On analytical properties of the diamagnetic permeability in the presence of the spatial dispersion

It is well known that the usual assumptions about analytical properties of the magnetic permeability mu result in a contradiction in the case of a diamagnetic. It occurs, that the permeability, as a function of the complex frequency omega, decreases monotonically along the imaginary half-axis in the upper half of the omega-plane and, consequently, can not reach the limiting value mu = 1 at vertical bar omega vertical bar -> 8 as it must do. It is discussed how the presence of the spatial dispersion may solve this paradox. (c) 2012 Wiley Periodicals, Inc.