随机介质中非局部静电学的连续极限
Continuum Limit of Nonlocal Electrostatics in Random Media
- South Dakota School of Mines and Technology（南达科他矿业与技术学院）
- Carnegie Mellon University（卡内基梅隆大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文推导了随机电荷密度场静电能量的双尺度连续极限，证明局部与非局部能量几乎必然收敛，并验证了独立单元随机位移模型中的相关假设。
AI中文摘要：
我们推导了在晶格平移下平稳且遍历的随机电荷密度场的静电能量的双尺度连续极限。每个微观单元在每次实现中都是电荷中性的，而其偶极矩可能波动并具有非零均值。在关于平稳微观势和有限体积场的假设下，局部和非局部能量几乎必然收敛到确定性极限。局部极限由系综平均的微观库仑能量和单元去极化项组成，而有效极化决定了非局部极限。单元去极化项在总能量中相互抵消，总能量由系综平均的微观单元能量和宏观静电场能量组成。确定性特例恢复了周期性双尺度极限。对于独立单元随机位移模型，我们验证了连续极限定理的假设，并表明居中的微观波动可以改变局部能量，而不改变有效极化或非局部能量。
英文摘要：
We derive a two-scale continuum limit for the electrostatic energy of random charge density fields that are stationary and ergodic under lattice translations. Each microscopic cell is charge neutral in every realization, while its dipole moment may fluctuate and have a nonzero mean. Under assumptions on the stationary microscopic potential and the finite-volume fields, the local and nonlocal energies converge almost surely to deterministic limits. The local limit consists of the ensemble-averaged microscopic Coulomb energy and a cell-depolarization term, whereas the effective polarization determines the nonlocal limit. The cell-depolarization terms cancel in the total energy, which consists of the ensemble-averaged microscopic cell energy and the macroscopic electrostatic field energy. The deterministic specialization recovers the periodic two-scale limit. For an independent-cell random-displacement model, we verify the assumptions of the continuum-limit theorem and show that centered microscopic fluctuations can change the local energy without changing the effective polarization or the nonlocal energy.
