# SKM 2023 – wissenschaftliches Programm

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# DY: Fachverband Dynamik und Statistische Physik

## DY 44: Poster: Statistical Physics

### DY 44.15: Poster

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

Ornstein-Uhlenbeck process and generalizations: influence of comb geometry and stochastic resetting on the particle dynamics — •Petar Jolakoski^{1}, Pece Trajanovski^{1}, Kiril Zelenkovski^{1}, Alexander Iomin^{2}, Ljupco Kocarev^{1,4}, and Trifce Sandev^{1,3,4} — ^{1}Macedonian Academy of Sciences and Arts, Skopje, Macedonia — ^{2}Department of Physics, Technion, Haifa, Israel — ^{3}University of Potsdam, Germany — ^{4}Ss. Cyril and Methodius University in Skopje, Macedonia

The Ornstein-Uhlenbeck (O-U) process can be interpreted as a Brownian motion in a harmonic potential. The process is an established Gauss-Markov process that has a bounded variance and admits a stationary probability distribution, in contrast to the standard Brownian motion. Over time, the process tends to drift towards its mean function: such a process is called mean-reverting. Here, we study the effects of stochastic resetting on the O-U process and its generalizations which were hitherto unexplored. In particular, we investigate the dynamics with and without resetting on comb-like structures. For the studied specific 2D comb geometry, we compute the first moment, the non-equilibrium stationary state and the mean squared displacement, and find that the global resetting hinders the particle’s transport in the two dimensions. Moreover, the two divergent forces, namely the resetting and the drift towards the mean, lead to compelling results both in the case of O-U process with resetting and its generalization on a 2D comb structure.