arXiv subjects

Regina Rusch

Publications and source records attributed to Regina Rusch.

4 recordsLinked to original sources

arXiv2026

Intermediate scattering function of Brownian particles in a tilted cosine potential

We solve the Fokker-Planck equation for a Brownian particle in a tilted cosine potential and derive the intermediate scattering function (ISF), which captures the full spatio-temporal dynamics of the system. The model consists of a single overdamped Brownian particle in one dimension. We derive a generalized ISF comprising two wave vectors to describe correlations in the periodic potential. Exploiting the periodicity via Bloch's theorem, we formulate the problem within a spectral-theoretical framework and numerically compute the corresponding eigenfunctions and eigenvalues, from which we obtain the ISF and the probability density. Using time-dependent perturbation theory, we expand the ISF and derive low-order moments, including the mean-square displacement, time-dependent diffusivity, skewness, and the non-Gaussian parameter. Our analytical results are validated by Brownian-dynamics simulations and analyzed focussing on different regimes of the tilting force. The results are compared to a harmonic approximation and the deterministic limit.

cond-mat.stat-mech↗

arXiv2025

Intermediate scattering function of colloids in a periodic laser field

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.

cond-mat.soft↗

arXiv2024

Intermediate scattering function of a gravitactic circle swimmer

We analyze gravitaxis of a Brownian circle swimmer by deriving and characterizing analytically the experimentally measurable intermediate scattering function (ISF). To solve the associated Fokker-Planck equation we use a spectral-theory approach and find formal expressions in terms of eigenfunctions and eigenvalues of the overdamped-noisy-driven-pendulum problem. We further perform a Taylor series of the ISF in the wavevector to read off the cumulants up to the fourth order. We focus on the skewness and kurtosis analyzed for four observation directions in the 2D-plane. Validating our findings involves conducting Langevin-dynamics simulations and interpreting the results using a harmonic approximation. The skewness and kurtosis are amplified as the orienting torque approaches the intrinsic angular drift of the circle swimmer from above, highlighting deviations from Gaussian behavior. Transforming the ISF to the comoving frame, again a measurable quantity, reveals gravitactic effects and diverse behaviors spanning from diffusive motion at low wavenumbers to circular motion at intermediate and directed motion at higher wavenumbers.

cond-mat.soft↗

arXiv2024

Noise-cancellation algorithm for simulations of Brownian particles

We investigate the usage of a recently introduced noise-cancellation algorithm for Brownian simulations to enhance the precision of measuring transport properties such as the mean-square displacement or the velocity-autocorrelation function. The algorithm is based on explicitly storing the pseudo-random numbers used to create the randomized displacements in computer simulations and subtracting them from the simulated trajectories. The resulting correlation function of the reduced motion is connected to the target correlation function up to a cross-correlation term. Using analytical theory and computer simulations, we demonstrate that the cross-correlation term can be neglected in all three systems studied in this aper. We further expand the algorithm to Monte Carlo simulations and analyze the performance of the algorithm and rationalize that it works particularly well for unbounded, weakly interacting systems in which the precision of the mean-square displacement can be improved by orders of magnitude.

physics.comp-ph↗