Loss of Percolation Transition in the Presence of Simple Tracer-Media Interactions

TL;DR

This study introduces the Sokoban random walk to investigate how simple tracer-media interactions affect percolation transitions, revealing that such interactions can confine particles and eliminate the traditional sharp transition in disordered media.

Contribution

It demonstrates that weak, localized tracer-media interactions can fundamentally alter transport behavior, destroying the percolation transition in disordered systems.

Findings

Sokoban random walk confines particles regardless of obstacle density

Percolation transition is lost due to tracer-media interactions

Weak interactions significantly impact transport phenomena

Abstract

Random motion in disordered media is sensitive to the presence of obstacles that prevent atoms, molecules, and other particles from moving freely in space. When obstacles are static, a sharp transition between confined motion and free diffusion occurs at a critical obstacle density: the percolation threshold. To test if this conventional wisdom continues to hold in the presence of simple tracer-media interactions, we introduce the Sokoban random walk. Akin to the protagonist of an eponymous video game, the Sokoban has some ability to push away obstacles that block its path. While one expects this will allow the Sokoban to venture further away, we surprisingly find that this is not always the case. Indeed, as it moves $\unicode{x2013}$ pushing obstacles around $\unicode{x2013}$ the Sokoban always confines itself to a finite region whose mean size is uniquely determined by the initial obstacle density. Consequently, the percolation transition is lost. This finding breaks from the ruling "ant in a labyrinth" paradigm, vividly illustrating that even weak and localized tracer-media interactions cannot be neglected when coming to understand transport phenomena.