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arXiv 2407.10568cond-mat.softcond-mat.mtrl-scicond-mat.stat-mechphysics.chem-ph
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电场驱动离子混合物中车道形成的随机密度泛函理论:基于流核的公式表述

Stochastic Density Functional Theory on Lane Formation in Electric-Field-Driven Ionic Mixtures: Flow-Kernel-Based Formulation

Hiroshi Frusawa

AI总结:

本研究以电场驱动二元离子混合物为原始模型,构建含乘性噪声的随机密度泛函理论,结合流核描述涨落流,通过渐近分析与二维逆傅里叶变换验证了车道形成的非平衡有序机制,拓展了确定性密度泛函理论。

摘要:

模拟与实验研究已证实受驱胶体悬浮液中存在非平衡有序现象:随着驱动力增大,均匀的胶体混合物会转变为局域相分离态,其特征为车道形成,即强各向异性的条状畴的出现。理论上,我们已发现密度动力学的线性稳定性分析可通过添加一个非平凡的平流项来解释这种非平衡有序。该平流源于与反向驱动迁移相关的非库仑相互作用导致的涨落流。近期基于无乘性噪声的动力学密度泛函理论(DFT,Dynamical Density Functional Theory)的研究引入了流核,用于对涨落速度进行通用描述。本文中,我们以电场驱动的二元离子混合物为原始模型,对上述确定性DFT进行评估与拓展。首先,我们构建了适用于车道现象的含乘性噪声的随机DFT。该考虑涨落流的随机DFT可用于确定稳态下的关联函数。特别地,对稳态电荷-电荷关联函数的渐近分析表明,上述用于线性稳定性分析的色散关系等价于确定电荷-电荷关联振荡波长的极点方程。其次,我们不仅通过极点方程证明了条状畴的出现,还在不预设电场方向各向同性均匀性的前提下,对电荷-电荷关联函数进行二维逆傅里叶变换,同样证实了条状畴的存在。

英文摘要:

Simulation and experimental studies have demonstrated non-equilibrium ordering in driven colloidal suspensions: with increasing driving force, a uniform colloidal mixture transforms into a locally demixed state characterized by the lane formation or the emergence of strongly anisotropic stripe-like domains. Theoretically, we have found that a linear stability analysis of density dynamics can explain the non-equilibrium ordering by adding a non-trivial advection term. This advection arises from fluctuating flows due to non-Coulombic interactions associated with oppositely driven migrations. Recent studies based on the dynamical density functional theory (DFT) without multiplicative noise have introduced the flow kernel for providing a general description of the fluctuating velocity. Here, we assess and extend the above deterministic DFT by treating electric-field-driven binary ionic mixtures as the primitive model. First, we develop the stochastic DFT with multiplicative noise for the laning phenomena. The stochastic DFT considering the fluctuating flows allows us to determine correlation functions in a steady state. In particular, asymptotic analysis on the stationary charge-charge correlation function reveals that the above dispersion relation for linear stability analysis is equivalent to the pole equation for determining the oscillatory wavelength of charge--charge correlations. Next, the appearance of stripe-like domains is demonstrated not only by using the pole equation but also by performing the 2D inverse Fourier transform of the charge--charge correlation function without the premise of anisotropic homogeneity in the electric field direction.

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