论文标题
可变形介质上的随机步行者
Random walkers on a deformable medium
论文作者
论文摘要
我们考虑随着介质移动而变形的随机步行者，从而在最近访问过的地区可以更快地进行运动。这引起了由介质介导的步行者之间的有效吸引力，该介质可以被视为空间度量，从而产生了一个统计力学玩具模型，要么通过可变形物质或适应性的几何形状进行重力，运动。在强构性方程中，我们发现扩散最初是由多孔培养基方程描述的，从而产生了最初局部局部粒子云的次传达行为。确实，虽然单个云的平均宽度将维持$σ\ sim t^{1/2} $增长，但整个合奏的组合宽度将在某个时间范围内像$σ\ sim t^{1/3} $一样生长。这种差异可以通过粒子之间的强相关性来解释，我们通过云质量中心的波动和经验丰富的预期值间接探索，并定义为粒子本身测量的平均密度。
We consider random walkers that deform the medium as they move, enabling a faster motion in regions which have been recently visited. This induces an effective attraction between walkers mediated by the medium, which can be regarded as a space metric, giving rise to a statistical mechanics toy model either for gravity, motion through deformable matter or adaptable geometry. In the strong-deformability regime, we find that diffusion is initially described by the porous medium equation, thus yielding subdiffusive behavior of an initially localized cloud of particles. Indeed, while the average width of a single cloud will sustain a $σ\sim t^{1/2}$ growth, the combined width of the whole ensemble will grow like $σ\sim t^{1/3}$ in a certain time regime. This difference can be accounted for by the strong correlations between the particles, which we explore indirectly through the fluctuations of the center of mass of the cloud and the expected value of the experienced density, defined as the average density measured by the particles themselves.
