  We study the signature of scale invariance in the far-from-equilibrium
quantum dynamics of two dimensional Bose gases. We show that the density
profile displays a scale invariant logarithmic singularity near the center. In
addition, the density oscillates due to quantum beats with universal
structures. Namely, the frequencies of the beats can be connected with one
another by a universal discrete scale transformation induced by the scale
invariance. The experimental applicability of these results is then discussed.
