current/height fluctuations that are dominated by super-diffusive shock dynamics. It is caused by two possible point-symmetric shock profiles and the KPZ mirror symmetry breakdown. Similar surprising relations between initial states and fluctuations might exist in other universality classes as well. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_06062 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Mirror symmetry breakdown in the Kardar-Parisi-Zhang universality class Schmidt, Johannes Schadschneider, Andreas Statistical Mechanics The current/height fluctuation statistics of Kardar-Parisi-Zhang (KPZ) universality in 1+1 dimensions are sensitive to the initial state. We find that the averages over the initial states exhibit universal and scale-invariant patterns when conditioning on fluctuations. To establish universality of our findings we demonstrate scale invariance at different times and heights using large-scale Monte-Carlo simulations of the totally asymmetric simple exclusion process (TASEP) which belongs to the KPZ universality class. Here we focus on current/height fluctuations in the steady state regime described by the Baik-Rains distribution. The conditioned probability distribution of an initial state order parameter shows a transition from uni- to bimodal. Bimodality occurs for negative current/height fluctuations that are dominated by super-diffusive shock dynamics. It is caused by two possible point-symmetric shock profiles and the KPZ mirror symmetry breakdown. Similar surprising relations between initial states and fluctuations might exist in other universality classes as well. |
| title | Mirror symmetry breakdown in the Kardar-Parisi-Zhang universality class |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2205.06062 |