Statistical electron densities

Abstract

It is known that in numerous interesting systems one-electron states appear with a multifractal internal structure. Physical intuition suggests, however, that electron densities should be smooth both at atomic distances and close to the macroscopic limit. Multifractal behavior is expected at intermediate length scales, with observable nontrivial statistical properties in considerably, but far from macroscopically sized clusters. We have demonstrated that differences of generalized Rényi entropies serve as relevant quantities for the global characterization of the statistical nature of such electron densities. Asymptotic expansion formulas are elaborated for these values as functions of the length scale of observation. The transition from deterministic electron densities to statistical ones along various lengths of resolution is traced both theoretically and by numerical calculations. © 1997 John Wiley & Sons, Inc.