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

Ofek Lauber BonomoShlomi Reuveni
Oct 2022
摘要
Random motion in disordered media is sensitive to the presence of obstaclesthat prevent atoms, molecules, and other particles from moving freely in space.When obstacles are static, a sharp transition between confined motion and freediffusion occurs at a critical obstacle density: the percolation threshold. Totest if this conventional wisdom continues to hold in the presence of simpletracer-media interactions, we introduce the Sokoban random walk. Akin to theprotagonist of an eponymous video game, the Sokoban has some ability to pushaway obstacles that block its path. While one expects this will allow theSokoban to venture further away, we surprisingly find that this is not alwaysthe case. Indeed, as it moves $\unicode{x2013}$ pushing obstacles around$\unicode{x2013}$ the Sokoban always confines itself to a finite region whosemean size is uniquely determined by the initial obstacle density. Consequently,the percolation transition is lost. This finding breaks from the ruling "ant ina labyrinth" paradigm, vividly illustrating that even weak and localizedtracer-media interactions cannot be neglected when coming to understandtransport phenomena.
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