论文标题
初始条件在$ 1D $扩散系统中的作用：可压缩性，超均匀性和长期记忆力
Role of initial conditions in $1D$ diffusive systems: compressibility, hyperuniformity and long-term memory
论文作者
论文摘要
我们分析了初始条件对一维扩散系统波动的持久影响。我们考虑了从阶梯式初始密度曲线开始的非相互作用扩散颗粒的电流波动，以及单文件扩散的均质系统中示踪剂的均方位移。在这两种情况下，我们在分析上（分别通过传播器和宏观波动理论）表明，初始条件的长期记忆是由单个静态数量介导的：一种量化初始状态的密度波动的广义可压缩性。因此，我们确定了一个高均匀初始状态的普遍类别，其动力学方差与先前研究的“淬火”病例一致。我们还描述了其他阶级的连续家庭，其中平衡（或“退火”）初始条件只是一个家庭成员。我们通过广泛的蒙特卡洛模拟来验证我们的预测。
We analyse the long-lasting effects of initial conditions on fluctuations in one-dimensional diffusive systems. We consider both the fluctuations of current for non-interacting diffusive particles starting from a step-like initial density profile, and the mean-square displacement of tracers in homogeneous systems with single-file diffusion. For these two cases, we show analytically (via the propagator and Macroscopic Fluctuation Theory, respectively) that the long-term memory of initial conditions is mediated by a single static quantity: a generalized compressibility that quantifies the density fluctuations of the initial state. We thereby identify a universality class of hyperuniform initial states whose dynamical variances coincide with the `quenched' cases studied previously; we also describe a continuous family of other classes among which equilibrated (or `annealed') initial conditions are but one family member. We verify our predictions through extensive Monte Carlo simulations.
