电荷亏损、电荷输运和尺寸比较
Charge Deficiency, Charge Transport and Comparison of Dimensions
摘要：
本文研究了两个正交无限维投影的相对指数，在有限维情况下，它是两个投影的维数之差。我们将相对指数与相应算符的Fredholm指数联系起来，讨论了它的基本性质，得到了它的各种计算公式，并将相对指数用于计算某些量子系统中费米能以下电子数的变化，并将其解释为电荷不足。我们研究的绝热电荷输运的概念，从考虑的绝热曲率的电荷不足的关系。结果表明，在一定的协方差齐性条件下，两者是相关的.相对折射率与Bellissard的霍尔效应霍尔效应理论有关。对于朗道哈密顿量的相对指数计算明确的所有朗道水平。
英文摘要：
We study the relative index of two orthogonal infinite dimensional projections which, in the finite dimensional case, is the difference in their dimensions. We relate the relative index to the Fredholm index of appropriate operators, discuss its basic properties, and obtain various formulas for it. We apply the relative index to counting the change in the number of electrons below the Fermi energy of certain quantum systems and interpret it as the charge deficiency. We study the relation of the charge deficiency with the notion of adiabatic charge transport that arises from the consideration of the adiabatic curvature. It is shown that, under a certain covariance, (homogeneity), condition the two are related. The relative index is related to Bellissard's theory of the Integer Hall effect. For Landau Hamiltonians the relative index is computed explicitly for all Landau levels.
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