标题： 胶体在周期性激光场中的中间散射函数 显示英文标题

标题： Intermediate scattering function of colloids in a periodic laser field

摘要： 我们使用中间散射函数(ISF)作为关键可观测量，研究一维周期势中单个胶体粒子的动力学。 我们阐述了一个理论框架，并推导出ISF的形式严格精确的解析表达式。 我们引入并分析了一个具有两个波矢的广义ISF，以捕捉周期势中超出标准ISF的相关性。 依靠周期系统的布洛赫定理，并通过求解过阻尼布朗粒子在余弦势中的斯莫卢霍夫斯基方程，我们通过数值求解该表达式的本征函数和本征值来评估ISF。 我们应用时间依赖微扰理论展开ISF并提取低阶矩，包括均方位移、时间依赖扩散系数和非高斯参数。 我们的解析结果通过二维胶体系统的布朗动力学模拟和实验得到验证，这些实验中的胶体系统暴露于由两束相互作用的激光束产生的光诱导周期势中。 显示英文摘要

摘要： We investigate the dynamics of individual colloidal particles in a one-dimensional periodic potential using the intermediate scattering function (ISF) as a key observable. We elaborate a theoretical framework and derive formally exact analytical expressions for the ISF. We introduce and analyze a generalized ISF with two wave vectors to capture correlations in a periodic potential beyond the standard ISF. Relying on Bloch's theorem for periodic systems and, by solving the Smoluchowski equation for an overdamped Brownian particle in a cosine potential, we evaluate the ISF by numerically solving for the eigenfunctions and eigenvalues of the expression. We apply time-dependent perturbation theory to expand the ISF and extract low-order moments, including the mean-square displacement, the time-dependent diffusivity, and the non-Gaussian parameter. Our analytical results are validated through Brownian-dynamics simulations and experiments on 2D colloidal systems exposed to a light-induced periodic potential generated by two interacting laser beams.