论文标题
蒙特卡洛法中的免费飞行步骤分析。测试用例：石墨烯中的电荷运输
The free flight step analysis in the Monte Carlo Method. Test case: charge transport in graphene
论文作者
论文摘要
现在，蒙特卡洛方法是研究半导体中电荷运输的绝对确定的方法。然而，关于分配功能的正确重建，这有很多缺点，必须在$ 0 $和$ 1 $之间进行界限。标准合奏蒙特卡洛方法无法正确包含Pauli排除原理，并且数值分布函数超过了最大值。进行了许多解决问题的尝试，最近已经开发了一种新的DSMC方案来克服该问题。所有改进通常基于涉及分布函数和散射项的一些近似值或计算技术。只有一次尝试才能及时地改变自由飞行步骤的表述，但是关于基于自由飞行的校正的蒙特卡洛方法的理论和计算分析，文献中仍然缺乏。在本文中，我们希望通过更深入地分析自由飞行步骤进入蒙特卡洛模拟，其物理特性以及使我们能够保留该方法的物理一致性的条件来实现这种差距。
Monte Carlo methods are now a definitively well established methods for studying the transport of charges in semiconductors. A lot of drawbacks are however present about the correct reconstruction of the distribution function, which has to be bounded between $0$ and $1$. The standard Ensemble Monte Carlo method is not able to properly include the Pauli exclusion principle and the numerical distribution functions exceed the maximum value. A lot of attempts were made to solve the problem and recently a new DSMC scheme has been developed to overcome the problem. All the improvements are generally based on some approximations or computational techniques involving the distribution function and the scattering terms. Only an attempt was devoted to opportunely change the formulation of the free flight step but there is still a lack in the literature regarding a both theoretical and computational analysis of corrected Monte Carlo methods based on the free flights. In this paper we would like to fulfill such a gap by analyzing deeper the role of the free flight step into a Monte Carlo simulation, its physical properties and the conditions that allow us to preserve the physical consistency of the method.
