随机运动量子点的非绝热量子抽运
Non-adiabatic quantum pumping by a randomly moving quantum dot
摘要：
我们研究了由经历随机横向运动的量子点表示的开放的一维量子系统中电荷随时间的涨落。在基本上非绝热设置中，我们研究了扩散和弹道（Levy）制度的障碍运动的电流以及净泵浦电荷经历随机波动的静态背景。我们表明，在大的时间限制，$t \to \infty$，波函数自然分离成贝里相位分量（导致在共同移动的框架中的波振幅的奇异部分）和非绝热校正（所产生的快速振荡，缓慢衰减的尾巴相同的振幅）。基于这种分离，我们报告两个关键结果：第一，无序平均波函数和电流是渐近主要由相同的Berry相位贡献，适用于绝热运动的情况下。第二，在一个短的过渡期后，泵浦的电荷表现出比绝热理论预测的增长快得多的波动。我们还推导出平均传播子（在共同移动的基础表示）的扩散和弹道类型的运动考虑的确切表达式。
英文摘要：
We look at the time dependent fluctuations of the electrical charge in an open 1D quantum system represented by a quantum dot experiencing random lateral motion. In essentially non-adiabatic settings we study both diffusive and ballistic (Levy) regimes of the barrier motion where the electric current as well as the net pumped electric charge experience random fluctuations over the static background. We show that in the large-time limit, $t \to \infty$, the wavefunction is naturally separated into the Berry-phase component (resulting from the singular part of the wave amplitude in the co-moving frame) and the non-adiabatic correction (arising from fast oscillating, slow decaying tails of the same amplitude). Based on this separation we report two key results: Firstly, the disorder averaged wave function and current are asymptotically mainly determined by the same Berry phase contribution that applies in the case of adiabatic motion. Secondly, after a short transition period the pumped electric charge exhibits fluctuations that grow much faster than predicted by the adiabatic theory. We also derive the exact expressions for the average propagator (in the co-moving basis representation) for the diffusive and ballistic types of motion considered.
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