Phenomena in the macroscopic world are described by classical physics while processes at atomic length and time scales are governed by the laws of quantum mechanics. The connection between microscopic and macroscopic physical quantities is far from being trivial and partly unexplained.
The electric polarization is a macroscopic quantity which describes the dipole moment of matter. The polarization originates from the peculiar electron distribution at the atomic scale in polar and ionic materials, among them the most interesting class of ferroelectrics. Their spontaneous electric polarization is widely applied in electronic sensors, memories, and switching devices. The link between polarizations, in particular time dependent ones, and microscopic electron densities is important for understanding and tailoring the properties of ferroelectrics.