有限体积中的离子涨落：分数噪声和超均匀性
Ionic fluctuations in finite volumes: fractional noise and hyperuniformity
摘要：
从显微镜到分子模拟，观察更大系统的有限区域是一种常见的经验。特别是在后者中，人们对通过跟踪有限观测量中的波动来预测热力学性质一直很感兴趣。然而，动力学性质受到较少的关注，特别是在离子溶液中，静电相互作用起决定性作用。在这里，我们探测离子波动与布朗动力学在有限体积和建立一个分析框架，再现我们的模拟结果，并广泛适用于其他系统与成对的相互作用。粒子数和电荷的相关性表现出丰富的现象与时间，其特征在于由多种时间尺度。这两个量的噪声频谱衰减为$1/f^{3/2}$，其中$f$是频率。分数噪声的这种特征显示了在有限域中观察扩散粒子时$1/f^{3/2}$标度的普遍性。电荷波动的超均匀行为，即相关性与观测体积的面积成比例，在时间上被保留。在足够长的时间内，相关性甚至与盒子的周长成正比。我们的研究结果为理解更复杂系统中的波动铺平了道路，从纳米孔到单粒子电化学。
英文摘要：
Observing finite regions of a bigger system is a common experience, from microscopy to molecular simulations. In the latter especially, there is ongoing interest in predicting thermodynamic properties from tracking fluctuations in finite observation volumes. However, kinetic properties have received less attention, especially not in ionic solutions, where electrostatic interactions play a decisive role. Here, we probe ionic fluctuations in finite volumes with Brownian dynamics and build an analytical framework that reproduces our simulation results and is broadly applicable to other systems with pairwise interactions. Particle number and charge correlations exhibit a rich phenomenology with time, characterized by a diversity of timescales. The noise spectrum of both quantities decays as $1/f^{3/2}$, where $f$ is the frequency. This signature of fractional noise shows the universality of $1/f^{3/2}$ scalings when observing diffusing particles in finite domains. The hyperuniform behaviour of charge fluctuations, namely that correlations scale with the area of the observation volume, is preserved in time. Correlations even become proportional to the box perimeter at sufficiently long times. Our results pave the way to understand fluctuations in more complex systems, from nanopores to single-particle electrochemistry.
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