# SKM 2023 – wissenschaftliches Programm

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# DY: Fachverband Dynamik und Statistische Physik

## DY 32: Focus Session: Physics of Fluctuating Paths (joint session DY/CPP)

### DY 32.8: Vortrag

### Mittwoch, 29. März 2023, 17:00–17:15, ZEU 160

**Kinetics of Imperfect Reactions for non-Markovian Random Walks** — •Toni Vieira Mendes and Thomas Guérin — Laboratoire Ondes et Matière d'Aquitaine, Université de Bordeaux

Most transport influenced reactions between two random walkers are usually imperfect, i.e., they do not occur at first contact between the reactants. For such imperfect reactions, recent work has been made to determine the statistics of first reaction time for Markovian random walkers in confinement. However, a lot of physical random walks are actually non-Markovian, i.e., their movement in the future depend on the trajectory they have followed up to then, thus displaying memory effects. These memory effects can be seen, for example, for beads moving inside complex fluids where the force fields do not equilibrate instantly. In this contribution, we describe an analytical theory giving access to the mean reaction time for imperfect reactions for random walkers with memory in confinement. Our theory clearly shows that, contrary to the Markovian case, the reaction time is not the sum of the mean first passage time and the time to react once within reactive distance. We show that the results of our theory match the results of simulations for both one and two dimensions. Then, the equations are analytically solved in the limit of weakly non-Markovian processes. Remarkably, in the limit of weakly reactive targets for fractional Brownian Motion, we find that the mean reaction time displays a non-trivial scaling as a function of the reactivity.