  The existence of heterogeneity in the dynamics of supercooled liquids is
believed to be one of the hallmarks of the glass transition. Intense research
has been carried out in the past to understand the origin of this heterogeneity
in dynamics and a possible length scale associated with it. We have done
extensive molecular dynamics simulations of few model glass-forming liquids in
three dimensions to understand the temporal evolution of the dynamic
heterogeneity and the heterogeneity length scale. We find that although the
strength of the dynamic heterogeneity is maximum at a timescale close to
characteristic $\alpha$-relaxation time of the system, dynamic heterogeneity
itself is well-developed at timescale as short as $\beta$-relaxation time and
survives up to a timescale as long as few tens of $\alpha$-relaxation time.
Moreover, we discovered that temperature dependence of heterogeneity length
remains the same in the whole time window although its absolute value changes
over time in a non-monotonic manner.
