标题： 非互易反对齐活性混合物：推导精确的玻尔兹曼碰撞算子 显示英文标题

标题： Non-reciprocal anti-aligning active mixtures: deriving the exact Boltzmann collision operator

摘要： 我们考虑在具有反对齐相互作用的自推进粒子二元混合物中非互易性的影响，其中类型A的粒子对类型B的粒子的反应与反之不同。 从一个已知的微观Langevin模型出发，建立相应的精确N粒子Fokker-Planck方程，并做出低密度和单侧分子混沌的假设，推导出带有精确碰撞算子的非线性活性Boltzmann方程。 在此推导中，显式地考虑了相空间压缩以及二元相互作用期间对相关性的建立，从而得到超越平均场的理论描述。 这扩展了之前关于互易相互作用的结果，其中发现纯反对齐相互作用的系统中可以出现取向序。 尽管运动方程比互易系统更复杂，但该理论仍然导致解析表达式和预测。 与基于代理的模拟比较显示，在低密度和/或小耦合极限下动态和静态行为有很好的定量一致性。 显示英文摘要

摘要： We consider the effect of non-reciprocity in a binary mixture of self-propelled particles with anti-aligning interactions, where a particle of type A reacts differently to a particle of type B than vice versa. Starting from a well-known microscopic Langevin-model for the particles, setting up the corresponding exact N-particle Fokker-Planck equation and making Boltzmann's assumptions of low density and one-sided molecular chaos, the non-linear active Boltzmann equation with the exact collision operator is derived. In this derivation, the effect of phase-space compression and the build-up of pair-correlations during binary interactions is explicitly taken into account, leading to a theoretical description beyond mean-field. This extends previous results for reciprocal interactions, where it was found that orientational order can emerge in a system with purely anti-aligning interactions. Although the equations of motion are more complex than in the reciprocal system, the theory still leads to analytical expressions and predictions. Comparisons with agent-based simulations show excellent quantitative agreement of the dynamic and static behavior in the low density and/or small coupling limit.