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Equilibrium properties of two-species reactive lattice gases on random catalytic chains
Physical Review E ( IF 2.4 ) Pub Date : 2020-09-14 , DOI: 10.1103/physreve.102.032121
Dmytro Shapoval , Maxym Dudka , Olivier Bénichou , Gleb Oshanin

We focus here on the thermodynamic properties of adsorbates formed by two-species A+B reactions on a one-dimensional infinite lattice with heterogeneous “catalytic” properties. In our model hard-core A and B particles undergo continuous exchanges with their reservoirs and react when dissimilar species appear at neighboring lattice sites in presence of a “catalyst.” The latter is modeled by supposing either that randomly chosen bonds in the lattice promote reactions (Model I) or that reactions are activated by randomly chosen lattice sites (Model II). In the case of annealed disorder in spatial distribution of a catalyst we calculate the pressure of the adsorbate by solving three-site (Model I) or four-site (Model II) recursions obeyed by the corresponding averaged grand-canonical partition functions. In the case of quenched disorder, we use two complementary approaches to find exact expressions for the pressure. The first approach is based on direct combinatorial arguments. In the second approach, we frame the model in terms of random matrices; the pressure is then represented as an averaged logarithm of the trace of a product of random 3×3 matrices—either uncorrelated (Model I) or sequentially correlated (Model II).

中文翻译:

随机催化链上两种反应性晶格气体的平衡性质

在这里,我们着重介绍两种物种形成的吸附物的热力学性质。 一种+一维无限晶格上具有非均相“催化”性质的反应。在我们的模型中一种在“催化剂”的存在下,相邻晶格位置上出现异种时,粒子与它们的储层进行连续交换并发生反应。通过假设晶格中随机选择的键促进反应(模型I)或随机选择的晶格位点激活反应(模型II)来对后者建模。在催化剂空间分布中出现退火紊乱的情况下,我们通过求解遵守相应平均平均正典分配函数的三位(模型I)或四位(模型II)递归来计算被吸附物的压力。在猝死症的情况下,我们使用两种互补的方法来找到确切的压力的表达。第一种方法基于直接组合参数。在第二种方法中,我们根据随机矩阵构建模型。然后将压力表示为随机乘积的轨迹的平均对数3×3 矩阵-不相关(模型I)或顺序相关(模型II)。
更新日期:2020-09-15
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