论文标题
无需集成性的随机模型
A stochastic model solvable without integrability
论文作者
论文摘要
我们介绍了一个具有扩散和蒸发/冷凝过程的模型，具体取决于3个参数，遵守某些不平等。可以在不使用集成性的情况下准确地计算所有相关函数的意义上解决该模型。 我们表明，平均场近似通常并不精确。这可以通过查看我们提供的两点相关函数的分析表达来显示。我们通过基于马尔可夫矩阵的直接对角线化（对于位点数量的较小值）以及蒙特 - 卡洛模拟（对于更高数量的站点）的直接对角线化来确认我们的分析。 尽管该模型的扩散速率是对称的，但它表现出由蒸发 /冷凝过程驱动的左 /右不对称性。我们还认为，该模型可以作为催化或破裂过程的一维模型。
We introduce a model with diffusive and evaporation/condensation processes, depending on 3 parameters obeying some inequalities. The model can be solved in the sense that all correlation functions can be computed exactly without the use of integrability. We show that the mean field approximation is not exact in general. This can be shown by looking at the analytical expression of the two-point correlation functions, that we provide. We confirm our analysis by numerics based on direct diagonalisation of the Markov matrix (for small values of the number of sites) and also by Monte-Carlo simulations (for a higher number of sites). Although the model is symmetric in its diffusive rates, it exhibits a left / right asymmetry driven by the evaporation/condensation processes. We also argue that the model can be taken as a one-dimensional model for catalysis or fracturing processes.
