Roughness of driven elastic interfaces in random media is typically understood to be characterized by a single roughness exponent $\zeta$. We show that at the depinning threshold, due to symmetry breaking caused by the direction of the driving force, elastic interfaces with local, long-range and mean-field elasticity exhibit asymmetric roughness. It is manifested as a skewed distribution of the local interface heights, and can be quantified by using detrended fluctuation analysis to compute a spectrum of local, segment-level scaling exponents. The asymmetry is observed as approximately linear dependence of the local scaling exponents on the difference of the segment height from the mean interface height.

中文翻译：

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固定阈值处弹性界面的不对称粗糙度

随机介质中驱动弹性界面的粗糙度通常被理解为以单个粗糙度指数 $\zeta$ 为特征。我们表明，在去钉扎阈值处，由于驱动力方向引起的对称性破坏，具有局部、远程和平均场弹性的弹性界面表现出不对称的粗糙度。它表现为局部界面高度的偏态分布，并且可以通过使用去趋势波动分析来计算局部、段级缩放指数的频谱来量化。不对称性被观察为局部缩放指数对段高度与平均界面高度之差的近似线性依赖性。