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Nearsightedness of electronic matter in one dimension

Domenii publicaţii > Fizica + Tipuri publicaţii > Articol în revistã ştiinţificã

Autori: E. Prodan

Editorial: Phys. Rev. B, 73, p.085108, 2006.


The concept of nearsightedeness of electronic matter (NEM) was introduced by Kohn in 1996 as the physical principle underlining Yang’s electronic structure algorithm of divide and conquer. It describes the fact that, for fixed chemical potential, local electronic properties at a point r, like the density n(r), depend significantly on the external potential v only at nearby points. Beyond a distance R, changes Δv of that potential, no matter how large, have limited effects on local electronic properties, which tend to zero as functions of R. This remains true even if the changes in the external potential completely surround the point r. NEM can be quantitatively characterized by the nearsightedness range R(r,Δn), defined as the smallest distance from r beyond which any change of the external potential produces a density change, at r, smaller than a given Δn. The present paper gives a detailed analysis of NEM for periodic metals and insulators in one dimension and includes sharp, explicit estimates of the nearsightedness range. Since NEM involves arbitrary changes of the external potential, strong, even qualitative changes can occur in the system, such as the quantization of the energy bands or the filling of the insulating gap of an insulator with continuum spectrum. In spite of such drastic changes, we show that Δv has only a limited effect on the density, which can be quantified in terms of simple parameters of the unperturbed system.

Cuvinte cheie: particle density, nearsightedness