起伏地形上滑移质点耦合模态动力学
Dynamics of coupled modes for sliding particles on a fluctuating landscape
摘要：
近年来发展起来的非线性波动流体力学（NLFH）的形式主义已在解开许多新的动力学普适类耦合驱动系统的多个守恒量。在原则上，这种形式主义需要知识的保守组件的局部保守电流的局部密度方面的确切表达。然而，对于大多数非平衡系统，精确的表达式是不可用的，重要的是要知道在这些情况下NLFH的预测会发生什么。我们解决这个问题的第一次在这里在一个系统中耦合的时间演化的波动的能量景观上的滑动粒子。在无序相中，该系统表现出短程关联，其确切形式未知，因此无法获得电流的精确表达式。我们使用基于平均场论和修正的近似表达式，使用数值模拟来测试NLFH的预测。在这个过程中，我们还发现了重要的有限尺寸效应，并展示了它们如何影响NLFH的预测。我们发现，我们的系统是丰富的，足以显示各种各样的普遍性类。从我们的分析和模拟，我们已经能够找到参数值，导致扩散，Kardar-Parisi-Zhang（KPZ），$5/3 $ Lévy和修改的KPZ普适性类。有趣的是，在修改后的KPZ情况下的标度函数原来是接近的Prähofer-Spohn函数，这是已知的描述通常的KPZ标度。我们的分析还预测了我们模型中的黄金平均值和$3/2$ Lévy普适性类，但我们的模拟无法验证这一点，可能是由于强烈的有限尺寸效应。
英文摘要：
The recently developed formalism of nonlinear fluctuating hydrodynamics (NLFH) has been instrumental in unraveling many new dynamical universality classes in coupled driven systems with multiple conserved quantities. In principle, this formalism requires knowledge of the exact expression of locally conserved current in terms of local density of the conserved components. However, for most nonequilibrium systems an exact expression is not available and it is important to know what happens to the predictions of NLFH in these cases. We address this question for the first time here in a system with coupled time evolution of sliding particles on a fluctuating energy landscape. In the disordered phase this system shows short-ranged correlations, this system shows short-ranged correlations, the exact form of which is not known, and so the exact expression for current cannot be obtained. We use approximate expressions based on mean-field theory and corrections to it, to test the prediction of NLFH using numerical simulations. In this process we also discover important finite size effects and show how they affect the predictions of NLFH. We find that our system is rich enough to show a large variety of universality classes. From our analytics and simulations we have been able to find parameter values which lead to diffusive, Kardar-Parisi-Zhang (KPZ), $5/3 $ Lévy and modified KPZ universality classes. Interestingly, the scaling function in the modified KPZ case turns out to be close to the Prähofer-Spohn function which is known to describe usual KPZ scaling. Our analytics also predict the golden mean and the $3/2$ Lévy universality classes within our model but our simulations could not verify this, perhaps due to strong finite size effects.
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