石墨烯层中电子输运的动力学模型
A kinetic model for the transport of electrons in a graphene layer
摘要：
在这篇文章中，我们提出了一个新的数值模型计算的电子在石墨烯器件的传输。石墨烯的基本量子模型是一个无质量的狄拉克方程，其本征值显示了一个锥形奇点，导致两种模式之间的非绝热跃迁。我们首先推导出一个动力学模型，它采取的形式是两个玻尔兹曼方程耦合的碰撞算子建模的非绝热转变。该碰撞项包括Landau-Zener转移项和跳跃算子，其存在是必不可少的，以确保在过渡期间良好的能量守恒。提出了一种粒子群方法求解动力学模型的算法实现。我们给出了该模型的分析理由，并提出了一系列的数值实验研究量子和动力学模型之间的各种来源的错误的影响。
英文摘要：
In this article, we propose a new numerical model for computation of the transport of electrons in a graphene device. The underlying quantum model for graphene is a massless Dirac equation, whose eigenvalues display a conical singularity responsible for non adiabatic transitions between the two modes. We first derive a kinetic model which takes the form of two Boltzmann equations coupled by a collision operator modeling the non-adiabatic transitions. This collision term includes a Landau-Zener transfer term and a jump operator whose presence is essential in order to ensure a good energy conservation during the transitions. We propose an algorithmic realization of the semi-group solving the kinetic model, by a particle method. We give analytic justification of the model and propose a series of numerical experiments studying the influences of the various sources of errors between the quantum and the kinetic models.
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