在Kardar-Parisi-Zhang的维度交叉中,增长的增长
Ismael S S Carrasco1, Tiago J Oliveira2
1International Center of Physics, Institute of Physics, University of Brasilia, 70910-900 Brasilia, Federal District, Brazil.
Physical review. E
|May 17, 2024
概括
研究人员探索了二维卡达尔-帕里西- (KPZ) 增长中的二维交叉. 他们发现,异构基板导致表面动态和高度分布从二维到一维缩放的过渡.
科学领域:
- 统计物理 统计物理
- 表面增长模型 表面增长模型
- 非平衡的动力学.
背景情况:
- 两维卡达尔-帕里西-张 (2D KPZ) 增长通常研究在方形基板上,侧面尺寸和相关长度是关键.
- 异型基板 (例如,圆柱形或矩形,L_x ≠ L_y) 引入一个方向相关长度 (ξ ~ L_x ≪ L_y).
研究的目的:
- 调查异型基质对二维KPZ生长的动态和缩放行为的影响.
- 在KPZ模型中识别和描述从2D到1D的维度交叉行为.
- 分析这些交叉过程中高度分布的演变.
主要方法:
- 在异型基板上对各种2DKPZ模型进行了广泛的数值模拟.
- 用时间 (t) 和系统维度 (L_x,L_y) 对表面粗度缩放的分析.
- 检查高度分布函数及其与已知分布的收.
主要成果:
- 在KPZ动态中演示了一个维交叉:粗度尺度为短时间的W ~ t^{β_{2D}}和长时间的W ~ t^{β_{1D}},交叉时间t_c ~ L_x^{1/z_{2D}}.
- 观察到的高度分布从2D平面/圆柱形转变为特雷西-维多姆分布 (GOE/GUE).
- 在增长速度和稳定状态模式中识别了2D到1D交叉,具有在2D和1D极限之间插曲的通用高度分布.
结论:
- 不同类型的条件在2D KPZ增长中诱导维度交叉,改变缩放规律和高度分布.
- 观察到的交叉现象得到了充分的描述,为解决二维KPZ模型提供了潜在的途径.
- 这项工作强调了基板几何学在确定表面增长的普遍性类中的重要性.
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