Laboratoire de Physique Théorique de la Matière Condensée, CNRS, UPMC, 4 Place Jussieu, 75005 Paris, France.
Laboratoire Ondes et Matière d'Aquitaine, University of Bordeaux, Unité Mixte de Recherche No. 5798, CNRS, 33400 Talence, France.
Phys Rev E. 2018 Aug;98(2-1):022125. doi: 10.1103/PhysRevE.98.022125.
It has been known for a long time that the kinetics of diffusion-limited reactions can be quantified by the time needed for a diffusing molecule to reach a target: the first-passage time (FPT). So far the general determination of the mean first-passage time to a target in confinement has left aside aging media, such as glassy materials, cellular media, or cold atoms in optical lattices. Here we consider general non-Markovian scale-invariant diffusion processes, which model a broad class of transport processes of molecules in aging media, and demonstrate that all the moments of the FPT obey universal scalings with the confining volume with nontrivial exponents. Our analysis shows that a nonlinear scaling with the volume of the mean FPT, which quantities the mean reaction time, is the hallmark of aging and provides a general tool to quantify its impact on reaction kinetics in confinement.
长期以来，人们已经知道扩散限制反应的动力学可以通过扩散分子到达目标所需的时间来量化：首次通过时间（FPT）。到目前为止，对受限环境中到达目标的平均首次通过时间的一般确定已经忽略了老化介质，例如玻璃状材料、细胞介质或光晶格中的冷原子。在这里，我们考虑一般的非马尔可夫标度不变扩散过程，这些过程模拟了老化介质中分子的广泛传输过程，并证明 FPT 的所有矩都与限制体积具有普适的标度关系，其指数是非平凡的。我们的分析表明，平均 FPT 的体积与平均反应时间之间的非线性标度是老化的标志，并提供了一种通用工具来量化其对受限环境中反应动力学的影响。
