# SKM 2023 – wissenschaftliches Programm

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# DY: Fachverband Dynamik und Statistische Physik

## DY 44: Poster: Statistical Physics

### DY 44.8: Poster

### Donnerstag, 30. März 2023, 13:00–16:00, P1

Transport Properties of Brownian Particles: Analytical Results and Computer Simulations — •Regina Rusch^{1}, Gerhard Jung^{2}, and Thomas Franosch^{1} — ^{1}Institute for Theoretical Physics, Universität Innsbruck, Innsbruck, Austria. — ^{2}Laboratoire Charles Coulomb (L2C), Université de Montpellier, CNRS, 34095 Montpellier, France.

The results of computer simulations for Brownian particles can be improved by using a novel noise cancellation algorithm, with which the velocity autocorrelation function (VACF) can be measured more precisely. The algorithm is based on the fact that the Brownian noise can be stored in computer simulations and thus the noise can be subtracted from a simulated trajectory. Doing this, a reduced motion of the particle due to interactions or an external force is obtained. It could be shown that the VACF of the reduced motion is connected with the original VACF up to a cross-correlation term, which is shown to be sufficiently small. For the system of a Brownian particle in a periodic step potential the noise cancellation algorithm decreases the error of the VACF by about one order of magnitude. A power-law decay in the VACF is found by employing Monte-Carlo simulations. We also present analytical results for the probability distribution of the particle position using the Bloch theorem. This enables us to compute further correlation functions such as the intermediate scattering function which is in quantitative agreement with simulations.