三分子反应模型涨落的临界行为

本文讨论了三分子反应模型在1+k₃A²<1+A((k₃D₁)/D₂)^1/2]²情况下的临界行为。由于在临界点附近不稳定模式是空间均匀的,因此可由总粒子数满足的生-灭方程来讨论。我们引入了涨落波的幅度作为描述涨落分布突变的参数。在利用重整化方法迴避了定态解在临界点上涨落发散所引起的困难后,得到了描述平均密度及涨落分布临界行为的广义Landau-Ginzburg方程。解析及数值分析表明,当B增大越过临界点B_m,平均密度达到周期变化的稳态,这和反应扩散方程结果是一致的,涨落二阶矩一般也达到一周期稳态,振幅很大而且主要由平均密度振动的幅度所决定。因此从涨落分布的突变来看,B_m并不与典型的二类相变类似。 关键词：

THE CRITICAL BEHAVIOR OF THE FLUCTUATION IN TRIMOLECULAR REACTION MODELX

In this article, the critical behavior of birth-death equation for trimolecular reactionmodel has been discussed. If 1+k₃A²<1+A((k₃D₁)/D₂)^1/2]², it is just the critical behaviorof the trimolecular model itself. The amplitudes of the unstable fluctuation waves have been taken as order parameters describing the change of fluctuation distribution near the critical point (B=B_m). By using the renormalization method to evade the difficulty due to the divergence of the fluctuation of steady solution at B_m, we obtain the generalized Landau-Ginzburg equations for the amplitudes of average values and fluctuation of partical numbers.The analytical and numerical analysis show that, as B increases beyond B_m, the variance also has a periodical stable part, the amplitude of which is very large and determined mainly by the saturated amplitudes of average particle numbers.