无排斥的有效硬核排斥：再论两物种对湮灭

中文摘要 AI 辅助

具有通过$A+B\to\emptyset$反应相互湮灭的两物种的反应扩散系统，总密度$\rho$会缓慢衰减，在低维中遵循反常幂律。对于一维硬核粒子，在对称扩散下该衰减遵循$\rho \sim t^{-1/4}$，在两物种间无相对偏置的非对称扩散下遵循$\rho \sim t^{-1/3}$。尤其$t^{-1/3}$行为迄今为止仅在具有硬核排斥的系统中被观测到。本文构建了一个无硬核排斥的粒子模型，可重现相同的$t^{-1/3}$标度。在该模型中，两物种均经历非对称扩散，其速率非线性依赖于局域密度；在无另一物种时，该输运为超扩散，属于Kardar-Parisi-Zhang普适类。当两物种中至少一种经历由粒子对微观过程诱导的非对称扩散时，会出现$t^{-1/3}$标度行为；而涉及三个粒子的非对称过程则会导致与对称扩散相关的$t^{-1/4}$标度。这表明，对湮灭的密度衰减指数并非仅由孤立粒子物种的输运性质决定。

英文摘要

Reaction-diffusion systems with two species that mutually annihilate through $A+B\to\emptyset$ reactions display a slow decay of the total density $ρ$ which follows an anomalous power law in low dimensions. For hardcore particles in one dimension, this decay follows $ρ\sim t^{-1/4}$ under symmetric diffusion and $ρ\sim t^{-1/3}$ under asymmetric diffusion without relative bias between the two species. The $t^{-1/3}$ behavior, in particular, has so far been observed exclusively in systems with hardcore exclusion. Here we construct a model of particles without hardcore exclusion that reproduces this same $t^{-1/3}$ scaling. In our model, both species undergo asymmetric diffusion with a rate that depends nonlinearly on the local density, a form of transport that, in the absence of the other species, is superdiffusive and falls into the Kardar-Parisi-Zhang universality class. The scaling behavior of $t^{-1/3}$ occurs when at least one of the two species undergoes asymmetric diffusion induced by microscopic processes involving pairs of particles, while asymmetric processes involving groups of three particles lead to $t^{-1/4}$ scaling associated with symmetric diffusion. This demonstrates that the pair annihilation density decay exponent is not determined exclusively by the transport properties of the isolated particle species.

发表机构

• The Catholic University of Korea（韩国天主教大学）
• Universität zu Köln（科隆大学）

机构由 AI 辅助整理，请以论文原文为准。