  We show, by solving the linearized Vlasov equations, that in the presence of
an attractive density-dependent vector, or tensor, mean field potential, under
a portion of the spinodal unstable phase region where the attractions among the
quarks are more dominant, the transverse modes, i.e., the fluctuations of the
current densities perpendicular to the wave vector, are activated due to
relativity. In particular, the current densities in both the transverse
directions oscillate with the same frequency, indicating the existence of the
spontaneous rotations of the dense clusters. These rotating clusters would
certainly create a local vortical flow field which, according to chiral (or
spin) vortical effect, leads to the macroscopic separation of the axial charges
or spins due to the spin-orbital interactions. Hence, for the first time, the
connection between the axial charge or spin in-homogeneity and the first-order
phase transition is proposed.
