Large fluctuations in diffusion-controlled absorption

Abstract

Suppose that $N_0$ independently diffusing particles, each with diffusivity $D$, are initially released at $x=\ell >0$ on the semi-infinite interval $0\le x<\infty$ with an absorber at $x=0$. We determine the probability $\mathcal{P}(N)$ that $N$ particles survive until time $t=T$. We also employ macroscopic fluctuation theory to find the most likely history of the system, conditional on there being exactly $N$ survivors at time $t=T$. Depending on the basic parameter $\ell /\sqrt{4DT}$, very different histories can contribute to the extreme cases of $N=N_0$ (all particles survive) and $N=0$ (no survivors). For large values of $\ell /\sqrt{4DT}$, the leading contribution to $\mathcal{P}(N=0)$ comes from an effective point-like quasiparticle that contains all the $N_0$ particles and moves ballistically toward the absorber until absorption occurs.

13 pages, 4 figures

References in corpus (6)

• The large deviation approach to statistical mechanics
• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• First passages for a search by a swarm of independent random searchers
• Mapping out of equilibrium into equilibrium in one-dimensional transport models
• Mapping Nonequilibrium onto Equilibrium: The Macroscopic Fluctuations of Simple Transport Models
• Extreme Fluctuations of Current in the Symmetric Simple Exclusion Process: a Non-Stationary Setting

Cited by in corpus (2)

• Mortality, Redundancy, and Diversity in Stochastic Search
• Survival of a static target in a gas of diffusing particles with exclusion