  We study the temperature dependence of static and dynamic responses of
Coulomb interacting particles in two-dimensional traps across the thermal
crossover from an amorphous solid- to liquid-like behaviors. While static
correlations, that investigate the translational and bond orientational order
in the confinements, show the footprints of hexatic-like phase at low
temperature, dynamics of the particles slow down considerably in this state --
reminiscent of a supercooled liquid. Using density correlations, we probe
intriguing signatures of long-lived inhomogeneities due to the interplay of the
irregularity in the confinement and long-range Coulomb interactions. The
relaxation at multiple time scales show stretched-exponential decay of spatial
correlations in irregular traps. Temperature dependence of characteristic time
scales, depicting the structural relaxation of the system, show striking
similarities with those observed for the glassy systems indicating that, some
of the key signatures of supercooled liquids emerge in confinements with lower
spatial symmetries.
