Controls that expedite first passage times in disordered systems

TL;DR

This paper investigates how removing the largest trapping times in disordered systems can significantly accelerate first passage times, revealing a method to improve transport efficiency in highly disordered environments.

Contribution

It introduces a novel approach inspired by the restart paradigm to expedite transport by removing dominant traps, especially effective in strongly disordered systems.

Findings

Removing maximum trapping times greatly speeds up transport.

The effect is dramatic in highly disordered systems.

In homogeneous systems, removal has little impact.

Abstract

First passage time statistics in disordered systems exhibiting scale invariance are studied widely. In particular, long trapping times in energy or entropic traps are fat-tailed distributed, which slow the overall transport process. We study the statistical properties of the first passage time of biased processes in different models, and employ the big jump principle that shows the dominance of the maximum trapping time on the first passage time. Inspired by the restart paradigm, we demonstrate that the removal of this maximum significantly expedites transport. As the disorder increases, the system enters a phase where the removal shows a dramatic effect. Our results show how we may speed up transport in strongly disordered systems exploiting scale invariance. In contrast to the disordered systems studied here, the removal principle has essentially no effect in homogeneous systems; this indicates that improving the conductance of a poorly conducting system is, theoretically, relatively easy as compared to a homogeneous system.