论文标题
随机不均匀性的变化巨星方程的经典限制
Classical limit for the varying-mass Schrödinger equation with random inhomogeneities
论文作者
论文摘要
变化的massSchrödinger方程（VMSE）已成功地应用于模拟半导体异构结构的电子性质，例如量子点和量子井。在本文中，我们将VMSE视为较小的随机异质性，并将辐射转移方程推导为其渐近极限。主要工具是在重新固定的Planck常数$ε\ ll 1 $并将Wigner方程扩展到适当的订单$ε$时，系统地将Wigner变换应用于经典制度。作为概念的证明，我们在数值上同时计算VMSE及其限制辐射转移方程，并表明他们的解决方案在经典制度中很好地吻合。
The varying-mass Schrödinger equation (VMSE) has been successfully applied to model electronic properties of semiconductor hetero-structures, for example, quantum dots and quantum wells. In this paper, we consider VMSE with small random heterogeneities, and derive a radiative transfer equation as its asymptotic limit. The main tool is to systematically apply the Wigner transform in the classical regime when the rescaled Planck constant $ε\ll 1$, and expand the Wigner equation to proper orders of $ε$. As a proof of concept, we numerically compute both VMSE and its limiting radiative transfer equation, and show that their solutions agree well in the classical regime.
