Scale Invariance and Dynamic Phase Transitions in Diffusion-Limited Reactions
Scale Invariance and Dynamic Phase Transitions in Diffusion-Limited Reactions
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扩散限制反应中的尺度不变性和动态相变
DOI：
10.1007/978-3-540-44838-9_47
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
U. Täuber
中科院分区：
文献类型：
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作者：
U. Täuber
许多可以用扩散限制的“化学”反应来描述的系统显示出非平衡的连续跃迁，将活性状态与非活性状态、吸收状态分开，在这种状态下随机波动完全停止。它们的临界性质可以通过相应的经典主方程的路径积分表示和动力学重整化群来分析。概述了随后的普适类在单物种的过程中，并概括了多粒子物种的反应进行了讨论。一般情况下，由过程A <==> A + A和A -> 0表示，它们映射到Reggeon场理论，具有定向渗流（DP）的临界指数。对于分支和零化无规行走（BARW）A ->（m+1）A和A + A -> 0，平均场速率方程仅预测一个活性态。但当d ≤2时，具有奇m的BARW出现DP跃迁.对于偶数子数m，粒子数宇称是局部守恒的。低于dc_4/3，这导致出现一个不活跃的阶段，其特征在于对湮灭过程的幂律。在过渡的临界指数是那些“宇称守恒”（PC）的普遍性类。对于没有记忆的局域过程，竞争对或三重态湮灭和裂变反应kA->（k -1）A，kA->（k+m）A（k= 2，3）似乎产生了唯一的其他普适性类，而这些普适性类没有被平均场理论描述。在这些反应中，场地占用数量限制起着至关重要的作用。
Many systems that can be described in terms of diffusion-limited `chemical' reactions display non-equilibrium continuous transitions separating active from inactive, absorbing states, where stochastic fluctuations cease entirely. Their critical properties can be analyzed via a path-integral representation of the corresponding classical master equation, and the dynamical renormalization group. An overview over the ensuing universality classes in single-species processes is given, and generalizations to reactions with multiple particle species are discussed as well. The generic case is represented by the processes A <==> A + A, and A -> 0, which map onto Reggeon field theory with the critical exponents of directed percolation (DP). For branching and annihilating random walks (BARW) A -> (m+1) A and A + A -> 0, the mean-field rate equation predicts an active state only. Yet BARW with oddmdisplay a DP transition for d ≤2. For even offspring numberm, the particle number parity is conserved locally. Below dc≈ 4/3, this leads to the emergence of an inactive phase that is characterized by the power laws of the pair annihilation process. The critical exponents at the transition are those of the `parity-conserving' (PC) universality class. For local processes without memory, competing pair or triplet annihilation and fission reactions k A -> (k - l) A, k A -> (k+m)A with k=2,3 appear to yield the only other universality classes not described by mean-field theory. In these reactions, site occupation number restrictions play a crucial role.