论文标题
波动的表面上的轻盈和重颗粒：束平衡，不可还原序列和局部密度高度相关性
Light and heavy particles on a fluctuating surface: Bunchwise balance, irreducible sequences and local density-height correlations
论文作者
论文摘要
我们研究了轻质模型中的早期和变形动力学，该系统由两种颗粒（$ light $和$ heavy $）组成，并耦合到波动的表面（由倾斜场描述）。颗粒和倾斜的动力学通过局部更新规则耦合，并且众所周知会导致不同有序和无序的稳态阶段，具体取决于显微镜速率。我们在非平衡系统中引入了广义的平衡机制，即$ bunchwise〜Balance $，其中传入和传出过渡电流在配置组之间平衡。这使我们能够准确确定该模型相图的子空间中的稳态。我们在此模型中介绍了$不可约束〜序列$ $的概念。这些序列是非本地的，我们表明它们在较晚的阶段中提供了长度尺寸。最后，我们提出了一个$ local $相关函数（$ \ Mathcal {s} $），该功能直接与不可序列的数量有直接关系，并且能够通过其粗糙属性区分该系统的几个阶段。从完全无序的初始配置开始，$ \ Mathcal {S} $显示出初始线性上升和广泛的最大值。随着系统向有序的稳态发展，$ \ MATHCAL {S} $进一步展示了在后期的电源法衰减，这些衰减编码了该方法对订购阶段的粗糙属性。为了关注早期动力学，我们提出了耦合的平均场进化方程，该方程是管理粒子和倾斜的，在短时间内，它们通过一组线性化方程式近似，我们可以在分析上求解。除了由晶格截止设定的时间尺度和在变形之前，我们的线性理论还可以预测中间幂律伸展的存在，我们在模拟系统的有序状态中也发现了这一点。
We study the early time and coarsening dynamics in the Light-Heavy model, a system consisting of two species of particles ($light$ and $heavy$) coupled to a fluctuating surface (described by tilt fields). The dynamics of particles and tilts are coupled through local update rules, and are known to lead to different ordered and disordered steady state phases depending on the microscopic rates. We introduce a generalized balance mechanism in non-equilibrium systems, namely $bunchwise~balance$, in which incoming and outgoing transition currents are balanced between groups of configurations. This allows us to exactly determine the steady state in a subspace of the phase diagram of this model. We introduce the concept of $irreducible~sequences$ of interfaces and bends in this model. These sequences are non-local, and we show that they provide a coarsening length scale in the ordered phases at late times. Finally, we propose a $local$ correlation function ($\mathcal{S}$) that has a direct relation to the number of irreducible sequences, and is able to distinguish between several phases of this system through its coarsening properties. Starting from a totally disordered initial configuration, $\mathcal{S}$ displays an initial linear rise and a broad maximum. As the system evolves towards the ordered steady states, $\mathcal{S}$ further exhibits power law decays at late times that encode coarsening properties of the approach to the ordered phases. Focusing on early time dynamics, we posit coupled mean-field evolution equations governing the particles and tilts, which at short times are well approximated by a set of linearized equations, which we solve analytically. Beyond a timescale set by a lattice cutoff and preceding the onset of coarsening, our linearized theory predicts the existence of an intermediate power-law stretch, which we also find in simulations of the ordered regime of the system.
