Nearsightedness of Electronic Matter

In an earlier paper, W. Kohn had qualitatively introduced the concept of "nearsightedness" of electrons in many-atom systems. It can be viewed as underlying such important ideas as Pauling's "chemical bond," "transferability" and Yang's computational principle of "divide and conquer." It describes the fact that, for fixed chemical potential, local electronic properties, like the density $n(r)$, depend significantly on the effective external potential only at nearby points. Changes of that potential, {\it no matter how large}, beyond a distance $\textsf{R}$ have {\it limited} effects on local electronic properties, which rapidly tend to zero as function of $\textsf{R}$. In the present paper, the concept is first sharpened for representative models of uncharged fermions moving in external potentials, followed by a discussion of the effects of electron-electron interactions and of perturbing external charges.