标题： 量子 MEP 流体力学模型用于电荷输运 显示英文标题

标题： Quantum MEP hydrodynamical model for charge transport

摘要： 一种已知的方法是通过使用Wigner方程来获得电荷输运的量子流体动力学模型，并如半经典方法中那样推导出矩方程的层次结构。 如果将矩层次截断为有限阶，得到的平衡方程组需要一些闭合假设，因为未知数的数量超过方程的数量。 在经典和半经典动能理论中，获得所需闭合关系的一种合理方法是基于最大熵原理（MEP）[13]（参见[20]中关于半导体中电荷输运的内容）。 在[9]中，通过引入基于平衡Wigner函数的量子修正[30]，为抛物线能带近似下的电荷输运设计了一个量子MEP流体动力学模型。 在[29]中，对在原始石墨烯中运动的电子进行了扩展。 在这里，我们提出一个量子流体动力学模型，该模型适用于一般能带，考虑通过使用MEP的量子版本从Wigner方程推导出的矩系统的闭合。 借助Moyal微积分，获得了硅和石墨烯在\hbar ^2阶的量子修正显式公式，消除了量子修正基于平衡Wigner函数的限制，如[9, 29]中所述。 作为应用，推导了迁移率的量子修正。 显示英文摘要

摘要： A well known procedure to get quantum hydrodynamical models for charge transport is to resort to the Wigner equations and deduce the hierarchy of the moment equations as in the semiclassical approach. If one truncates the moment hierarchy to a finite order, the resulting set of balance equations requires some closure assumption because the number of unknowns exceed the number of equations. In the classical and semiclassical kinetic theory a sound approach to get the desired closure relations is that based on the Maximum Entropy Principle (MEP) [13] (see[20] for charge transport in semiconductors). In [9] a quantum MEP hydrodynamical model has been devised for charge transport in the parabolic band approximation by introducing quantum correction based on the equilibrium Wigner function [30]. An extension to electron moving in pristine graphene has been obtained in [29]. Here we present a quantum hydrodynamical model which is valid for a general energy band considering a closure of the moment system deduced by the Wigner equation resorting to a quantum version of MEP. Explicit formulas for quantum correction at order \hbar^2 are obtained with the aid of the Moyal calculus for silicon and graphene removing the limitation that the quantum corrections are based on the equilibrium Wigner function as in [9, 29]. As an application, quantum correction to the mobilities are deduced.