  Few-electron eigenstates confined in coupled concentric double quantum rings
are studied by the exact diagonalization technique. We show that the magnetic
field suppresses the tunnel coupling between the rings localizing the
single-electron states in the internal ring, and the few-electron states in the
external ring. The magnetic fields inducing the ground-state angular momentum
transitions are determined by the distribution of the electron charge between
the rings. The charge redistribution is translated into modifications of the
fractional Aharonov-Bohm period. We demonstrate that the electron distribution
can be deduced from the cusp pattern of the chemical potentials governing the
single-electron charging properties of the system. The evolution of the
electron-electron correlations to the high field limit of a classical Wigner
molecule is discussed.
