Intermediate scattering function of colloids in a periodic laser field
arXiv:2507.11756 · doi:10.1039/D5SM00211G
Abstract
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.
8 Figures, 20 pages
References in corpus (17)
- SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
- Differential Dynamic Microscopy: Probing wave vector dependent dynamics with a microscope
- Probing the spatiotemporal dynamics of catalytic Janus particles with single-particle tracking and differential dynamic microscopy
- Intermediate scattering function of an anisotropic active Brownian particle
- Mode-coupling theory of the glass transition for confined fluids
- Diffusion coefficient of a Brownian particle in equilibrium and nonequilibrium: Einstein model and beyond
- Characterization and Control of the Run-and-Tumble Dynamics of {\it Escherichia Coli}
- Intermediate scattering function of an anisotropic Brownian circle swimmer
- Spectral theory of fluctuations in time-average statistical mechanics of reversible and driven systems
- Mode-coupling theory for multiple decay channels
- Impact of chirality on active Brownian particle: Exact moments in two and three dimensions
- Two-dimensional Brownian motion of anisotropic dimers
- Resonant diffusion of a gravitactic circle swimmer
- Memory effects in colloidal motion under confinement and driving
- Intermediate scattering function of a gravitactic circle swimmer
- Colloids in a periodic potential: driven lattice gas in continuous space
- Precisely controlled colloids: A playground for path-wise non-equilibrium physics