稀磁偶极网络中反常自旋输运的连续时间随机游走描述
Continuous-Time Random Walk Description of Anomalous Spin Transport in Dilute Dipolar Networks
- University of California, Berkeley（加州大学伯克利分校）
- University of Southampton（南安普顿大学）
- Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
研究稀磁偶极网络中反常自旋输运，用连续时间随机游走描述¹³C极化输运，构建速率矩阵并采样轨迹。发现无序平均动力学致反常输运，分析等待时间分布等特征，追溯微观起源，联系全局输运与穿越时间，表明需超越菲克扩散方程的描述。
AI中文摘要：
核自旋扩散通常由单一扩散系数概括，但在稀固体中这种粗粒度描述可能失效，其中位置无序和长程偶极耦合会产生广泛的跳跃率分布。我们针对天然丰度金刚石（1.1%）中¹³C极化输运开发了连续时间随机游走（CTRW）描述，从偶极介导的翻转耦合构建速率矩阵并采样精确的连续时间轨迹。尽管位点间跳跃是马尔可夫的，但无序平均动力学导致出现反常输运。经验等待时间分布呈现重尾，指数α = 0.64且指数截止t_cutoff = 19 s；平均跳跃长度在τ≥0.1 s时与等待时间τ相关；均方位移在步数和物理时间上均呈亚线性增长，指数分别为γ = 0.56和δ = 0.87。我们将这些特征的微观起源追溯到几何捕获：极化可在强耦合簇内快速交换，而弱簇间链接控制长程探索。动力学渗流构建将全局输运与簇间穿越时间联系起来，并确定相应穿越时间约为20 s，与t_cutoff一致。最后，将顺磁杂质映射到硬球陷阱上，将CTRW框架与反应扩散理论中的经典捕获研究联系起来，并再现了实验测量弛豫的定性时间尺度，而连续扩散方程描述则不行。这些结果表明，稀磁偶极自旋网络需要超越菲克扩散方程的微观、网络解析输运描述。
英文摘要：
Nuclear spin diffusion is often summarized by a single diffusion coefficient, but this coarse-grained description can fail in dilute solids where positional disorder and long-range dipolar couplings generate a broad distribution of hopping rates. We develop a continuous-time random-walk (CTRW) description of $^{13}$C polarization transport in natural-abundance diamond (1.1%), constructing the rate matrix from dipolar-mediated flip-flop couplings and sampling exact continuous-time trajectories. Although site-to-site hopping is Markovian, the disorder-averaged dynamics give rise to emergent, anomalous transport. The empirical waiting-time distribution exhibits a heavy tail with exponent $α=0.64$ and exponential cutoff $t_{\rm cutoff}=19$ s; the mean jump length becomes correlated with the waiting time $τ$ for $τ\gtrsim0.1$ s; and the mean-squared displacement grows sublinearly in both step number and physical time, with exponents $γ=0.56$ and $δ=0.87$ respectively. We trace the microscopic origin of these signatures to geometric trapping: polarization can rapidly exchange within strongly coupled clusters, including dimers, while weak inter-cluster links control long-range exploration. A kinetic percolation construction links global transport to inter-cluster crossing times, and identifies a corresponding crossing time of $\sim20$ s, consistent with $t_{\rm cutoff}$. Finally, mapping paramagnetic impurities onto hard-sphere traps connects the CTRW framework to classic studies of trapping in reaction-diffusion theory and reproduces the qualitative timescale of experimentally measured relaxation, whereas a continuum diffusion equation description does not. These results show that dilute dipolar spin networks require a microscopic, network-resolved transport description beyond the Fickian diffusion equation.
