The dipole moment of any finite and neutral system, having asquare-integrable wavefunction, is a well defined quantity. The same quantityis ill-defined for an extended system, whose wavefunction invariably obeysperiodic (Born-von Karman) boundary conditions. Despite this fact, macroscopicpolarization is a theoretically accessible quantity, for either uncorrelated orcorrelated many-electron systems: in both cases, polarization is a rather"exotic" observable. For an uncorrelated-either Hartree-Fock orKohn-Sham-crystalline solid, polarization has been expressed and computed as aBerry phase of the Bloch orbitals (since 1993). The case of a correlated and/ordisordered system received a definitive solution only very recently (1998):this latest development allows us present here the whole theory from a novel,and very general, viewpoint. The modern theory of polarization is even relevantto the foundations of density functional theory in extended systems.
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