Scale Invariant Dynamics and Universal Quantum Beats in Bose Gases

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.