Gaia PozzoliBenjamin de Bruyne 1
Gaia Pozzoli, Benjamin de Bruyne. Transport properties of diffusive particles conditioned to survive in trapping environments. Journal of Statistical Mechanics: Theory and Experiment, 2022, 2022 (11), pp.113205. ⟨10.1088/1742-5468/aca0e4⟩. ⟨hal-03903875⟩
Abstract We consider a one-dimensional Brownian motion with diffusion coefficient D in the presence of n partially absorbing traps with intensity β , separated by a distance L and evenly spaced around the initial position of the particle. We study the transport properties of the process conditioned to survive up to time t . We find that the surviving particle first diffuses normally, before it encounters the traps, then undergoes a period of transient anomalous diffusion, after which it reaches a final diffusive regime. The asymptotic regime is governed by an effective diffusion coefficient D eff , which is induced by the trapping environment and is typically different from the original one. We show that when the number of traps is finite , the environment enhances diffusion and induces an effective diffusion coefficient that is systematically equal to D eff = 2 D , independently of the number of the traps, the trapping intensity β and the distance L . On the contrary, when the number of traps is infinite , we find that the environment inhibits diffusion with an effective diffusion coefficient that depends on the traps intensity β and the distance L through a non-trivial scaling function D eff = D F ( β L / D ) , for which we obtain a closed-form. Moreover, we provide a rejection-free algorithm to generate surviving trajectories by deriving an effective Langevin equation with an effective repulsive potential induced by the traps. Finally, we extend our results to other trapping environments.
- 1. LPTMS – Laboratoire de Physique Théorique et Modèles Statistiques