在灭的卡达尔 - 巴里西 - 张等级中沉浸. 一,映射,模拟和算法
Gauthier Mukerjee1, Juan A Bonachela2, Miguel A Muñoz3
1Laboratoire de Physique de l'École Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris-Diderot, Sorbonne Paris Cité, 24 rue Lhomond, 75005 Paris, France.
Physical review. E
|June 17, 2023
概括
灭的Kardar-Parisi-Zhang (qKPZ) 全面性类描述了无序系统中的依赖性. 这项研究证明qKPZ是各种模型的有效场理论,统一了它们的关键行为.
科学领域:
- 凝聚物质物理学 凝聚物质物理学
- 统计力学 统计力学
- 非线性动力学是一种非线性动力学.
背景情况:
- 在无序介质中的依赖通常是通过灭的爱德华兹-威尔金森 (qEW) 方程来建模的.
- 不和和和非潜在的力量可以导致不同的取决行为,特别是卡达尔-帕里西-张 (KPZ) 术语,创建灭的KPZ (qKPZ) 普遍性类.
研究的目的:
- 在数值和分析上研究灭的KPZ (qKPZ) 全面性类.
- 证明 qKPZ 类统一了多种不同的描述模型,包括 qKPZ 方程,无声描述和 Tang-Leschhorn 细胞自动机.
- 建立qKPZ作为这些系统的有效场理论.
主要方法:
- 准确的映射连接不同的模型在qKPZ类.
- 开发关键指数的缩放参数,包括雪崩的大小和持续时间.
- 对指数的数值估计,有效力相关因子,相关长度,有效弹性和KPZ非线性.
- 对系统参数进行数值估计的算法开发.
主要成果:
- 对于d=1,2的qKPZ通用性类包括qKPZ方程,无声描述和唐-莱斯霍恩细胞自动机.
- 为关键指数和雪崩动态开发了缩放参数.
- 获得指数和系统依赖参数的数值估计.
- 在所有研究的系统中,为d=1发现了通用KPZ振幅A=1.10(2).
结论:
- 灭的KPZ (qKPZ) 方程是无序系统中一系列定义现象的有效场理论.
- KPZ 振幅的普遍性证实了 qKPZ 框架的统一力量.
- 这项工作为 qKPZ 类的领域理论的进一步发展提供了基础.
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