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High Temperature Virial Expansion to Universal Quench Dynamics

High temperature virial expansion is a powerful tool in equilibrium statistical mechanics. In this letter we generalize the high temperature virial expansion approach to treat far-from-equilibrium quench dynamics. As an application of our framework, we study the dynamics of a Bose gas quenched from non-interacting to unitarity, and we compare our theoretical results with unexplained experimental results by the Cambridge group [Eigen et al., Nature 563, 221 (2018)]. We show that, during the quench dynamics, the momentum distribution decreases for low-momentum part with $k<k^*$, and increases for high-momentum part with $k>k^*$, where $k^*$ is a characteristic momentum scale separating the low- and the high-momentum regimes. We determine the universal value of $k^*λ$ that agrees perfectly with the experiment, with $λ$ being the thermal de Broglie wave length. We also find a jump of the half-way relaxation time across $k^*λ$ and the non-monotonic behavior of energy distribution, both of which agree with the experiment. Finally, we address the issue whether the long-time steady state thermalizes or not, and we find that this state does thermalize except for the very high momentum tail with $kλ\gg 1$. Our framework can also be applied to quench dynamics in other systems.