抽象绝热电荷泵
Abstract adiabatic charge pumping
摘要：
本文分析了一般情况下描述量子绝热电荷泵的抽象公式。我们考虑封闭系统的特点是一个缓慢变化的依赖于时间的哈密顿量取决于外部参数$α$。电流算符被定义为哈密顿算子相对于$α$的导数，一旦在某个时间间隔上积分，就产生在该时间跨度上通过系统泵送的电荷。在通常的能隙假设下，我们确定了泵浦电荷绝热参数的前两个主导项。特别地，在哈密顿量是时间周期性的并且具有离散的非简并谱的情况下，在一个周期上泵浦的电荷通过对应的动力学和几何相位的关于$α$的导数被赋予前导阶。
英文摘要：
This paper is devoted to the analysis of an abstract formula describing quantum adiabatic charge pumping in a general context. We consider closed systems characterized by a slowly varying time-dependent Hamiltonian depending on an external parameter $α$. The current operator, defined as the derivative of the Hamiltonian with respect to $α$, once integrated over some time interval, gives rise to a charge pumped through the system over that time span. We determine the first two leading terms in the adiabatic parameter of this pumped charge under the usual gap hypothesis. In particular, in case the Hamiltonian is time periodic and has discrete non-degenerate spectrum, the charge pumped over a period is given to leading order by the derivative with respect to $α$ of the corresponding dynamical and geometric phases.
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