Mirror symmetry breakdown in the Kardar-Parisi-Zhang universality class

Johannes Schmidt; Andreas Schadschneider

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arXiv · 2205.06062

Mirror symmetry breakdown in the Kardar-Parisi-Zhang universality class

Johannes Schmidt·Andreas Schadschneider

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Abstract

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.

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Johannes Schmidt, Andreas Schadschneider. 2022-05-12. Mirror symmetry breakdown in the Kardar-Parisi-Zhang universality class. https://arxiv.org/abs/2205.06062

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