  The crystalline or liquid character of the downward cusp states in N-electron
parabolic quantum dots (QD's) at high magnetic fields is investigated using
conditional probability distributions obtained from exact diagonalization.
These states are of crystalline character for fractional fillings covering both
low and high values, unlike the liquid Jastrow-Laughlin wave functions, but in
remarkable agreement with the rotating-Wigner-molecule ones [Phys. Rev. B 66,
115315 (2002)]. The crystalline arrangement consists of concentric polygonal
rings that rotate independently of each other, with the electrons on each ring
rotating coherently. We show that the rotation stabilizes the Wigner molecule
relative to the static one defined by the broken-symmetry
unrestricted-Hartree-Fock solution. We discuss the non-rigid behavior of the
rotating Wigner molecule and pertinent features of the excitation spectrum,
including the occurrence of a gap between the ground and first excited states
that underlies the incompressibility of the system. This leads us to conjecture
that the rotating crystal (and not the static one) remains the relevant ground
state for low fractional fillings even at the thermodynamic limit.
