论文标题
数学步行进入Bloch振荡的悖论
A mathematical walk into the paradox of Bloch oscillations
论文作者
论文摘要
我们在数学上描述了明显的矛盾现象，即半导体中的电子电流会由于碰撞而流动，而不是尽管它们进行流动。考虑了一个在一维半导体晶体中的电荷传输模型，每个电子都遵循由半导体带结构确定的周期性汉密尔顿轨迹，并与声子浴发生非弹性碰撞。从详细的相空间模型开始，获得了平均数量的ODES封闭系统。但是，这种简化的模型仍然能够描述瞬态Bloch振荡，它们的阻尼以及随之而来的稳定电流流的发作，这与可用的实验数据非常吻合。
We describe mathematically the apparently paradoxical phenomenon that an electronic current in a semiconductor can flow because of collisions, and not despite them. A transport model of charge transport in a one-dimensional semiconductor crystal is considered, where each electron follows the periodic hamiltonian trajectories, determined by the semiconductor band structure, and undergoes non-elastic collisions with a phonon bath. Starting from the detailed phase-space model, a closed system of ODEs is obtained for averaged quantities. Such a simplified model is nevertheless capable of describing transient Bloch oscillations, their damping and the consequent onset of a steady current flow, which is in good agreement with the available experimental data.
