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

IF 2.4 3区 物理与天体物理 Q1 Mathematics
Johannes Schmidt, Andreas Schadschneider
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引用次数: 0

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, which belongs to the KPZ universality class. Here we focus on current (or 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 superdiffusive 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.

Abstract Image

卡达尔-帕里斯-张普遍性类别中的镜像对称性崩溃
1+1维卡达尔-帕里西-张(KPZ)普遍性的电流/高度波动统计对初始状态很敏感。我们发现,以波动为条件时,初始状态的平均值表现出普遍和尺度不变的模式。为了确定我们发现的普遍性,我们利用大规模蒙特卡罗模拟完全不对称的简单排他性过程,证明了不同时间和高度下的尺度不变性,该过程属于 KPZ 普遍性类别。在此,我们重点讨论白-雷兹分布(Baik-Rains distribution)所描述的稳态机制中的电流(或高度)波动。初始状态阶次参数的条件概率分布显示了从单峰到双峰的过渡。双峰性出现在由超扩散冲击动力学主导的负电流/高度波动中。它是由两种可能的点对称冲击剖面和 KPZ 镜像对称性破坏造成的。在其他普遍性类别中,初始状态与波动之间也可能存在类似的惊人关系。
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来源期刊
Physical review. E
Physical review. E 物理-物理:流体与等离子体
CiteScore
4.60
自引率
16.70%
发文量
0
审稿时长
3.3 months
期刊介绍: Physical Review E (PRE), broad and interdisciplinary in scope, focuses on collective phenomena of many-body systems, with statistical physics and nonlinear dynamics as the central themes of the journal. Physical Review E publishes recent developments in biological and soft matter physics including granular materials, colloids, complex fluids, liquid crystals, and polymers. The journal covers fluid dynamics and plasma physics and includes sections on computational and interdisciplinary physics, for example, complex networks.
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