Microscopic structure of travelling wave solutions in a class of stochastic interacting particle systems
Microscopic structure of travelling wave solutions in a class of stochastic interacting particle systems
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一类随机相互作用粒子系统行波解的微观结构
DOI：
10.1088/1367-2630/5/1/145
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发表时间：
2003
影响因子：
3.3
通讯作者：
G. Schütz
中科院分区：
文献类型：
--
作者：
K. Krebs;F. H. Jafarpour;G. Schütz
我们获得了三类具有开边界的随机一维非平衡格点模型的精确行波解。这些解决方案描述的扩散运动和微观结构（i）冲击的部分不对称排斥过程与开放的边界，（ii）在反应扩散系统中的格点Fisher波，和（iii）在非平衡Glauber-Kawasaki动力学与磁化电流的畴壁。对于这些系统中的每一个，我们定义了一个微观冲击的位置，并计算精确的跳跃率的行波的过渡率的微观模型。在稳定状态下，行波偏置的反转标志着一级非平衡相变，类似于一级相变动力学的泽尔多维奇理论。具有n个冲击的排除过程的平稳分布可以用矩阵乘积状态的n维表示来描述。
We obtain exact travelling wave solutions for three families of stochastic one-dimensional non-equilibrium lattice models with open boundaries. These solutions describe the diffusive motion and microscopic structure of (i) shocks in the partially asymmetric exclusion process with open boundaries, (ii) a lattice Fisher wave in a reaction–diffusion system, and (iii) a domain wall in non-equilibrium Glauber–Kawasaki dynamics with magnetization current. For each of these systems we define a microscopic shock position and calculate the exact hopping rates of the travelling wave in terms of the transition rates of the microscopic model. In the steady state a reversal of the bias of the travelling wave marks a first-order non-equilibrium phase transition, analogous to the Zel’dovich theory of kinetics of first-order transitions. The stationary distributions of the exclusion process with n shocks can be described in terms of n-dimensional representations of matrix product states.