Field-Theory Approaches to Nonequilibrium Dynamics
Field-Theory Approaches to Nonequilibrium Dynamics
复制标题
非平衡动力学的场论方法
DOI：
10.1007/3-540-69684-9_7
复制
发表时间：
2007
期刊：
影响因子：
--
通讯作者：
U. Täuber
中科院分区：
文献类型：
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作者：
U. Täuber
AbstractIt解释了如何场论方法和动态重整化组（RG）可以应用于研究系统的普遍标度性质，无论是经历连续相变或显示通用标度不变性，无论是近和远的热平衡。第一部分介绍（非线性）Langevin方程的响应泛函场论表示。RG被用来计算几个普适性类的标度指数，这些普适性类控制着平衡态下二阶相变附近的临界动态。简要讨论了可逆模式耦合项、从随机初始条件到临界点的猝灭以及违反详细平衡约束的影响。它示出了如何相同的形式主义可以应用到非平衡系统，如驱动扩散晶格气体。第2部分描述了如何随机粒子反应过程的主方程可以映射到场论行动。RG然后被用来分析简单的扩散限制湮没反应，以及通用的连续过渡，从活跃到不活跃，吸收状态，其特征在于由幂律（临界）定向渗流。某些其他重要的普适性类被提及，并列出了一些开放的问题。
AbstractIt is explained how field-theoretic methods and the dynamic renormalisation group (RG) can be applied to study the universal scaling properties of systems that either undergo a continuous phase transition or display generic scale invariance, both near and far from thermal equilibrium. Part 1 introduces the response functional field theory representation of (nonlinear) Langevin equations. The RG is employed to compute the scaling exponents for several universality classes governing the critical dynamics near second-order phase transitions in equilibrium. The effects of reversible mode-coupling terms, quenching from random initial conditions to the critical point, and violating the detailed balance constraints are briefly discussed. It is shown how the same formalism can be applied to nonequilibrium systems such as driven diffusive lattice gases. Part 2 describes how the master equation for stochastic particle reaction processes can be mapped onto a field theory action. The RG is then used to analyse simple diffusion-limited annihilation reactions as well as generic continuous transitions from active to inactive, absorbing states, which are characterised by the power laws of (critical) directed percolation. Certain other important universality classes are mentioned, and some open issues are listed.