We investigate the totally asymmetric simple exclusion process (TASEP) in the presence of obstacles that dynamically bind and unbind from the lattice. The model is motivated by biological processes such as transcription in the presence of DNA-binding proteins. Similar models have been studied before using the mean-field approximation, but the exact relation between the particle current and density remains elusive. Here, we first show using extensive Monte Carlo simulations that the current-density relation in this model assumes a quasiparabolic form similar to that of the ordinary TASEP without obstacles. We then attempt to explain this relation using exact calculations in the limit of low and high density of particles. Our results suggest that the symmetric, quasiparabolic current-density relation arises through a nontrivial cancellation of higher-order terms, similarly as in the standard TASEP.

中文翻译：

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具有动态障碍的排斥过程中的电流-密度关系

我们研究了动态结合和从晶格解开的障碍物的存在下的完全不对称简单排除过程（TASEP）。该模型受生物学过程（例如在DNA结合蛋白存在下的转录）的驱动。在使用平均场近似之前，已经研究了类似的模型，但是粒子电流与密度之间的确切关系仍然难以捉摸。在这里，我们首先使用广泛的蒙特卡洛模拟表明，该模型中的电流密度关系采用与普通TASEP相似的无障碍准拟抛物线形式。然后，我们尝试使用精确的计算方法在粒子的低密度和高密度的极限范围内解释这种关系。我们的结果表明，