High Temperature Virial Expansion to Universal Quench Dynamics.

Abstract

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 noninteracting 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 the 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 wavelength. We also find a jump of the halfway relaxation time across k^{*}λ and the nonmonotonic behavior of energy distribution, both of which agree with the experiment. Finally, we address the issue whether the longtime steady state thermalizes or not, and we find that this state reaches a partial thermalization, namely, it thermalizes for the low-energy part with kλ≲1 but does not thermalize for the very high momentum tail with kλ≫1. Our framework can also be applied to quench dynamics in other systems.